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This is PART 17: Centers X(32001) - X(34000)

Introduction and Centers X(1) - X(1000) Centers X(1001) - X(3000) Centers X(3001) - X(5000)
Centers X(5001) - X(7000) Centers X(7001) - X(10000) Centers X(10001) - X(12000)
Centers X(12001) - X(14000) Centers X(14001) - X(16000) Centers X(16001) - X(18000)
Centers X(18001) - X(20000) Centers X(20001) - X(22000) Centers X(22001) - X(24000)
Centers X(24001) - X(26000) Centers X(26001) - X(28000) Centers X(28001) - X(30000)
Centers X(30001) - X(32000) Centers X(32001) - X(34000) Centers X(34001) - X(36000)
Centers X(36001) - X(38000) Centers X(38001) - X(40000) Centers X(40001) - X(42000)
Centers X(42001) - X(44000) Centers X(44001) - X(46000) Centers X(46001) - X(48000)
Centers X(48001) - X(50000) Centers X(50001) - X(52000) Centers X(52001) - X(54000)
Centers X(54001) - X(56000) Centers X(56001) - X(58000) Centers X(58001) - X(60000)
Centers X(60001) - X(62000) Centers X(62001) - X(64000) Centers X(64001) - X(66000)
Centers X(66001) - X(68000) Centers X(68001) - X(70000) Centers X(70001) - X(72000)


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Points II-Caph: X(32001)-X(32007)

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This preamble and centers X(32001)-X(32007) were contributed by Clark Kimberling and Peter Moses, April 15, 2019.

Suppose that P = p:q:r (barycentrics). The Point II-Caph of P is the point given by

2qr - (p+q+r)p : 2rp - (p+q+r)q : 2pq - (p+q+r)r.

The points in a Caph family of a point P all lie on the line PP*, where P* is the isotomic conjugate of P.

The appearance of {i,j} in the following list means that X(j) = Point II-Caph of X(i):

{1,3875}, {2,2}, {3,20477}, {6,7754}, {8,21296}, {9,30625}, {10,319}, {30,1494}, {37,25264}, {75,17144}, {141,7768}, {511,290}, {512,670}, {513,668}, {514,190}, {516,18025}, {517,18816}, {518,2481}, {519,903}, {520,6528}, {521,18026}, {522,664}, {523,99}, {524,671}, {525,648}, {527,1121}, {528,18821}, {532,11117}, {533,11118}, {536,3227}, {537,18822}, {538,3228}, {542,5641}, {543,18823}, {690,892}, {696,18824}, {698,3225}, {712,18825}, {714,18826}, {726,3226}, {732,14970}, {740,18827}, {758,14616}, {782,18828}, {804,18829}, {812,4562}, {824,4586}, {826,4577}, {888,886}, {891,889}, {900,4555}, {918,666}, {2574,15164}, {2575,15165}, {2799,2966}, {3413,6190}, {3414,6189}, {3900,4569}, {3910,6648}, {4083,18830}, {4777,4597}, {4977,6540}, {6362,6606}, {6368,18831}, {6550,6635}, {9033,16077}, {23870,23895}, {23871,23896}


X(32001) = POINT II-CAPH OF X(4)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 + 2*b^2*c^2 + 3*c^4) : :
Barycentrics    6 cot A - csc 2A : :
Barycentrics    (csc 2A) (3 cos^2 A - 1) : :
Barycentrics    tan A - cot A + cot B + cot C - cot ω : :
X(32001) lies on these lines: {2, 15905}, {4, 69}, {7, 5081}, {8, 7282}, {24, 3964}, {30, 6527}, {95, 3525}, {141, 3087}, {183, 8889}, {186, 9723}, {193, 297}, {253, 3146}, {273, 21296}, {281, 4416}, {290, 16774}, {319, 7046}, {320, 1119}, {325, 6353}, {393, 524}, {427, 15589}, {458, 3620}, {491, 3536}, {492, 3535}, {599, 6748}, {648, 11008}, {1270, 1585}, {1271, 1586}, {1597, 14929}, {1990, 6144}, {1992, 17907}, {2897, 6925}, {3089, 7776}, {3529, 20477}, {3763, 6749}, {3879, 7952}, {3933, 7487}, {3945, 17555}, {4417, 7490}, {4869, 26003}, {5232, 11109}, {6515, 6820}, {6995, 10513}, {7714, 7788}, {9308, 20080}, {10002, 11477}, {10312, 14069}, {11180, 16264}, {14362, 16096}, {18950, 19166}

X(32001) = isotomic conjugate of X(15077)
X(32001) = anticomplement of X(15905)
X(32001) = polar conjugate of isotomic conjugate of X(32831)
X(32001) = {X(4),X(69)}-harmonic conjugate of X(32000)
X(32001) = polar conjugate of isogonal conjugate of X(37672)


X(32002) = POINT II-CAPH OF X(5)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - b^2*c^2 + c^4) : :
Barycentrics    3 tan A - cot A : :
Barycentrics    4 cot A - 3 csc 2A : :
Barycentrics    csc 2A sin(A + π/6) sin(A - π/6) : :

X(32002) lies on these lines: {2, 10985}, {4, 69}, {5, 95}, {53, 648}, {99, 2383}, {183, 5064}, {216, 17035}, {265, 6528}, {275, 467}, {290, 15321}, {297, 3589}, {302, 473}, {303, 472}, {325, 428}, {382, 20477}, {458, 3763}, {1007, 7714}, {1078, 15559}, {1273, 18354}, {1494, 15687}, {1907, 7750}, {1994, 14129}, {2052, 13579}, {3087, 17907}, {3518, 7769}, {3855, 8797}, {3964, 5198}, {5081, 5564}, {5976, 22480}, {6144, 9308}, {6390, 6756}, {6527, 17578}, {7282, 7321}, {7752, 9723}, {7806, 10311}, {14111, 20572}, {14516, 19169}

X(32002) = isotomic conjugate of X(3519)
X(32002) = anticomplement of X(22052)
X(32002) = polar conjugate of X(2963)


X(32003) = POINT II-CAPH OF X(7)

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

X(32003) lies on these lines: {2, 5543}, {7, 8}, {57, 29616}, {145, 3160}, {150, 962}, {279, 519}, {347, 4460}, {348, 3241}, {392, 28644}, {527, 30695}, {664, 20050}, {728, 1445}, {1323, 3633}, {1434, 4720}, {2481, 7319}, {3187, 18624}, {3188, 12536}, {3598, 4848}, {3621, 9312}, {3623, 31721}, {3632, 10481}, {3672, 6738}, {3875, 20008}, {3912, 5435}, {4323, 7179}, {4328, 5232}, {4350, 6765}, {4384, 5226}, {5175, 20244}, {5228, 29611}, {5273, 25935}, {5704, 24203}, {5734, 17181}, {6049, 17081}, {7264, 18391}, {10405, 20059}, {10914, 23839}, {12630, 14189}, {17077, 27253}, {20111, 26531}, {25719, 31145}

X(32003) = {X(7),X(8)}-harmonic conjugate of X(31994)


X(32004) = POINT II-CAPH OF X(86)

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

X(32004) lies on these lines: {1,6626}, {10,86}, {65,664}, {81,2295}, {99,3244}, {145,17103}, {274,4714}, {333,16826}, {519,1509}, {524,23905}, {648,1855}, {757,5255}, {1931,29588}, {2106,3780}, {2329,5325}, {3635,6629}, {3874,4360}, {5711,17377}, {5937,23361}, {6625,20090}, {8033,17144}, {16834,24378}, {17378,17528}, {17778,20337}


X(32005) = POINT II-CAPH OF X(192)

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

X(32005) lies on these lines: {1,87}, {2,20943}, {239,3928}, {333,16722}, {350,20105}, {385,5204}, {499,19570}, {1107,4699}, {1278,17448}, {1478,13571}, {1575,21219}, {1655,5550}, {2275,20081}, {3240,21223}, {3360,21762}, {3614,7777}, {3617,21226}, {3621,17759}, {3634,27318}, {4352,17383}, {5217,7783}, {5229,7774}, {7354,7837}, {7779,9597}, {7905,9651}, {9263,20050}, {16815,24621}, {16969,25269}, {17232,24215}, {19701,29595}, {19862,27269}, {20036,20072}, {27268,31997}

X(32005) = anticomplement of X(20943)


X(32006) = POINT II-CAPH OF X(69)

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

Let A'B'C' be the anticevian triangle of X(69). Let A" be the orthogonal projection of A' on the line through X(69) parallel to line BC, and define B" and C" cyclically. The lines AA", BB", CC" concur in X(32006) = Point II-Caph of X(69). See X(33006).png (Angel Montesdeoca, December 6, 2022)

X(32006) lies on these lines: {2, 3053}, {3, 1007}, {4, 69}, {5, 3785}, {20, 325}, {30, 3926}, {32, 14064}, {83, 18841}, {99, 3529}, {115, 14023}, {127, 28696}, {148, 7946}, {183, 3091}, {193, 5254}, {290, 15077}, {350, 5225}, {376, 7763}, {381, 7767}, {382, 3933}, {385, 14063}, {388, 25303}, {491, 6459}, {492, 6460}, {524, 6392}, {543, 7916}, {546, 14929}, {626, 7737}, {631, 7752}, {754, 3767}, {1078, 3090}, {1285, 7934}, {1369, 7394}, {1370, 3266}, {1384, 8361}, {1657, 6390}, {1909, 5229}, {1975, 3146}, {1992, 5286}, {2207, 20806}, {2548, 6683}, {2549, 7759}, {2896, 16924}, {2996, 20080}, {3096, 16045}, {3314, 14035}, {3436, 20553}, {3524, 7769}, {3525, 7771}, {3528, 7814}, {3543, 7788}, {3545, 7811}, {3618, 6656}, {3619, 7770}, {3788, 3849}, {3832, 15589}, {3855, 6249}, {3972, 14069}, {4417, 7406}, {4872, 21605}, {5025, 7735}, {5177, 16992}, {5188, 7694}, {5304, 7851}, {5319, 7861}, {5475, 7800}, {5866, 11413}, {6340, 7396}, {6655, 7738}, {6658, 7897}, {6781, 7888}, {6997, 26235}, {7386, 11059}, {7388, 9540}, {7389, 13935}, {7391, 9464}, {7503, 15574}, {7736, 7785}, {7739, 7838}, {7746, 23055}, {7747, 7795}, {7748, 7758}, {7753, 7935}, {7754, 11008}, {7756, 7903}, {7775, 7830}, {7779, 20105}, {7782, 17538}, {7799, 11001}, {7803, 7812}, {7815, 31415}, {7822, 14537}, {7832, 14039}, {7833, 7941}, {7847, 7926}, {7858, 7910}, {7862, 21843}, {7866, 18907}, {7879, 8370}, {7881, 19687}, {7890, 11648}, {7893, 14041}, {7912, 14712}, {7917, 15682}, {7921, 7924}, {7929, 16044}, {7931, 14037}, {7933, 16989}, {7938, 16898}, {7939, 11361}, {7945, 19569}, {8356, 31400}, {8357, 9605}, {8362, 15484}, {8743, 22151}, {9292, 20022}, {9723, 11414}, {10159, 18844}, {10513, 17578}, {11285, 31404}, {12215, 14927}, {14062, 17129}, {14068, 17128}, {14570, 28728}, {19695, 31859}, {20556, 21281}


X(32007) = POINT II-CAPH OF X(142)

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

X(32007) lies on these lines: {1, 17078}, {7, 8}, {57, 32019}, {79, 2481}, {99, 1434}, {142, 32008}, {145, 17079}, {150, 18480}, {241, 29569}, {279, 3623}, {348, 3622}, {527, 32024}, {553, 3912}, {664, 3244}, {728, 17298}, {1125, 9436}, {2099, 7185}, {3254, 4569}, {3633, 9312}, {3649, 16823}, {4089, 11009}, {4346, 15956}, {4384, 4654}, {4675, 27253}, {4872, 12699}, {4887, 6738}, {5228, 17367}, {5845, 27000}, {5905, 30854}, {7146, 24803}, {7196, 29824}, {10025, 21258}, {11553, 17320}, {17084, 24798}, {17092, 17317}, {17181, 18493}, {17776, 21454}, {21314, 25716}

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Points III-Caph: X(32008)-X(32023)

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This preamble and centers X(32008)-X(32023) were contributed by Clark Kimberling and Peter Moses, April 15, 2019.

Suppose that P = p:q:r (barycentrics). The Point III-Caph of P is the point given by

(p + q)(p + r) : (q + r)(q + p) : (r + p)(r + q)

The points in a Caph family of a point P all lie on the line PP*, where P* is the isotomic conjugate of P.

The appearance of {i,j} in the following list means that X(j) = Point III-Caph of X(i):

{1,86}, {2,2}, {3,95}, {4,264}, {6,83}, {7,85}, {8,75}, {10,1268}, {13,11119}, {14,11120}, {20,69}, {22,1799}, {23,2373}, {30,1494}, {63,333}, {65,31643}, {69,76}, {75,274}, {76,308}, {81,14534}, {85,31618}, {92,31623}, {95,31617}, {99,4590}, {100,4998}, {110,18020}, {141,10159}, {144,8}, {145,7}, {146,3260}, {147,325}, {148,523}, {149,693}, {150,3261}, {153,3262}, {190,1016}, {192,1}, {193,4}, {194,6}, {239,673}, {261,31620}, {264,276}, {279,30705}, {287,9476}, {297,6330}, {308,31622}, {315,1502}, {316,18023}, {317,18027}, {320,20568}, {321,30710}, {323,2986}, {325,8781}, {329,312}, {330,87}, {346,30701}, {347,348}, {385,98}, {394,801}, {401,287}, {487,491}, {488,492}, {511,290}, {512,670}, {513,668}, {514,190}, {516,18025}, {517,18816}, {518,2481}, {519,903}, {520,6528}, {521,18026}, {522,664}, {523,99}, {524,671}, {525,648}, {527,1121}, {528,18821}, {532,11117}, {533,11118}, {536,3227}, {537,18822}, {538,3228}, {542,5641}, {543,18823}, {599,10302}, {616,298}, {617,299}, {621,300}, {622,301}, {627,302}, {628,303}, {648,23582}, {649,4598}, {650,30610}, {659,8709}, {661,27805}, {664,1275}, {668,31625}, {669,3222}, {690,892}, {693,4554}, {696,18824}, {698,3225}, {712,18825}, {714,18826}, {726,3226}, {732,14970}, {740,18827}, {758,14616}, {782,18828}, {804,18829}, {812,4562}, {824,4586}, {826,4577}, {850,6331}, {858,30786}, {888,886}, {891,889}, {894,1220}, {900,4555}, {908,4997}, {918,666}, {962,309}, {1046,18812}, {1270,5490}, {1271,5491}, {1272,7799}, {1278,330}, {1330,313}, {1352,327}, {1369,8024}, {1370,305}, {1494,31621}, {1577,15455}, {1654,10}, {1655,37}, {1764,14829}, {1909,1221}, {1944,8777}, {1992,598}, {1993,275}, {2397,5376}, {2475,1441}, {2574,15164}, {2575,15165}, {2799,2966}, {2888,311}, {2889,1232}, {2890,1233}, {2891,1269}, {2892,1236}, {2893,349}, {2895,321}, {2896,141}, {2897,1231}, {2975,261}, {2998,3224}, {3056,18299}, {3091,8797}, {3100,31637}, {3146,253}, {3151,306}, {3152,307}, {3153,328}, {3164,3}, {3177,9}, {3180,13}, {3181,14}, {3187,27}, {3210,57}, {3261,31624}, {3413,6190}, {3414,6189}, {3434,6063}, {3436,3596}, {3448,850}, {3580,16080}, {3616,30598}, {3617,5936}, {3620,18840}, {3621,4373}, {3622,28626}, {3623,30712}, {3648,319}, {3729,1222}, {3732,15742}, {3868,286}, {3869,314}, {3870,21453}, {3875,1434}, {3900,4569}, {3904,13136}, {3910,6648}, {3952,7035}, {3995,1255}, {4025,658}, {4083,18830}, {4232,10603}, {4329,304}, {4360,1509}, {4373,27818}, {4388,7018}, {4391,6335}, {4393,14621}, {4427,4600}, {4440,514}, {4452,279}, {4461,1219}, {4462,646}, {4467,4573}, {4468,3699}, {4552,4564}, {4560,662}, {4580,827}, {4608,4632}, {4645,334}, {4777,4597}, {4977,6540}, {4998,31619}, {5032,18842}, {5080,20566}, {5189,18019}, {5207,18896}, {5484,4357}, {5596,315}, {5744,30608}, {5889,8795}, {5905,92}, {5942,318}, {5984,9473}, {6193,317}, {6194,183}, {6223,322}, {6224,320}, {6225,14615}, {6327,561}, {6360,63}, {6362,6606}, {6368,18831}, {6392,393}, {6462,3068}, {6463,3069}, {6515,2052}, {6527,3926}, {6542,335}, {6550,6635}, {6563,4563}, {6646,257}, {6655,9229}, {6758,24041}, {7057,4146}, {7192,799}, {7253,811}, {7391,18018}, {7396,6340}, {7500,13575}, {7665,468}, {7674,6604}, {7766,3407}, {7774,262}, {7777,7608}, {7779,1916}, {7785,3613}, {7791,31360}, {7837,14492}, {7840,5503}, {8024,1241}, {8055,18743}, {8264,32}, {8266,1078}, {8267,251}, {8272,2896}, {8591,524}, {8782,385}, {8859,10153}, {8878,427}, {8892,8889}, {9033,16077}, {9143,9141}, {9147,9150}, {9168,9170}, {9263,513}, {9295,9267}, {9308,1105}, {9312,23618}, {9485,6082}, {9740,11172}, {9742,1007}, {9870,9084}, {9965,189}, {10025,14942}, {10336,7792}, {10340,1843}, {10453,6384}, {10529,7318}, {10754,9154}, {11004,7578}, {11054,18818}, {11061,316}, {11148,1992}, {11160,5485}, {11415,20570}, {11442,18022}, {11606,9477}, {11794,27867}, {11851,1119}, {12221,24243}, {12222,24244}, {12272,683}, {12383,340}, {12384,30737}, {12649,273}, {13174,17731}, {13219,3267}, {14360,3266}, {14361,15466}, {14570,249}, {14618,30450}, {14683,13485}, {14712,67}, {14721,6333}, {14731,3268}, {14779,4427}, {14790,20564}, {14807,22339}, {14808,22340}, {14957,18024}, {15412,18315}, {16017,556}, {16018,174}, {16019,188}, {16552,17277}, {16704,24624}, {17006,10185}, {17008,7607}, {17018,2296}, {17035,5}, {17036,11}, {17037,20}, {17134,17206}, {17135,310}, {17136,4620}, {17137,6385}, {17140,873}, {17147,81}, {17148,58}, {17149,31008}, {17154,7192}, {17161,4610}, {17165,3112}, {17166,4623}, {17217,4602}, {17257,31359}, {17300,17758}, {17316,27475}, {17350,17743}, {17479,2167}, {17480,269}, {17483,30690}, {17484,18359}, {17485,9285}, {17486,31}, {17487,519}, {17488,3679}, {17489,82}, {17490,8056}, {17493,1581}, {17494,100}, {17495,88}, {17496,651}, {17497,897}, {17498,162}, {17499,18082}, {17732,17233}, {17751,1240}, {17759,291}, {17778,226}, {17781,4102}, {17784,8817}, {17794,350}, {17896,13149}, {17950,1952}, {18105,6573}, {18133,18140}, {18287,6353}, {18301,323}, {18662,2185}, {18663,2184}, {18666,72}, {18667,1214}, {18668,2349}, {18906,3114}, {19565,292}, {19566,9468}, {19569,11058}, {19570,1989}, {19577,8791}, {19789,15474}, {20011,8049}, {20016,6650}, {20018,1246}, {20040,20028}, {20042,6548}, {20045,675}, {20055,27494}, {20059,10405}, {20061,7219}, {20064,7357}, {20065,66}, {20072,80}, {20073,1000}, {20075,13577}, {20076,8048}, {20077,8044}, {20078,2994}, {20080,2996}, {20081,2998}, {20086,1029}, {20088,1031}, {20090,6625}, {20092,8046}, {20095,8047}, {20099,13574}, {20101,7224}, {20111,6601}, {20211,329}, {20212,1034}, {20213,1032}, {20222,1444}, {20245,28660}, {20294,4561}, {20295,1978}, {20344,3263}, {20345,1921}, {20347,18031}, {20348,27424}, {20533,3912}, {20534,18297}, {20535,7155}, {20536,11599}, {20537,30545}, {20553,18895}, {20554,18891}, {21124,8052}, {21215,1760}, {21216,19}, {21217,38}, {21218,55}, {21219,192}, {21220,661}, {21221,1577}, {21222,3257}, {21223,3223}, {21224,649}, {21225,101}, {21226,256}, {21270,1969}, {21275,1928}, {21278,18833}, {21281,6383}, {21285,20567}, {21286,28659}, {21287,27801}, {21288,20641}, {21289,1930}, {21290,3264}, {21294,20948}, {21295,24037}, {21299,18832}, {21301,6386}, {21302,4572}, {22113,19712}, {22114,19713}, {22647,22468}, {23870,23895}, {23871,23896}, {24068,4360}, {24349,870}, {25046,20022}, {25054,512}, {25237,2346}, {25257,2991}, {25259,1897}, {25268,5382}, {25332,3978}, {26853,8050}, {27340,2297}, {27377,14860}, {27484,4384}, {27835,27813}, {28604,1224}, {29824,31002}, {29840,7249}, {30562,5333}, {30564,5235}, {30577,3911}, {30578,4358}, {30579,16704}, {30660,1920}, {30661,171}, {30662,30669}, {30667,238}, {30669,30663}, {30694,281}, {30695,346}, {30699,278}, {31087,1390}, {31125,10415}, {31290,3952}, {31296,110}, {31298,9295}, {31308,16826}, {31372,148}, {31527,31627}, {31670,14387}, {31859,11169}

The Point III-Caph of P is the cevapoint of X(2) and P, and the isotomic conjugate of the complement of P, and also the polar conjugate of the crosspoint of X(4) and the polar conjugate of P. (Randy Hutson, April 22, 2019)


X(32008) = POINT III-CAPH OF X(9)

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

X(32008) lies on these lines: {1, 31269}, {2, 220}, {6, 27253}, {8, 344}, {9, 85}, {10, 10482}, {29, 1861}, {92, 3305}, {189, 7367}, {190, 20880}, {218, 14828}, {257, 17260}, {312, 728}, {333, 1174}, {349, 6559}, {664, 1212}, {672, 1434}, {673, 1334}, {1121, 6606}, {1213, 27023}, {1220, 17353}, {1698, 28874}, {2338, 17095}, {2481, 3294}, {3730, 14377}, {3740, 28058}, {4422, 17947}, {4473, 17128}, {4513, 27304}, {4518, 16823}, {4997, 5316}, {5278, 29616}, {6706, 10025}, {6738, 25072}, {9312, 31169}, {14829, 29627}, {16284, 17335}, {16788, 17687}, {17338, 17743}, {18359, 26591}, {21872, 27000}, {25500, 30608}, {25878, 26059}, {27065, 30690}, {28980, 30806}

X(32008) = isogonal conjugate X(1475)
X(32008) = isotomic conjugate of X(142)
X(32008) = cevapoint of X(2) and X(9)
X(32008) = X(19)-isoconjugate of X(22053)
X(32008) = trilinear pole of line X(522)X(3935) (the isotomic conjugate of the circumconic centered at X(1212))


X(32009) = POINT III-CAPH OF X(37)

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

X(32009) lies on these lines: {1, 872}, {2, 1500}, {10, 30571}, {37, 274}, {57, 16831}, {75, 4099}, {81, 213}, {83, 5284}, {86, 3294}, {88, 29578}, {89, 29595}, {105, 8708}, {190, 17175}, {239, 1255}, {277, 17321}, {279, 26125}, {291, 1125}, {330, 5283}, {335, 21816}, {595, 985}, {668, 16589}, {959, 4323}, {961, 7677}, {1002, 3616}, {1107, 3227}, {1224, 17289}, {1258, 3230}, {1390, 16823}, {2664, 9401}, {3963, 25661}, {4384, 25430}, {4393, 27789}, {4698, 16819}, {5291, 16912}, {5550, 7786}, {16369, 28615}, {16818, 17263}, {17260, 20963}, {17320, 24790}, {18140, 27255}, {19742, 25417}

X(32009) = isogonal conjugate X(20963)
X(32009) = isotomic conjugate of X(3739)
X(32009) = cevapoint of X(2) and X(37)
X(32009) = X(19)-isoconjugate of X(22060)


X(32010) = POINT III-CAPH OF X(38)

Barycentrics    (a + b)*(a + c)*(b^2 + a*c)*(a*b + c^2) : :
Barycentrics    1/(sin(B + ω) + sin(C + ω)) : :

X(32010)lies on these lines: {2, 694}, {38, 799}, {57, 14534}, {86, 1431}, {99, 17596}, {239, 257}, {244, 873}, {256, 314}, {261, 1178}, {354, 2668}, {756, 7035}, {805, 9073}, {846, 4154}, {870, 982}, {984, 7033}, {2669, 3752}, {3027, 9791}, {3863, 27164}, {4389, 14616}, {4562, 16587}, {4594, 27922}, {4603, 6654}, {5009, 7305}, {7192, 8034}, {16739, 18021}, {16975, 18826}, {18822, 18829}

X(32010) = isogonal conjugate X(20964)
X(32010) = isotomic conjugate of X(1215)
X(32010) = polar conjugate of X(1840)
X(32010) = cevapoint of X(2) and X(38)
X(32010) = trilinear pole of line X(812)X(4560)
X(32010) = X(19)-isoconjugate of X(22061)


X(32011) = POINT III-CAPH OF X(43)

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

X(32011) lies on these lines: {2, 16969}, {42, 31002}, {43, 6384}, {75, 16569}, {86, 6685}, {310, 899}, {335, 3752}, {1575, 27447}, {17490, 27494}, {17754, 27498}

X(32011) = isogonal conjugate X(22343)
X(32011) = isotomic conjugate of X(3840)
X(32011) = cevapoint of X(2) and X(43)
X(32011) = X(19)-isoconjugate of X(22066)


X(32012) = POINT III-CAPH OF X(44)

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

X(32012) lies on these lines: {2, 1017}, {44, 20568}, {668, 17349}, {3679, 4595}, {4671, 16816}, {5219, 25529}, {5235, 17292}, {16704, 30866}, {21385, 23598}

X(32012) = isotomic conjugate of X(3834)
X(32012) = cevapoint of X(2) and X(44)
X(32012) = X(19)-isoconjugate of X(22067)


X(32013) = POINT III-CAPH OF X(45)

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

X(32013) lies on these lines: {45, 20569}, {519, 16484}, {4358, 16815}, {16704, 29569}

X(32013) = isotomic conjugate of X(34824)
X(32013) = isotomic conjugate of complement of X(45)
X(32013) = cevapoint of X(2) and X(45)
X(32013) = X(19)-isoconjugate of X(22068)


X(32014) = POINT III-CAPH OF X(86)

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

X(31014) lies on these lines: {2, 1171}, {10, 86}, {76, 15668}, {83, 17398}, {98, 6578}, {99, 1125}, {226, 1434}, {274, 321}, {671, 23905}, {873, 18140}, {2368, 8701}, {3624, 17103}, {3634, 17731}, {4052, 16712}, {4080, 4632}, {4102, 29574}, {4596, 13576}, {4608, 5466}, {6539, 6542}, {6540, 17175}, {6626, 19862}, {6629, 19878}, {10159, 17245}, {11140, 26541}, {14534, 20337}, {18157, 30126}, {24051, 24058}, {25508, 28615}, {27797, 31011}

X(31014) = isogonal conjugate X(20970)
X(32014) = isotomic conjugate of X(1213)
X(32014) = polar conjugate of X(430)
X(32014) = cevapoint of X(2) and X(86)
X(32014) = barycentric product X(30593)*X(30594)
X(32014) = X(19)-isoconjugate of X(22080)


X(32015) = POINT III-CAPH OF X(142)

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

X(32015) lies on these lines: {8, 3826}, {85, 10012}, {1125, 14942}, {3912, 4102}, {6706, 31640}, {17282, 31359}, {17743, 27147}

X(32015) = isotomic conjugate of X(6666)
X(32015) = cevapoint of X(2) and X(142)


X(32016) = POINT III-CAPH OF X(244)

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

X(32016) lies on these lines: {239, 6631}, {244, 7035}, {350, 1266}, {4885, 27191}, {5437, 6654}, {7033, 17063}, {10436, 27922}, {27195, 31286}

X(32016) = isotomic conjugate of X(24003)
X(32016) = cevapoint of X(2) and X(244)


X(32017) = POINT III-CAPH OF X(312)

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

X(32017) lies on these lines: {1, 341}, {57, 312}, {75, 8056}, {76, 279}, {81, 4358}, {88, 321}, {105, 1261}, {274, 16736}, {278, 7017}, {291, 3840}, {668, 3452}, {961, 1476}, {985, 29649}, {1022, 1577}, {1224, 19864}, {1432, 3912}, {1997, 3596}, {4671, 26745}, {6685, 30571}, {14829, 29529}, {17786, 30827}, {25430, 30829}, {30710, 30818}

X(32017) = isogonal conjugate X(20228)
X(32017) = isotomic conjugate of X(3752)
X(32017) = polar conjugate of X(1828)
X(32017) = cevapoint of X(2) and X(312)
X(32017) = trilinear pole of line X(513)X(4397)
X(32017) = X(19)-isoconjugate of X(22344)


X(32018) = POINT III-CAPH OF X(319)

Barycentrics    b*c*(a + 2*b + c)*(a + b + 2*c) : :
Barycentrics    b c/(a r + S) : :

X(32018) lies on these lines: {2, 7230}, {75, 1089}, {76, 6539}, {79, 319}, {85, 4102}, {274, 321}, {286, 31902}, {304, 29602}, {334, 6538}, {668, 4647}, {767, 8701}, {870, 1126}, {1909, 31013}, {2481, 6540}, {4632, 18359}, {4717, 25303}, {4980, 18145}, {6385, 27801}, {7278, 17762}, {20568, 20911}, {20569, 30589}

X(32018) = isotomic conjugate of X(1100)
X(32018) = polar conjugate of X(2355)
X(32018) = cevapoint of X(2) and X(319)
X(32018) = trilinear pole of line X(693)X(4036)


X(32019) = POINT III-CAPH OF X(344)

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

X(32019) lies on these lines: {1, 17263}, {81, 17244}, {105, 3871}, {274, 17279}, {277, 344}, {1224, 17371}, {1255, 17367}, {2006, 30829}, {25417, 29569}

X(32019) = isotomic conjugate of X(17278)
X(32019) = cevapoint of X(2) and X(344)


X(32020) = POINT III-CAPH OF X(350)

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

X(32020) lies on these lines: {1, 668}, {2, 1978}, {28, 811}, {57, 4554}, {76, 330}, {81, 799}, {89, 30964}, {105, 8709}, {192, 20671}, {274, 4602}, {291, 350}, {670, 25534}, {727, 789}, {1002, 17794}, {1022, 20568}, {1221, 26971}, {1921, 20363}, {1929, 1966}, {3123, 18830}, {3227, 18145}, {3403, 8056}, {3840, 7018}, {9263, 18135}, {17027, 20457}, {18895, 27918}, {20372, 20610}, {21297, 31002}, {24625, 27853}, {29438, 29454}, {29750, 29811}

X(32020) = isogonal conjugate X(21760)
X(32020) = isotomic conjugate of X(1575)
X(32020) = cevapoint of X(2) and X(350)
X(32020) = X(19)-isoconjugate of X(20777)


X(32021) = POINT III-CAPH OF X(354)

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

X(32021) lies on these lines: {2481, 3742}, {4384, 5437}, {7271, 25496}

X(32021) = isotomic conjugate of X(3740)
X(32021) = cevapoint of X(2) and X(354)


X(32022) = POINT III-CAPH OF X(391)

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

X(32022) lies on these lines: {2, 2271}, {4, 17277}, {10, 344}, {69, 17758}, {76, 966}, {98, 25446}, {226, 4384}, {321, 28809}, {2478, 13576}, {3424, 7385}, {5224, 18840}, {5392, 26592}, {6625, 17349}, {7379, 14484}, {16827, 31405}, {17352, 18841}, {25006, 30701}

X(32022) = isogonal conjugate X(5021)
X(32022) = isotomic conjugate of X(4648)
X(32022) = polar conjugate of X(4196)
X(32022) = cevapoint of X(2) and X(391)


X(32023) = POINT III-CAPH OF X(497)

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

X(32023) lies on these lines: {2, 14936}, {11, 6063}, {55, 4998}, {75, 24386}, {85, 3817}, {497, 4554}, {693, 15283}, {982, 3663}, {1699, 7196}, {2481, 5274}, {3061, 3452}, {3263, 3705}, {3675, 7185}, {3794, 9309}, {6384, 27498}, {13577, 15284}, {14727, 18821}, {15149, 17917}, {20295, 26910}

X(32023) = isotomic conjugate of X(1376)
X(32023) = cevapoint of X(2) and X(497)

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Points IV-Caph: X(32024)-X(32035)

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This preamble and centers X(32024)-X(32035) were contributed by Clark Kimberling and Peter Moses, April 15, 2019.

Suppose that P = p:q:r (barycentrics). The Point IV-Caph of P is the point given by

qr - (p + q + r)p : rp - (p + q + r)q : pq - (p + q + r)r

The points in a Caph family of a point P all lie on the line PP*, where P* is the isotomic conjugate of P.

The appearance of {i,j} in the following list means that X(j) = Point IV-Caph of X(i):

{1,4360}, {2,2}, {4,317}, {6,7760}, {7,6604}, {8,69}, {20,6527}, {30,1494}, {69,315}, {75,17143}, {144,30695}, {145,4452}, {192,194}, {193,6392}, {194,8264}, {511,290}, {512,670}, {513,668}, {514,190}, {516,18025}, {517,18816}, {518,2481}, {519,903}, {520,6528}, {521,18026}, {522,664}, {523,99}, {524,671}, {525,648}, {527,1121}, {528,18821}, {532,11117}, {533,11118}, {536,3227}, {537,18822}, {538,3228}, {542,5641}, {543,18823}, {690,892}, {696,18824}, {698,3225}, {712,18825}, {714,18826}, {726,3226}, {732,14970}, {740,18827}, {758,14616}, {782,18828}, {804,18829}, {812,4562}, {824,4586}, {826,4577}, {888,886}, {891,889}, {900,4555}, {918,666}, {2574,15164}, {2575,15165}, {2799,2966}, {3413,6190}, {3414,6189}, {3900,4569}, {3910,6648}, {4083,18830}, {4560,14570}, {4777,4597}, {4977,6540}, {5905,6515}, {6362,6606}, {6368,18831}, {6542,6653}, {6550,6635}, {7057,7}, {7192,4576}, {9033,16077}, {16017,329}, {16018,3210}, {16019,3177}, {20346,6327}, {20534,8}, {20555,21275}, {23870,23895}, {23871,23896}

Let Gp be the centroid of ABCP (= complement of the complement of P). Let A'B'C' be the reflection in Gp of the cevian triangle of P. A'B'C' is perspective to ABC for all P, and the perspector is the isotomic conjugate of the Point IV-Caph of P. (Randy Hutson, April 20, 2019)

Let P' be the complement of P. Let A'B'C' be the anticevian triangle of P'. Let Gp' be the centroid of A'B'C'P'. Then the Point IV-Caph of P is the isotomic conjugate of the anticomplement of Gp'. (Randy Hutson, April 20, 2019)


X(32024) = POINT IV-CAPH OF X(9)

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

X(32024) lies on these lines: {1, 31169}, {8, 190}, {9, 85}, {45, 27253}, {63, 30854}, {144, 6604}, {220, 664}, {728, 25728}, {1212, 10025}, {2481, 16552}, {3730, 3732}, {3929, 4384}, {4640, 28058}, {5282, 6559}, {6554, 31640}, {6558, 25278}, {14512, 31852}, {14828, 16601}, {16284, 17336}, {17257, 26561}, {17277, 20880}, {17350, 27288}, {17781, 25935}


X(32025) = POINT IV-CAPH OF X(10)

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

X(32025) lies on these lines: {2, 4445}, {6, 29593}, {8, 4026}, {10, 86}, {37, 29615}, {69, 3617}, {75, 537}, {141, 27191}, {190, 594}, {192, 17251}, {239, 17239}, {313, 25280}, {320, 4691}, {391, 17354}, {519, 17322}, {524, 28604}, {536, 17252}, {599, 4699}, {894, 4690}, {966, 17233}, {1100, 29610}, {1213, 4478}, {1278, 17253}, {1698, 17394}, {2321, 17256}, {2345, 17346}, {3589, 29591}, {3626, 4357}, {3631, 26806}, {3632, 17393}, {3661, 17275}, {3662, 28634}, {3664, 4745}, {3686, 17289}, {3729, 17328}, {3739, 17287}, {3759, 4034}, {3763, 16816}, {3875, 4668}, {3949, 18714}, {3995, 4102}, {4001, 19797}, {4007, 4664}, {4021, 4746}, {4361, 17238}, {4363, 17343}, {4384, 17228}, {4389, 4452}, {4393, 17327}, {4399, 17302}, {4431, 17258}, {4464, 4701}, {4470, 20080}, {4472, 20090}, {4645, 4733}, {4651, 30966}, {4657, 29617}, {4659, 17329}, {4665, 6646}, {4669, 17320}, {4686, 17254}, {4687, 17294}, {4688, 17288}, {4698, 17310}, {4708, 17319}, {4740, 17255}, {4741, 17118}, {4751, 17296}, {4772, 7232}, {4788, 24441}, {4851, 29576}, {4852, 17326}, {4889, 29580}, {5257, 17315}, {5790, 10446}, {5839, 17381}, {6540, 30594}, {7081, 30761}, {7227, 20072}, {8013, 17731}, {10436, 17360}, {10453, 31341}, {12531, 18654}, {15668, 17373}, {16777, 20055}, {16815, 17231}, {16826, 17372}, {16831, 17386}, {16832, 17241}, {16833, 17370}, {16834, 17400}, {17045, 20016}, {17116, 17344}, {17117, 17237}, {17119, 17236}, {17121, 17385}, {17143, 18133}, {17151, 17249}, {17229, 17260}, {17230, 17259}, {17248, 17299}, {17263, 29594}, {17268, 31333}, {17280, 17330}, {17281, 17331}, {17286, 17335}, {17292, 17348}, {17293, 17349}, {17303, 17363}, {17309, 27268}, {17312, 31238}, {17317, 24603}, {17337, 29587}, {17352, 29611}, {17361, 25590}, {17374, 28633}, {17772, 19856}, {17791, 18698}, {20653, 31620}, {21277, 21677}, {25498, 29584}, {26048, 26979}, {26244, 30179}, {29446, 30866}, {31025, 31143}

X(32025) = isotomic conjugate of isogonal conjugate of X(33771)


X(32026) = POINT IV-CAPH OF X(37)

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

X(32026) lies on these lines: {1, 190}, {37, 274}, {39, 27195}, {192, 5283}, {194, 4704}, {213, 17261}, {350, 25092}, {536, 16819}, {668, 1500}, {1107, 4681}, {1621, 7760}, {2276, 18140}, {3616, 7757}, {3807, 4075}, {3995, 27163}, {4043, 10471}, {4098, 24215}, {4099, 17762}, {4360, 16552}, {9331, 24524}, {16589, 17759}, {16712, 27097}, {16818, 17320}, {16997, 31451}, {17160, 29773}, {17263, 24790}, {17280, 25499}, {17319, 20963}, {18145, 27020}, {18827, 24051}, {21070, 30966}


X(32027) = POINT IV-CAPH OF X(141)

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

X(32027) lies on these lines: {2, 7826}, {39, 31168}, {69, 3096}, {76, 338}, {83, 141}, {99, 2896}, {110, 14247}, {183, 7899}, {194, 7865}, {315, 3620}, {384, 7848}, {385, 7849}, {524, 7859}, {538, 7928}, {542, 10357}, {626, 14061}, {1078, 3314}, {1975, 7936}, {3329, 7882}, {3631, 6656}, {3734, 7929}, {3763, 7878}, {3785, 7835}, {3933, 7831}, {3934, 7809}, {5008, 19694}, {5041, 16897}, {6179, 7868}, {6292, 7779}, {6392, 7790}, {6683, 7840}, {7751, 7919}, {7752, 16990}, {7754, 7937}, {7759, 16986}, {7766, 7914}, {7767, 7832}, {7770, 7850}, {7771, 7881}, {7780, 7931}, {7786, 7788}, {7793, 7869}, {7795, 7811}, {7796, 7800}, {7801, 7904}, {7805, 7948}, {7808, 7946}, {7810, 7836}, {7812, 21356}, {7814, 15271}, {7815, 7897}, {7818, 31276}, {7822, 7893}, {7824, 7895}, {7827, 22165}, {7846, 14023}, {7853, 17129}, {7855, 7876}, {7871, 11285}, {7873, 17128}, {7885, 9466}, {7898, 17130}, {7905, 8362}, {7933, 17131}, {7935, 20081}, {7941, 31239}, {7942, 8667}, {7943, 14614}, {7949, 11174}, {8370, 10302}, {19577, 21248}


X(32028) = POINT IV-CAPH OF X(190)

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

X(32028) lies on these lines: {99, 666}, {144, 30225}, {190, 514}, {660, 6372}, {668, 4462}, {898, 4367}, {4378, 9266}, {4440, 6547}, {4499, 6004}, {4562, 6540}, {6546, 6634}, {6630, 17487}, {17350, 24281}, {27191, 31647}


X(32029) = POINT IV-CAPH OF X(239)

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

X(32029) lies on these lines: {1, 17755}, {2, 1280}, {6, 190}, {8, 26561}, {69, 1086}, {75, 16973}, {81, 4576}, {141, 27191}, {145, 20533}, {193, 4440}, {239, 335}, {291, 27919}, {511, 24813}, {524, 903}, {537, 3751}, {545, 1992}, {664, 9263}, {742, 17160}, {883, 1462}, {900, 10755}, {918, 1814}, {1015, 4561}, {1100, 24358}, {1386, 6651}, {2786, 10754}, {2796, 8593}, {2876, 25048}, {3416, 29617}, {3564, 24833}, {3570, 26273}, {3589, 29586}, {3618, 4422}, {3874, 30133}, {3881, 30130}, {3961, 24631}, {4384, 16496}, {4432, 16475}, {4716, 5847}, {5032, 17487}, {5039, 24815}, {5093, 24844}, {5263, 31317}, {5846, 6653}, {6542, 9053}, {6776, 29243}, {12167, 24814}, {14839, 20455}, {14853, 24828}, {14912, 24817}, {16593, 17316}, {16830, 31306}, {16972, 17393}, {17275, 25357}, {17449, 24602}, {18440, 24827}, {19459, 24822}, {20042, 31058}, {20132, 31314}, {20154, 27484}, {20172, 24349}, {24547, 25898}


X(32030) = POINT IV-CAPH OF X(244)

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

X(32030) lies on these lines: {244, 7035}, {668, 24191}, {903, 4106}, {3999, 17160}, {7192, 18822}


X(32031) = POINT IV-CAPH OF X(319)

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

X(32031) lies on these lines: {79, 319}, {668, 1330}, {2481, 7768}, {6327, 17143}, {7264, 17361}


X(32032) = POINT IV-CAPH OF X(320)

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

X(32032) lies on these lines: {2, 1017}, {69, 150}, {80, 320}, {316, 2481}, {3570, 10708}, {4555, 12531}, {4597, 6224}, {4738, 17360}, {17143, 21283}, {17378, 24222}


X(32033) = POINT IV-CAPH OF X(330)

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

X(32033) lies on these lines: {1, 87}, {1278, 18830}, {1575, 6384}, {2162, 4360}, {2998, 3226}, {3963, 26077}, {4361, 4598}, {4393, 21759}, {6383, 24621}, {16606, 30963}, {17302, 27341}, {21226, 26069}, {27424, 28366}


X(32034) = POINT IV-CAPH OF X(346)

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

X(32034) lies on these lines: {2, 20432}, {20, 190}, {279, 304}, {668, 30695}, {3227, 6553}, {3621, 30225}, {4461, 17143}, {7738, 17262}, {7791, 20073}


X(32035) = POINT IV-CAPH OF X(350)

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

X(32035) lies on these lines: {2, 20671}, {8, 76}, {39, 27195}, {75, 17793}, {194, 1015}, {274, 12263}, {291, 350}, {310, 4576}, {537, 4479}, {538, 3227}, {1078, 8671}, {2810, 18906}, {3097, 30963}, {4440, 18830}, {7033, 24260}, {9263, 20081}, {9902, 17144}, {12782, 18140}, {20457, 24514}, {27076, 31276}

leftri

Points Chara: X(32036)-X(32042)

rightri

This preamble and centers X(32036)-X(32042) were contributed by Clark Kimberling and Peter Moses, April 15, 2019.

Suppose that P = p:q:r (barycentrics). The Point Chara of P is the point given by

(p - q)(p - r) : (q - r)(q - p) : (r - p)(r - q).

Point Chara of P is the trilinear pole of the line PX(2), so that it lies on the Steiner circumellipse. (Randy Hutson, April 20, 2019)


X(32036) = POINT CHARA OF X(17)

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

X(32036) lies on the Steiner circumellipse and these lines: {2, 11087}, {17, 671}, {99, 16806}, {110, 930}, {338, 11130}, {530, 8172}, {531, 11600}, {648, 17402}, {1576, 14185}, {3228, 21461}, {4558, 23895}, {10409, 23872}, {11118, 11139}, {14570, 23896}

X(32036) = reflection of X(11117) in X(2)
X(32036) = Steiner circumellipse antipode of X(11117)
X(32036) = trilinear pole of line X(2)X(17)


X(32037) = POINT CHARA OF X(18)

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

X(32037) lies on the Steiner circumellipse and these lines: {2, 11082}, {18, 671}, {99, 16807}, {110, 930}, {338, 11131}, {530, 11601}, {531, 8173}, {648, 17403}, {1576, 14187}, {3228, 21462}, {4558, 23896}, {10410, 23873}, {11117, 11138}, {14570, 23895}

X(32037) = reflection of X(11118) in X(2)
X(32037) = Steiner circumellipse antipode of X(11118)
X(32037) = trilinear pole of line X(2)X(18)


X(32038) = POINT CHARA OF X(65)

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

X(32038) lies on the Steiner circumellipse and these lines: {99, 651}, {100, 6648}, {108, 648}, {190, 4551}, {646, 21859}, {664, 1020}, {668, 4552}, {670, 4554}, {903, 4654}, {941, 2481}, {959, 3227}, {1121, 31359}, {1415, 4612}, {2006, 14616}, {2092, 31643}, {4664, 9578}, {18816, 27339}

X(32038) = trilinear pole of line X(2)X(65)


X(32039) = POINT CHARA OF X(87)

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

X(32039) lies on the Steiner circumellipse and these lines: {190, 932}, {330, 3226}, {668, 4598}

X(32039) = trilinear pole of line X(2)X(87)


X(32040) = POINT CHARA OF X(165)

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

X(32040) lies on the Steiner circumellipse and these lines: {2, 18025}, {99, 26716}, {190, 2398}, {648, 4241}, {668, 30728}, {671, 2784}, {903, 1992}, {1121, 3241}, {1494, 31144}, {2481, 16834}, {3226, 14614}, {4569, 24015}

X(32040) = reflection of X(2) in X(23972)
X(32040) = reflection of X(18025) in X(2)
X(32040) = Steiner circumellipse antipode of X(18025)
X(32040) = antipode of X(2) in hyperbola {{A,B,C,X(2),X(658)}}
X(32040) = trilinear pole of line X(2)X(165)
X(32040) = isotomic conjugate of isogonal conjugate of X(26716)


X(32041) = POINT CHARA OF X(210)

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

X(32041) lies on the Steiner circumellipse and these lines: {2, 2481}, {99, 644}, {100, 666}, {190, 1026}, {376, 2808}, {528, 14947}, {646, 670}, {648, 4238}, {651, 6606}, {664, 1018}, {668, 30730}, {671, 2795}, {903, 4664}, {1002, 3227}, {1121, 3679}, {2279, 3226}, {4552, 4569}, {4876, 18827}, {7208, 9331}, {7233, 20680}, {14727, 30610}, {17294, 18025}, {17310, 18821}

X(32041) = reflection of X(2) in X(6184)
X(32041) = reflection of X(2481) in X(2)
X(32041) = isotomic conjugate of X(4762)
X(32041) = Steiner circumellipse antipode of X(2481)
X(32041) = trilinear pole of line X(2)X(210) (the line through the centroids of ABC, the intouch and extouch triangles)


X(32042) = POINT CHARA OF X(319)

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

X(32042) lies on the Steiner circumellipse and these lines: {99, 8652}, {100, 6540}, {668, 4427}, {903, 10436}, {1121, 3929}, {3227, 25417}, {3228, 28625}, {4632, 13486}, {17393, 30597}

X(32042) = isotomic conjugate of X(4802)
X(32042) = trilinear pole of line X(2)X(319)


X(32043) = X(2)X(4432)∩X(320)X(24628)

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

X(32043) lies on these lines: {2,4432}, {320,24628}, {1121,4384}, {1125,17694}, {1698,16060}, {2482,24603}, {3912,6174}, {4369,24636}, {4750,4763}, {4997,17738}, {24602,27757}


X(32044) = X(899)X(13466)∩X(1086)X(30970)

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

X(32044) lies on these lines: {899,13466}, {1086,30970}, {3248,30950}, {3768,4465}, {4033,30964}, {4379,17793}


X(32045) = X(2)X(24821)∩X(3227)X(16826)

Barycentrics    a^4+3 a^3 b+3 a^2 b^2-2 a b^3+3 a^3 c-6 a^2 b c-9 a b^2 c+3 b^3 c+3 a^2 c^2-9 a b c^2+9 b^2 c^2-2 a c^3+3 b c^3 : :

X(32045) lies on these lines: {2,24821}, {3227,16826}, {4375,6544}, {4767,29584}, {5461,29610}, {24709,29615}

leftri

Circumcenters and centroids of not-equilateral central triangles: X(32046)-X(32084)

rightri

This preamble and centers X(32046)-X(32084) were contributed by César Eliud Lozada, April 16, 2019.

The appearance of (T, n) in the following list means that the circumcenter of triangle T is X(n):

(ABC, 3), (ABC-X3 reflections, 3), (anti-Aquila, 1385), (anti-Ara, 4), (anti-Artzt, 599), (anti-Ascella, 3), (anti-Atik, 18951), (1st anti-Brocard, 98), (4th anti-Brocard, 11258), (5th anti-Brocard, 3398), (6th anti-Brocard, 182), (2nd anti-circumperp-tangential, 1), (1st anti-circumperp, 3), (anti-Conway, 32046), (2nd anti-Conway, 143), (anti-Euler, 20), (3rd anti-Euler, 11412), (4th anti-Euler, 5889), (anti-excenters-reflections, 3627), (2nd anti-extouch, 12161), (anti-inner-Grebe, 3312), (anti-outer-Grebe, 3311), (anti-Honsberger, 19154), (anti-Hutson intouch, 12084), (anti-incircle-circles, 7387), (anti-inverse-in-incircle, 14790), (anti-Mandart-incircle, 11248), (anti-McCay, 671), (6th anti-mixtilinear, 140), (anti-orthocentroidal, 399), (1st anti-orthosymmedial, 19164), (1st anti-Sharygin, 19210), (anti-tangential-midarc, 32047), (anti-Ursa minor, 13371), (anti-Wasat, 52), (antiAOA, 15132), (anticomplementary, 4), (AOA, 15114), (Apollonius, 970), (Aquila, 40), (Ara, 7387), (Aries, 32048), (Artzt, 7610), (Ascella, 3), (Atik, 9856), (1st Auriga, 11252), (2nd Auriga, 11253), (Ayme, 11259), (1st Brocard-reflected, 11261), (1st Brocard, 182), (2nd Brocard, 182), (4th Brocard, 381), (5th Brocard, 9821), (6th Brocard, 11257), (circummedial, 3), (circumorthic, 3), (2nd circumperp tangential, 11249), (1st circumperp, 3), (2nd circumperp, 3), (circumsymmedial, 3), (inner-Conway, 8), (Conway, 20), (2nd Conway, 962), (3rd Conway, 1), (Ehrmann-cross, 30), (Ehrmann-mid, 4), (Ehrmann-side, 4), (Ehrmann-vertex, 18377), (1st Ehrmann, 8546), (2nd Ehrmann, 11255), (Euler, 5), (2nd Euler, 5), (3rd Euler, 5), (4th Euler, 5), (5th Euler, 5), (excenters-midpoints, 11260), (excenters-reflections, 7982), (excentral, 40), (1st excosine, 155), (extangents, 8141), (extouch, 1158), (2nd extouch, 4), (3rd extouch, 11254), (inner-Fermat, 628), (outer-Fermat, 627), (Feuerbach, 5), (Fuhrmann, 355), (2nd Fuhrmann, 16159), (inner-Garcia, 3), (outer-Garcia, 355), (Garcia-reflection, 32049), (Gossard, 11251), (inner-Grebe, 1161), (outer-Grebe, 1160), (3rd Hatzipolakis, 32050), (hexyl, 1), (Honsberger, 390), (Hutson extouch, 32051), (inner-Hutson, 9836), (Hutson intouch, 1), (outer-Hutson, 9837), (1st Hyacinth, 11264), (2nd Hyacinth, 1147), (incentral, 8143), (incircle-circles, 1), (intangents, 8144), (intouch, 1), (inverse-in-incircle, 942), (Johnson, 4), (inner-Johnson, 10525), (outer-Johnson, 10526), (1st Johnson-Yff, 1478), (2nd Johnson-Yff, 1479), (K798e, 11263), (K798i, 10), (1st Kenmotu diagonals, 11265), (2nd Kenmotu diagonals, 11266), (Kosnita, 1658), (Lemoine, 8145), (Lucas antipodal, 32052), (Lucas central, 8155), (Lucas homothetic, 10669), (Lucas inner, 6407), (Lucas tangents, 1151), (Lucas(-1) antipodal, 32053), (Lucas(-1) central, 8156), (Lucas(-1) homothetic, 10673), (Lucas(-1) inner, 6408), (Lucas(-1) tangents, 1152), (Macbeath, 8146), (Mandart-excircles, 32054), (Mandart-incircle, 1), (McCay, 7617), (medial, 5), (midarc, 1), (2nd midarc, 1), (midheight, 5893), (mixtilinear, 8147), (2nd mixtilinear, 8159), (3rd mixtilinear, 3), (4th mixtilinear, 3), (5th mixtilinear, 1482), (6th mixtilinear, 1), (1st Neuberg, 8149), (2nd Neuberg, 8150), (orthic, 5), (orthocentroidal, 381), (1st orthosymmedial, 5480), (2nd orthosymmedial, 5480), (2nd Pamfilos-Zhou, 7596), (1st Parry, 351), (2nd Parry, 351), (3rd Parry, 351), (Pelletier, 11247), (reflection, 195), (1st Schiffler, 32055), (2nd Schiffler, 11256), (Schroeter, 10279), (1st Sharygin, 9840), (2nd Sharygin, 659), (Soddy, 32056), (inner-Soddy, 176), (2nd inner-Soddy, 32057), (outer-Soddy, 175), (2nd outer-Soddy, 32058), (inner-squares, 32059), (outer-squares, 32060), (Steiner, 8151), (submedial, 3628), (symmedial, 8152), (tangential, 26), (tangential-midarc, 8091), (2nd tangential-midarc, 8092), (inner tri-equilateral, 11267), (outer tri-equilateral, 11268), (1st tri-squares-central, 13720), (2nd tri-squares-central, 13843), (3rd tri-squares-central, 8981), (4th tri-squares-central, 13966), (1st tri-squares, 13663), (2nd tri-squares, 13783), (3rd tri-squares, 13879), (4th tri-squares, 13933), (Trinh, 11250), (Ursa-major, 12672), (Ursa-minor, 65), (inner-Vecten, 642), (outer-Vecten, 641), (Wasat, 946), (X-parabola-tangential, 32061), (X3-ABC reflections, 3), (Yff central, 8351), (Yff contact, 5592), (inner-Yff, 55), (outer-Yff, 56), (inner-Yff tangents, 10679), (outer-Yff tangents, 10680), (Yiu, 8154), (1st Zaniah, 12608), (2nd Zaniah, 10)

The appearance of (T, n) in the following list means that the centroid of triangle T is X(n):

(ABC, 2), (ABC-X3 reflections, 376), (anti-Aquila, 551), (anti-Ara, 428), (anti-Artzt, 2), (anti-Ascella, 11402), (anti-Atik, 18950), (1st anti-Brocard, 2), (4th anti-Brocard, 111), (5th anti-Brocard, 12150), (6th anti-Brocard, 5182), (2nd anti-circumperp-tangential, 5434), (1st anti-circumperp, 2979), (anti-Conway, 11402), (2nd anti-Conway, 51), (anti-Euler, 376), (3rd anti-Euler, 2979), (4th anti-Euler, 5890), (anti-excenters-reflections, 32062), (2nd anti-extouch, 11402), (anti-inner-Grebe, 19053), (anti-outer-Grebe, 19054), (anti-Honsberger, 19153), (anti-Hutson intouch, 10606), (anti-incircle-circles, 32063), (anti-inverse-in-incircle, 32064), (anti-Mandart-incircle, 4421), (anti-McCay, 2), (6th anti-mixtilinear, 3819), (anti-orthocentroidal, 110), (1st anti-orthosymmedial, 9157), (1st anti-Sharygin, 19209), (anti-tangential-midarc, 32065), (3rd anti-tri-squares, 1328), (4th anti-tri-squares, 1327), (anti-Ursa minor, 23332), (anti-Wasat, 51), (antiAOA, 15131), (anticomplementary, 2), (AOA, 15113), (Apollonius, 32066), (Aquila, 3679), (Ara, 9909), (Aries, 11206), (Artzt, 2), (Ascella, 11227), (Atik, 5927), (1st Auriga, 11207), (2nd Auriga, 11208), (Ayme, 11221), (1st Brocard-reflected, 2), (1st Brocard, 2), (2nd Brocard, 10166), (3rd Brocard, 11196), (4th Brocard, 6032), (5th Brocard, 7811), (6th Brocard, 7833), (circummedial, 9829), (circumorthic, 5890), (2nd circumperp tangential, 11194), (1st circumperp, 165), (2nd circumperp, 3576), (circumsymmedial, 353), (inner-Conway, 3681), (Conway, 11220), (2nd Conway, 9812), (3rd Conway, 10439), (4th Conway, 32067), (5th Conway, 11233), (Ehrmann-cross, 18556), (Ehrmann-mid, 3845), (Ehrmann-side, 18435), (Ehrmann-vertex, 18376), (1st Ehrmann, 182), (2nd Ehrmann, 11216), (Euler, 381), (2nd Euler, 5891), (3rd Euler, 3817), (4th Euler, 10175), (5th Euler, 10162), (excenters-midpoints, 10164), (excenters-reflections, 11224), (excentral, 165), (1st excosine, 154), (extangents, 11190), (extouch, 210), (2nd extouch, 5927), (3rd extouch, 11212), (4th extouch, 11213), (5th extouch, 11214), (inner-Fermat, 2), (outer-Fermat, 2), (Feuerbach, 5947), (Fuhrmann, 5587), (2nd Fuhrmann, 1699), (inner-Garcia, 5692), (outer-Garcia, 3679), (Garcia-reflection, 1699), (Gossard, 1651), (inner-Grebe, 5861), (outer-Grebe, 5860), (3rd Hatzipolakis, 32068), (hexyl, 3576), (Honsberger, 7671), (Hutson extouch, 5918), (inner-Hutson, 11222), (Hutson intouch, 5919), (outer-Hutson, 11223), (1st Hyacinth, 11232), (2nd Hyacinth, 11245), (incentral, 1962), (incircle-circles, 5049), (intangents, 11189), (intouch, 354), (inverse-in-incircle, 354), (Johnson, 381), (inner-Johnson, 11235), (outer-Johnson, 11236), (1st Johnson-Yff, 11237), (2nd Johnson-Yff, 11238), (K798e, 11230), (K798i, 11231), (1st Kenmotu diagonals, 11241), (2nd Kenmotu diagonals, 11242), (Kosnita, 11202), (Lemoine, 32069), (Lucas antipodal tangents, 32070), (Lucas central, 11198), (Lucas homothetic, 12152), (Lucas inner, 32072), (Lucas tangents, 11199), (Lucas(-1) antipodal tangents, 32071), (Lucas(-1) central, 32077), (Lucas(-1) homothetic, 12153), (Lucas(-1) inner, 32073), (Lucas(-1) tangents, 32074), (Macbeath, 11197), (Mandart-excircles, 11246), (Mandart-incircle, 3058), (McCay, 2), (medial, 2), (midarc, 11191), (2nd midarc, 11234), (midheight, 5943), (mixtilinear, 11200), (2nd mixtilinear, 11201), (3rd mixtilinear, 32075), (4th mixtilinear, 32076), (5th mixtilinear, 3241), (6th mixtilinear, 165), (1st Neuberg, 2), (2nd Neuberg, 2), (orthic, 51), (orthocentroidal, 5640), (1st orthosymmedial, 51), (2nd orthosymmedial, 11226), (2nd Pamfilos-Zhou, 11211), (1st Parry, 9123), (2nd Parry, 9185), (3rd Parry, 11215), (Pelletier, 11193), (reflection, 3060), (1st Schiffler, 11218), (2nd Schiffler, 11219), (Schroeter, 10278), (1st Sharygin, 11203), (2nd Sharygin, 1635), (Soddy, 32079), (inner-Soddy, 32080), (2nd inner-Soddy, 32082), (outer-Soddy, 32081), (2nd outer-Soddy, 32083), (inner-squares, 11209), (outer-squares, 11210), (Steiner, 11123), (submedial, 6688), (symmedial, 11205), (tangential, 154), (tangential-midarc, 11192), (2nd tangential-midarc, 11217), (inner tri-equilateral, 11243), (outer tri-equilateral, 11244), (1st tri-squares-central, 3068), (2nd tri-squares-central, 3069), (3rd tri-squares-central, 13846), (4th tri-squares-central, 13847), (1st tri-squares, 3068), (2nd tri-squares, 3069), (3rd tri-squares, 13846), (4th tri-squares, 13847), (Trinh, 11204), (Ursa-major, 5927), (Ursa-minor, 354), (inner-Vecten, 2), (outer-Vecten, 2), (Wasat, 3817), (X-parabola-tangential, 8029), (X3-ABC reflections, 381), (Yff central, 11195), (Yff contact, 6546), (inner-Yff, 10056), (outer-Yff, 10072), (inner-Yff tangents, 11239), (outer-Yff tangents, 11240), (Yiu, 32084), (1st Zaniah, 3742), (2nd Zaniah, 3740)

X(32046) = CIRCUMCENTER OF THE ANTI-CONWAY TRIANGLE

Barycentrics    a^2*(a^8-3*(b^2+c^2)*a^6+(3*b^4+2*b^2*c^2+3*c^4)*a^4-(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2-(b^2-c^2)^2*b^2*c^2) : :
Barycentrics    Sin[A] (Cos[A] + 2 Cos[A - B] Cos[A - C]) : :
Trilinears    cos A + 2 cos(C - A) cos(A - B) : :
X(32046) = X(3)+3*X(11402) = 3*X(3)+X(12160) = 3*X(5050)+X(19459) = 9*X(11402)-X(12160) = 3*X(11402)-X(12161) = X(12160)-3*X(12161)

X(32046) is the center of the circle that is the locus of the crosssum of nine-point circle antipodes. (Randy Hutson, June 7, 2019)

Let A'B'C' be the antipedal triangle of X(3) (the tangential triangle). X(32046) is the radical center of the nine-point circles of triangles AA'X(3), BB'X(3), CC'X(3). (cf. Anopolis #2105, Antreas Hatzipolakis, December 1, 2014) (Randy Hutson, June 7, 2019)

Let AeBeCe and AiBiCi be the Ae and Ai triangles (aka K798e and K798i triangles). Let A'B'C' be the orthic triangle. X(32046) is the radical center of the circumcircles of triangles A'AeAi, B'BeBi, C'CeCi. (Randy Hutson, June 7, 2019)

X(32046) lies on these lines: {2,49}, {3,54}, {4,567}, {5,156}, {6,26}, {17,3206}, {18,3205}, {20,31815}, {22,10263}, {24,5944}, {25,10095}, {30,578}, {35,9666}, {36,9653}, {52,7502}, {68,11264}, {110,1656}, {140,141}, {154,13364}, {155,7514}, {185,18570}, {206,18583}, {215,498}, {343,7568}, {378,13491}, {381,1614}, {382,15033}, {389,1658}, {394,7516}, {399,15058}, {499,2477}, {511,7525}, {546,6759}, {548,13346}, {549,1092}, {550,10984}, {568,1199}, {575,2393}, {576,7555}, {597,23410}, {631,9545}, {1176,1351}, {1181,5663}, {1353,19131}, {1385,31811}, {1437,6924}, {1498,31861}, {1511,17928}, {1698,9622}, {1899,13561}, {1974,7715}, {1994,6243}, {2070,3567}, {2930,15462}, {2931,13358}, {2937,3060}, {3043,15061}, {3044,15561}, {3047,14643}, {3071,9677}, {3090,9544}, {3091,10540}, {3133,20775}, {3167,7393}, {3202,11272}, {3431,16867}, {3448,11597}, {3517,12167}, {3523,13339}, {3526,9703}, {3574,11750}, {3579,31812}, {3624,9621}, {3627,11424}, {3628,9306}, {3767,9604}, {3796,13391}, {3843,14157}, {3845,26883}, {5050,6642}, {5070,9705}, {5073,8718}, {5092,5447}, {5093,19121}, {5392,25043}, {5422,7506}, {5446,17714}, {5504,14528}, {5576,14389}, {5622,15132}, {5640,26882}, {5876,7503}, {6241,14130}, {6639,18912}, {6640,18911}, {6644,12006}, {6676,13292}, {6689,10116}, {6800,7517}, {7387,11426}, {7395,14128}, {7507,11565}, {7508,13323}, {7509,15067}, {7527,18439}, {7529,18874}, {7530,10982}, {7542,11245}, {7575,16227}, {7741,9667}, {7746,9697}, {7951,9652}, {8141,11428}, {8144,11429}, {8227,9587}, {8254,10274}, {8548,9937}, {9586,31423}, {9603,31401}, {9696,31455}, {9701,26363}, {9702,26364}, {9714,9777}, {9729,12038}, {9730,13367}, {9781,18378}, {9786,18324}, {9818,19347}, {9833,11818}, {9908,19139}, {10020,13567}, {10024,12022}, {10625,22352}, {11179,18281}, {11250,11430}, {11425,12084}, {11427,14790}, {11432,14070}, {11438,15331}, {11441,15060}, {11449,15045}, {11454,18364}, {11464,15037}, {11702,15101}, {11746,20773}, {11935,15720}, {12041,13148}, {12100,13347}, {12105,15826}, {12107,16881}, {12241,15761}, {12370,15760}, {12383,15089}, {13142,16618}, {13154,17811}, {13371,23292}, {13406,18390}, {13470,18569}, {13482,15681}, {13564,15080}, {14265,14355}, {14789,23236}, {14805,15032}, {14912,18951}, {15024,15047}, {15028,15038}, {15083,31834}, {18128,20299}, {18377,18388}, {18379,18396}, {18420,18925}, {18580,26937}, {19125,19155}, {19365,32047}, {19467,30522}, {22146,26216}, {23042,23326}

X(32046) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 12161}, {5, 31804}, {20, 31815}, {550, 31802}, {1181, 7526}, {1385, 31811}, {3579, 31812}, {6101, 31810}, {6102, 31807}, {12228, 13198}
X(32046) = isogonal conjugate of X(16837)
X(32046) = X(5)-of-2nd-anti-extouch triangle
X(32046) = anti-Conway-isogonal conjugate of X(12161)
X(32046) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1993, 6101), (49, 13353, 2), (11412, 11422, 195)


X(32047) = CIRCUMCENTER OF THE ANTI-TANGENTIAL-MIDARC TRIANGLE

Barycentrics    a*(a^6-(b-c)^2*a^4-(b^4+c^4+(b-c)^2*b*c)*a^2+(b^2-c^2)*(b-c)*(b^3+c^3)) : :
X(32047) = X(7352)-3*X(32065)

X(32047) lies on these lines: {1,30}, {3,1398}, {4,18447}, {5,34}, {11,15761}, {12,13371}, {20,18455}, {26,56}, {33,3627}, {35,11250}, {36,1658}, {52,1425}, {55,12084}, {65,8141}, {140,1038}, {143,19366}, {155,221}, {156,26888}, {222,24475}, {278,6917}, {347,6868}, {382,6198}, {388,14790}, {495,23335}, {498,18281}, {499,10201}, {517,4347}, {548,1040}, {550,1062}, {614,10154}, {952,21147}, {999,7387}, {1068,6923}, {1154,7352}, {1159,17016}, {1325,2906}, {1394,24467}, {1428,19154}, {1448,24470}, {1456,5887}, {1465,6924}, {1478,18569}, {1482,4318}, {1565,7210}, {1657,3100}, {1718,24914}, {1745,1807}, {2067,11265}, {3157,16266}, {3270,10575}, {3295,12085}, {3304,9645}, {3529,9538}, {3564,19471}, {3585,18377}, {3600,31305}, {3628,19372}, {3850,9817}, {3868,23070}, {3869,22136}, {4299,9630}, {4302,9627}, {4670,30147}, {5010,10226}, {5073,9642}, {5204,18324}, {5262,5708}, {5432,23336}, {5433,10020}, {5563,17714}, {5663,6238}, {5690,8270}, {5889,19368}, {6502,11266}, {6644,11398}, {7051,11267}, {7191,9909}, {7280,15331}, {7530,11399}, {7741,13406}, {7747,9595}, {7756,9594}, {7951,10224}, {9632,23251}, {9634,13903}, {9641,17800}, {10267,15832}, {11255,19369}, {11268,19373}, {11412,19367}, {11436,13630}, {11446,12290}, {11461,12279}, {11700,26286}, {12161,19349}, {13383,15325}, {15952,20254}, {18513,18567}, {18915,18951}, {19175,19210}, {19365,32046}

X(32047) = midpoint of X(i) and X(j) for these lines: {i,j}: {6238, 7355}, {19469, 19505}
X(32047) = reflection of X(8144) in X(1)
X(32047) = anti-tangential-midarc-isogonal conjugate of X(7352)
X(32047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (34, 1060, 5), (1870, 4296, 3)


X(32048) = CIRCUMCENTER OF THE ARIES TRIANGLE

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^12-2*(b^2+c^2)*a^10-(b^2+c^2)^2*a^8+4*(b^2+c^2)*(b^4+c^4)*a^6-(b^8+6*b^4*c^4+c^8)*a^4-2*(b^4-c^4)*(b^2-c^2)^3*a^2+(b^2-c^2)^6) : :
X(32048) = 3*X(154)-X(15316) = X(9908)-3*X(9909) = 3*X(9909)+X(12309) = 3*X(10201)-2*X(20302) = 3*X(11206)-X(12420) = X(12301)-3*X(14070)

X(32048) lies on these lines: {3,125}, {22,68}, {23,6193}, {24,12118}, {25,1147}, {26,19908}, {30,9932}, {154,15316}, {155,6243}, {156,14984}, {161,1498}, {403,8907}, {539,9908}, {1069,9673}, {1598,5448}, {1658,9938}, {2937,12429}, {3157,9658}, {3167,18378}, {3564,15581}, {5480,9820}, {5654,10594}, {5899,12164}, {6642,11425}, {6644,12241}, {7506,10982}, {7530,22660}, {7689,11414}, {8185,9928}, {8548,19127}, {9591,9896}, {10117,12419}, {10201,20302}, {10625,26283}, {11206,12420}, {11411,12088}, {11477,20987}, {12083,12163}, {12166,15083}, {12225,25715}, {12301,14070}, {12319,16868}, {12328,20872}, {13371,18382}, {13383,15577}, {15761,22661}

X(32048) = midpoint of X(i) and X(j) for these lines: {i,j}: {7387, 9937}, {9908, 12309}
X(32048) = reflection of X(i) in X(j) for these (i,j): (9938, 1658), (19908, 26), (22661, 15761), (23307, 13383)
X(32048) = {X(9909), X(12309)}-harmonic conjugate of X(9908)
X(32048) = Aries-isogonal conjugate of X(12420)
X(32048) = X(1158)-of-tangential-triangle if ABC is acute


X(32049) = CIRCUMCENTER OF THE GARCIA-REFLECTION TRIANGLE

Barycentrics    a^4-(b+c)*a^3+6*b*c*a^2+(b+c)*(b^2-4*b*c+c^2)*a-(b^2-c^2)^2 : :
X(32049) = X(145)-3*X(25568) = 2*X(946)-3*X(11236) = 3*X(1699)-X(3680) = 3*X(1699)-2*X(13463) = 5*X(3617)-3*X(24477) = 3*X(3679)-X(6762) = 2*X(3813)-3*X(5587) = 6*X(3829)-7*X(7989) = 2*X(4297)-3*X(4421) = 3*X(5587)-X(12629) = 3*X(5790)-2*X(10916) = 3*X(5886)-2*X(22837) = 4*X(6684)-3*X(11194) = 2*X(8666)-3*X(26446) = X(10912)-3*X(11236) = 3*X(11235)-4*X(19925) = 3*X(11235)-2*X(21627) = X(11519)-3*X(24392) = X(11531)-3*X(28609)

X(32049) lies on these lines: {1,1329}, {2,11260}, {3,10915}, {4,3880}, {7,8}, {10,999}, {11,11256}, {40,529}, {42,30960}, {46,1145}, {56,6735}, {57,8256}, {72,12647}, {78,10944}, {80,3633}, {145,1837}, {153,12679}, {354,5554}, {355,381}, {495,28628}, {515,3913}, {516,12640}, {517,6256}, {528,2136}, {612,30778}, {758,25413}, {908,2098}, {952,3811}, {956,10039}, {958,31397}, {960,3421}, {1001,5795}, {1012,8668}, {1056,3812}, {1155,20076}, {1222,3705}, {1319,5552}, {1376,6736}, {1388,27385}, {1420,3035}, {1478,10914}, {1537,5854}, {1699,3680}, {1709,27870}, {1836,14923}, {2478,5919}, {2646,10528}, {2800,12676}, {2802,10742}, {2886,4853}, {3057,3436}, {3086,5123}, {3241,26129}, {3244,5722}, {3304,24982}, {3338,3679}, {3419,3632}, {3434,3893}, {3445,5121}, {3476,7080}, {3555,5570}, {3617,24477}, {3621,4863}, {3626,5708}, {3813,5587}, {3814,11373}, {3829,7989}, {3838,5261}, {3869,25414}, {3870,10950}, {3885,5080}, {3890,4679}, {3895,6284}, {3899,5559}, {4018,10052}, {4028,15232}, {4297,4421}, {4515,24247}, {4861,11375}, {4999,31434}, {5084,10179}, {5178,31145}, {5220,5837}, {5289,21075}, {5541,10483}, {5787,12437}, {5790,10916}, {5881,6765}, {5886,22837}, {6684,11194}, {6734,18967}, {7991,17768}, {8583,9711}, {8666,26446}, {8679,31785}, {8715,18481}, {9623,25466}, {10072,17619}, {10529,17606}, {10827,24390}, {11376,11681}, {11519,24392}, {11531,28609}, {13600,26333}, {15888,19860}, {17728,25005}, {19861,21031}, {20070,28534}, {24928,26364}

X(32049) = midpoint of X(i) and X(j) for these lines: {i,j}: {2136, 5691}, {3632, 11523}, {5881, 6765}
X(32049) = reflection of X(i) in X(j) for these (i,j): (1, 12607), (3, 10915), (1482, 21077), (3680, 13463), (10912, 946), (11256, 11), (12513, 10), (12629, 3813), (18481, 8715), (21627, 19925), (24391, 3626)
X(32049) = anticomplement of X(11260)
X(32049) = Garcia-reflection-isogonal conjugate of X(3680)
X(32049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 17757, 25681), (8, 388, 5836), (388, 5836, 5880)


X(32050) = CIRCUMCENTER OF THE 3rd HATZIPOLAKIS TRIANGLE

Barycentrics    (SB+SC)*((178*R^4-65*SW*R^2+6*SW^2)*S^2+(64*R^4-23*SW*R^2+2*SW^2)*(8*R^2+SA-2*SW)*SA) : :
X(32050) = X(2929)+7*X(15043) = 3*X(5946)+X(22962) = 5*X(10574)+3*X(22971) = 5*X(15026)-X(22816) = 9*X(15045)-X(22549) = X(31985)-3*X(32068)

X(32050) lies on these lines: {6,2929}, {5946,22962}, {10574,22971}, {15026,22816}, {15045,22549}, {15087,22955}, {31985,32068}

X(32050) = 3rd-Hatzipolakis-isogonal conjugate of X(31985)


X(32051) = CIRCUMCENTER OF THE HUTSON EXTOUCH TRIANGLE

Barycentrics
a*(a^9-(b+c)*a^8-4*(b^2+5*b*c+c^2)*a^7+2*(b+c)*(2*b^2-3*b*c+2*c^2)*a^6+2*(3*b^4+3*c^4+2*(15*b^2+17*b*c+15*c^2)*b*c)*a^5-6*(b+c)*(b^4+c^4-(3*b^2+4*b*c+3*c^2)*b*c)*a^4-4*(b^2+c^2)*(b^4+c^4+(15*b^2+8*b*c+15*c^2)*b*c)*a^3+2*(b^2-c^2)*(b-c)*(2*b^4+2*c^4-(5*b^2+22*b*c+5*c^2)*b*c)*a^2+(b^4+c^4+2*(10*b^2-13*b*c+10*c^2)*b*c)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c)*(b^2-4*b*c+c^2)) : :
X(32051) = 3*X(5918)-X(31968)

X(32051) lies on these lines: {9,946}, {516,12731}, {5918,31968}, {9943,12702}, {12699,22992}, {12857,16138}

X(32051) = reflection of X(12699) in X(22992)
X(32051) = Hutson-extouch-isogonal conjugate of X(31968)


X(32052) = CIRCUMCENTER OF THE LUCAS ANTIPODAL TRIANGLE

Barycentrics    (S^2-SB*SC)*(2*(SW+4*R^2)*S^2+2*S*(S-SA)*(S+SA)-SW^3) : :

X(32052) lies on these lines: {3,69}, {511,12977}, {2996,19406}, {12984,13061}, {13881,19422}, {18980,23698}

X(32052) = midpoint of X(3) and X(19490)
X(32052) = Lucas-antipodal-isogonal conjugate of X(31970)
X(32052) = {X(3), X(9723)}-harmonic conjugate of X(32053)


X(32053) = CIRCUMCENTER OF THE LUCAS(-1) ANTIPODAL TRIANGLE

Barycentrics    (S^2-SB*SC)*(2*(SW+4*R^2)*S^2-2*S*(-S-SA)*(-S+SA)-SW^3) : :

X(32053) lies on these lines: {3,69}, {511,13068}, {2996,19407}, {12985,13062}, {13881,19423}, {18981,23698}

X(32053) = midpoint of X(3) and X(19491)
X(32053) = Lucas(-1)-antipodal-isogonal conjugate of X(31971)
X(32053) = {X(3), X(9723)}-harmonic conjugate of X(32052)


X(32054) = CIRCUMCENTER OF THE MANDART-EXCIRCLES TRIANGLE

Barycentrics
a*(a^9-(b+c)*a^8-2*(b+c)^2*a^7+2*(b+c)*(b^2+3*b*c+c^2)*a^6+2*(5*b^2-8*b*c+5*c^2)*b*c*a^5-8*(b+c)*(b^2+b*c+c^2)*b*c*a^4+2*(b^4+c^4-4*(b^2-3*b*c+c^2)*b*c)*(b+c)^2*a^3-2*(b+c)*(b^6+c^6-(b^4+c^4+(5*b^2-14*b*c+5*c^2)*b*c)*b*c)*a^2-(b^2-c^2)^2*(b-c)^2*(b^2+4*b*c+c^2)*a+(b^2-c^2)^4*(b+c)) : :
X(32054) = 3*X(11246)-X(31977)

X(32054) lies on these lines: {19,1598}, {65,12912}, {999,12522}, {3338,12659}, {3555,17656}, {5048,12876}, {5708,12442}, {11246,31977}, {12621,17757}, {12655,25415}, {18257,25681}, {21077,21632}

X(32054) = midpoint of X(3555) and X(17656)
X(32054) = reflection of X(12522) in X(12907)
X(32054) = Mandart-excircles-isogonal conjugate of X(31977)


X(32055) = CIRCUMCENTER OF THE 1st SCHIFFLER TRIANGLE

Barycentrics
a*(a^12-2*(b+c)*a^11-(4*b^2-9*b*c+4*c^2)*a^10+(b+c)*(10*b^2-9*b*c+10*c^2)*a^9+(5*b^4+5*c^4-(33*b^2-17*b*c+33*c^2)*b*c)*a^8-2*(b+c)*(10*b^4+10*c^4-(15*b^2-19*b*c+15*c^2)*b*c)*a^7+(48*b^4+48*c^4-(29*b^2-49*b*c+29*c^2)*b*c)*b*c*a^6+(b+c)*(20*b^6+20*c^6-(36*b^4+36*c^4-(44*b^2-29*b*c+44*c^2)*b*c)*b*c)*a^5-(5*b^8+5*c^8+(36*b^6+36*c^6-(35*b^4-6*b^2*c^2+35*c^4)*b*c)*b*c)*a^4-(b+c)*(10*b^8+10*c^8-(9*b^2-16*b*c+9*c^2)*(2*b^4+2*c^4+(2*b^2+b*c+2*c^2)*b*c)*b*c)*a^3+(b^2-c^2)^2*(4*b^6+4*c^6+(15*b^4+15*c^4-(23*b^2-5*b*c+23*c^2)*b*c)*b*c)*a^2+(b^2-c^2)^3*(b-c)*(2*b^4+2*c^4+(b+c)^2*b*c)*a-(b^2-c^2)^4*(b-c)^2*(b^2+5*b*c+c^2)) : :

X(32055) lies on the line {12745,31870}


X(32056) = CIRCUMCENTER OF THE SODDY TRIANGLE

Barycentrics
7*a^7-13*(b+c)*a^6+(9*b^2+2*b*c+9*c^2)*a^5-11*(b^2-c^2)*(b-c)*a^4+(9*b^2+34*b*c+9*c^2)*(b-c)^2*a^3-3*(b^2-c^2)^2*(b+c)*a^2+(7*b^2+10*b*c+7*c^2)*(b-c)^4*a-5*(b^2-c^2)^3*(b-c) : :

X(32056) lies on the line {1,4}


X(32057) = CIRCUMCENTER OF THE 2nd INNER-SODDY TRIANGLE

Barycentrics
a*((a+b+c)*(6*a^6-9*(b+c)*a^5-3*(5*b^2+8*b*c+5*c^2)*a^4+4*(b+c)*(7*b^2+2*b*c+7*c^2)*a^3-2*(b^4+c^4-2*(7*b^2-6*b*c+7*c^2)*b*c)*a^2-(b^2-c^2)*(b-c)*(11*b^2+34*b*c+11*c^2)*a+(3*b^4+3*c^4-2*(b^2+7*b*c+c^2)*b*c)*(b-c)^2)-2*S*(13*(b+c)*a^4-2*(4*b^2-3*b*c+4*c^2)*a^3-8*(b+2*c)*(2*b+c)*(b+c)*a^2+2*(4*b^4+4*c^4+(b^2-24*b*c+c^2)*b*c)*a+(b^2-c^2)*(b-c)*(3*b^2+14*b*c+3*c^2))) : :

Let A', B', C' be as at X(7133). A'B'C' is perspective to the 2nd inner Soddy triangle at X(32057). (Randy Hutson, June 7, 2019)

X(32057) lies on these lines: {1,372}, {482,11246}, {6284,31533}, {10252,16213}

X(32057) = midpoint of X(31533) and X(31568)
X(32057) = 2nd-inner-Soddy-isogonal conjugate of X(482)


X(32058) = CIRCUMCENTER OF THE 2nd OUTER-SODDY TRIANGLE

Barycentrics
a*((a+b+c)*(6*a^6-9*(b+c)*a^5-3*(5*b^2+8*b*c+5*c^2)*a^4+4*(b+c)*(7*b^2+2*b*c+7*c^2)*a^3-2*(b^4+c^4-2*(7*b^2-6*b*c+7*c^2)*b*c)*a^2-(b^2-c^2)*(b-c)*(11*b^2+34*b*c+11*c^2)*a+(3*b^4+3*c^4-2*(b^2+7*b*c+c^2)*b*c)*(b-c)^2)+2*S*(13*(b+c)*a^4-2*(4*b^2-3*b*c+4*c^2)*a^3-8*(b+2*c)*(2*b+c)*(b+c)*a^2+2*(4*b^4+4*c^4+(b^2-24*b*c+c^2)*b*c)*a+(b^2-c^2)*(b-c)*(3*b^2+14*b*c+3*c^2))) : :

X(32058) lies on these lines: {1,371}, {481,11246}, {6284,31532}, {10253,16214}

X(32058) = midpoint of X(31532) and X(31567)
X(32058) = 2nd-outer-Soddy-isogonal conjugate of X(481)


X(32059) = CIRCUMCENTER OF THE INNER-SQUARES TRIANGLE

Barycentrics    (3*SA-5*SW)*S^2-S*(2*S^2+(SA+2*SW)*(SB+SC))-4*(4*R^2-SW)*SB*SC : :

X(32059) lies on these lines: {4,371}, {11209,31987}, {11315,26958}, {31406,32060}


X(32060) = CIRCUMCENTER OF THE OUTER-SQUARES TRIANGLE

Barycentrics    (3*SA-5*SW)*S^2+S*(2*S^2+(SA+2*SW)*(SB+SC))-4*(4*R^2-SW)*SB*SC : :

X(32060) lies on these lines: {4,372}, {11210,31988}, {11316,26958}, {31406,32059}


X(32061) = CIRCUMCENTER OF THE X-PARABOLA-TANGENTIAL TRIANGLE

Barycentrics
2*a^16-6*(b^2+c^2)*a^14+3*(b^4+8*b^2*c^2+c^4)*a^12+5*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*a^10-(3*b^8+3*c^8+4*(2*b^4-13*b^2*c^2+2*c^4)*b^2*c^2)*a^8-2*(b^2+c^2)*(b^8+c^8-(10*b^4-21*b^2*c^2+10*c^4)*b^2*c^2)*a^6-(b^12+c^12-2*(5*b^8+5*c^8-(21*b^4-34*b^2*c^2+21*c^4)*b^2*c^2)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*(3*b^8+3*c^8-(13*b^4-21*b^2*c^2+13*c^4)*b^2*c^2)*a^2-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^6 : :
X(32061) = 3*X(8029)-X(31990)

X(32061) lies on these lines: {4,542}, {8029,31990}

X(32061) = X-parabola-tangential-isogonal conjugate of X(31990)


X(32062) = CENTROID OF THE ANTI-EXCENTERS-REFLECTIONS TRIANGLE

Barycentrics    a^2*((b^2+c^2)*a^6-(b^2-3*c^2)*(3*b^2-c^2)*a^4+3*(b^4-c^4)*(b^2-c^2)*a^2-(b^4+10*b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(32062) = 4*X(4)-X(185) = 5*X(4)-2*X(389) = 11*X(4)-5*X(3567) = 3*X(4)-X(5890) = 7*X(4)-X(6241) = 13*X(4)-7*X(9781) = 7*X(4)-4*X(10110) = 2*X(4)+X(11381) = 5*X(4)+X(12290) = 13*X(4)-4*X(13382) = X(4)+2*X(13474) = 5*X(51)-4*X(389) = 11*X(51)-10*X(3567) = 3*X(51)-2*X(5890) = 7*X(51)-2*X(6241) = 13*X(51)-14*X(9781) = 7*X(51)-8*X(10110) = 3*X(3917)-4*X(5891) = 5*X(3917)-8*X(15060) = 7*X(3917)-8*X(15067) = X(3917)-4*X(16194) = 2*X(5891)-3*X(15030) = 5*X(5891)-6*X(15060) = 7*X(5891)-6*X(15067) = X(5891)-3*X(16194) = 5*X(15030)-4*X(15060) = 7*X(15030)-4*X(15067) = 7*X(15060)-5*X(15067) = 2*X(15060)-5*X(16194) = 2*X(15067)-7*X(16194)

X(32062) lies on these lines: {4,51}, {5,14855}, {6,14490}, {20,3819}, {24,11204}, {25,10606}, {30,3917}, {33,32065}, {34,11189}, {52,3853}, {53,1562}, {64,5198}, {74,13603}, {125,1596}, {154,1593}, {184,1597}, {235,23332}, {373,381}, {376,5650}, {378,1495}, {382,5562}, {428,15311}, {511,3543}, {546,10575}, {1154,3627}, {1204,1598}, {1216,5073}, {1498,11402}, {1531,31723}, {1533,15760}, {1656,14641}, {1843,2781}, {1885,16621}, {1906,6247}, {1907,2883}, {1974,10249}, {2390,12688}, {2393,12294}, {2777,7576}, {2979,3146}, {3091,6688}, {3292,18451}, {3357,10594}, {3426,10605}, {3529,11793}, {3534,10170}, {3545,16836}, {3575,16656}, {3830,13754}, {3832,9729}, {3839,5943}, {3845,9730}, {3855,11695}, {3861,13491}, {4550,12083}, {5056,17704}, {5059,13348}, {5076,5446}, {5447,17800}, {5640,13570}, {5651,21312}, {5663,14831}, {5946,14893}, {6102,12102}, {7418,10568}, {7998,15683}, {9818,22352}, {10282,14865}, {10301,10990}, {10982,12315}, {11017,15712}, {11190,11471}, {11216,11470}, {11241,11473}, {11242,11474}, {11243,11475}, {11244,11476}, {11430,13596}, {11456,13366}, {11459,15682}, {11472,18534}, {11744,15321}, {11746,17856}, {11820,22112}, {12099,17853}, {12111,13598}, {12112,15033}, {12292,13417}, {13363,23046}, {13399,13567}, {13403,16659}, {13419,18560}, {13445,13595}, {13488,16655}, {14269,16226}, {15058,15644}, {15082,15692}, {15684,23039}, {15752,31978}, {15761,18488}, {16658,18400}, {16980,31673}, {18356,18555}, {19124,19153}, {19169,19209}, {19416,32070}, {19417,32071}

X(32062) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 11455}, {51, 11381}, {382, 18435}, {2979, 3146}, {3543, 15305}, {11459, 15682}, {15684, 23039}
X(32062) = reflection of X(i) in X(j) for these (i,j): (20, 3819), (51, 4), (185, 51), (2979, 5907), (3534, 10170), (3917, 15030), (5562, 18435), (5650, 16261), (5946, 14893), (9730, 3845), (11381, 11455), (11455, 13474), (14855, 5), (15030, 16194), (15072, 5943), (16226, 14269), (17853, 12099)
X(32062) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 11381, 185), (4, 12290, 389), (4, 13474, 11381)


X(32063) = CENTROID OF THE ANTI-INCIRCLE-CIRCLES TRIANGLE

Barycentrics    a^2*(3*a^8-10*(b^2+c^2)*a^6+4*(3*b^4-b^2*c^2+3*c^4)*a^4-6*(b^4-c^4)*(b^2-c^2)*a^2+(b^4+10*b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(32063) = 5*X(3)-2*X(64) = X(3)+2*X(1498) = 7*X(3)-4*X(3357) = X(3)-4*X(6759) = 13*X(3)-10*X(8567) = 5*X(3)-8*X(10282) = 3*X(3)-2*X(10606) = 3*X(3)-4*X(11202) = 5*X(3)-4*X(11204) = 2*X(3)+X(12315) = 4*X(3)-X(13093) = 2*X(3)-5*X(14530) = 7*X(3)-10*X(17821) = X(64)-5*X(154) = X(64)+5*X(1498) = 7*X(64)-10*X(3357) = X(64)-10*X(6759) = X(64)-4*X(10282) = 3*X(64)-5*X(10606) = 4*X(140)-X(12324)

X(32063) lies on these lines: {3,64}, {4,11402}, {5,32064}, {6,3531}, {20,25712}, {24,12174}, {25,5890}, {30,3167}, {51,1181}, {54,11403}, {110,11820}, {140,12324}, {156,12085}, {159,399}, {161,5899}, {184,1597}, {185,3517}, {206,10249}, {221,7373}, {376,6090}, {378,3426}, {381,597}, {382,2883}, {548,12250}, {550,6225}, {578,15811}, {999,10535}, {1154,7387}, {1173,3527}, {1351,2393}, {1384,1971}, {1398,9638}, {1495,10605}, {1593,1614}, {1596,6776}, {1625,15905}, {1656,14216}, {1657,5878}, {1660,22115}, {1853,5055}, {2192,6767}, {2390,10680}, {2777,15681}, {2979,11414}, {3089,18914}, {3197,22147}, {3295,11189}, {3311,11241}, {3312,11242}, {3332,15762}, {3515,6241}, {3516,9707}, {3526,6247}, {3534,15311}, {3542,26944}, {3796,15030}, {3830,18400}, {3843,18376}, {3851,14862}, {5020,5892}, {5054,10192}, {5064,16658}, {5070,20299}, {5073,17845}, {5076,5893}, {5093,17813}, {5596,15760}, {5644,14845}, {5663,14070}, {5895,17800}, {6001,10179}, {6199,17819}, {6221,10533}, {6395,17820}, {6398,10534}, {6623,19118}, {6688,11484}, {6696,15720}, {6800,15305}, {7485,15052}, {7507,16659}, {9715,12111}, {9777,15032}, {9899,31663}, {9909,13754}, {10117,12308}, {10182,15701}, {10193,15707}, {10306,11190}, {10620,15647}, {10675,11244}, {10676,11243}, {11216,11482}, {11381,19357}, {11410,11464}, {11425,13474}, {11472,18475}, {12163,16195}, {13488,18925}, {13567,15152}, {14269,18405}, {15693,23328}, {15694,23329}, {15696,20427}, {15750,26882}, {18358,20079}, {18494,31383}, {18909,21841}, {19173,19209}, {19418,32070}, {19419,32071}, {19709,23325}

X(32063) = midpoint of X(i) and X(j) for these lines: {i,j}: {154, 1498}, {5656, 11206}
X(32063) = reflection of X(i) in X(j) for these (i,j): (3, 154), (64, 11204), (154, 6759), (10249, 206), (10606, 11202), (11204, 10282), (14216, 23332), (23332, 16252), (32064, 5)
X(32063) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 12315, 13093), (1498, 6759, 3), (12315, 14530, 3)


X(32064) = CENTROID OF THE ANTI-INVERSE-IN-INCIRCLE TRIANGLE

Barycentrics    -8*(4*R^2-SA)*S^2+16*SB*SC*SW : :
Barycentrics    3 a sec(A + ω) - b sec(B + ω) - c sec(C + ω) : :
X(32064) = 5*X(2)-4*X(10192) = 3*X(2)-4*X(23332) = 5*X(4)-2*X(5878) = 4*X(4)-X(6225) = 2*X(4)+X(12324) = X(4)+2*X(14216) = X(4)+8*X(14864) = 3*X(4)-4*X(18376) = X(4)-4*X(18381) = 5*X(4)-8*X(18383) = 7*X(4)-4*X(22802) = X(154)-3*X(1853) = 5*X(154)-6*X(10192) = 4*X(154)-3*X(11206) = 5*X(1853)-2*X(10192) = 4*X(1853)-X(11206) = 3*X(1853)-2*X(23332) = 8*X(5878)-5*X(6225) = 4*X(5878)+5*X(12324) = X(5878)+5*X(14216) = 3*X(5878)-10*X(18376) = X(5878)-10*X(18381) = X(5878)-4*X(18383) = 7*X(5878)-10*X(22802) = X(6225)+2*X(12324) = X(6225)+8*X(14216) = 3*X(6225)-16*X(18376) = X(6225)-16*X(18381) = 8*X(10192)-5*X(11206) = 3*X(10192)-5*X(23332) = 4*X(10249)-3*X(25406) = 3*X(11206)-8*X(23332)

X(32064) lies on these lines: {2,154}, {4,51}, {5,32063}, {6,7378}, {20,343}, {22,14927}, {25,23291}, {64,3146}, {66,69}, {107,459}, {125,6353}, {159,3619}, {161,6636}, {184,8889}, {193,15583}, {221,5261}, {376,11204}, {381,5644}, {382,12250}, {388,32065}, {394,5921}, {427,6776}, {428,26869}, {469,3332}, {497,11189}, {546,12315}, {631,9833}, {1154,11411}, {1352,3819}, {1368,14826}, {1498,3091}, {1585,5871}, {1586,5870}, {1593,18945}, {1619,1995}, {1892,10360}, {1992,11216}, {1993,8549}, {2192,5274}, {2390,3436}, {2550,11190}, {2777,15682}, {2781,3448}, {2883,3832}, {3068,11241}, {3069,11242}, {3088,6146}, {3089,16655}, {3090,6759}, {3147,23294}, {3357,3529}, {3410,16063}, {3434,21270}, {3522,6696}, {3524,23329}, {3525,10282}, {3535,14242}, {3536,14227}, {3541,18925}, {3542,16659}, {3543,15311}, {3545,23325}, {3546,12134}, {3556,5260}, {3566,8029}, {3575,18913}, {3580,7500}, {3618,5133}, {3620,9924}, {3627,13093}, {3628,14530}, {3681,3827}, {3818,6688}, {3839,23324}, {3917,9747}, {4232,26958}, {5032,23326}, {5056,16252}, {5059,5894}, {5064,11245}, {5159,8780}, {5225,6285}, {5229,7355}, {5284,18621}, {5422,19149}, {5480,7409}, {5891,6643}, {5892,7401}, {5895,17578}, {6145,15740}, {6193,23335}, {6619,11547}, {6622,26883}, {6756,26944}, {6815,20791}, {6995,13567}, {6997,11451}, {7394,7693}, {7408,17810}, {7492,15579}, {7493,23293}, {7494,21243}, {7496,15581}, {7667,10519}, {8972,17819}, {9143,15131}, {9306,16051}, {9544,15139}, {9920,21357}, {9934,15081}, {9968,15019}, {10182,15709}, {10193,15698}, {10250,14912}, {10299,25563}, {10303,17821}, {10304,23328}, {10535,10589}, {10588,26888}, {11180,31152}, {11225,20423}, {11243,11488}, {11244,11489}, {11392,18915}, {11393,18922}, {11432,16198}, {11548,12017}, {12174,23047}, {12278,30552}, {12279,31978}, {12359,31305}, {12964,31412}, {13364,18952}, {13941,17820}, {14683,23315}, {14855,18474}, {15246,15577}, {16419,18358}, {18435,18531}, {18533,18931}, {18917,31723}, {19174,19209}, {19420,32070}, {19421,32071}, {22967,31371}

X(32064) = reflection of X(i) in X(j) for these (i,j): (2, 1853), (20, 10606), (154, 23332), (193, 17813), (3543, 18405), (5596, 19153), (5656, 381), (9143, 15131), (9833, 11202), (9920, 21357), (10606, 6247), (11202, 20299), (11206, 2), (17813, 15583), (19153, 23300), (32063, 5)
X(32064) = isotomic conjugate of the isogonal conjugate of X(33582)
X(32064) = anticomplement of X(154)
X(32064) = anticomplementary conjugate of X(17037)
X(32064) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (154, 1853, 23332), (154, 23332, 2)


X(32065) = CENTROID OF THE ANTI-TANGENTIAL-MIDARC TRIANGLE

Barycentrics    a^2*(a+b-c)*(a-b+c)*((b^2+3*b*c+c^2)*a^4-2*(b^3+c^3)*(b+c)*a^2+(b^2-c^2)*(b-c)*(b^3+c^3)) : :
X(32065) = 4*X(1)-X(6285) = 2*X(1)+X(7355) = 2*X(3028)+X(19505) = X(6285)+2*X(7355) = X(7352)+2*X(32047)

X(32065) lies on these lines: {1,6000}, {12,23332}, {31,56}, {33,32062}, {34,51}, {35,11204}, {36,11202}, {55,10606}, {64,3303}, {65,278}, {354,5603}, {388,32064}, {497,12940}, {517,11214}, {960,6349}, {999,10535}, {1038,3819}, {1058,12950}, {1060,5891}, {1062,14855}, {1154,7352}, {1394,30493}, {1398,11402}, {1428,19153}, {1464,2352}, {1469,2393}, {1498,3304}, {1503,5434}, {1853,11237}, {1870,5890}, {2067,11241}, {2260,21767}, {2330,10249}, {2781,3028}, {2818,3576}, {2979,4296}, {3058,15311}, {3295,10076}, {3357,3746}, {3584,23329}, {3585,18376}, {3868,18633}, {4309,20427}, {4317,9833}, {4857,22802}, {4995,23328}, {5270,18381}, {5298,10192}, {5563,6759}, {5895,9670}, {6198,11455}, {6247,15888}, {6502,11242}, {6688,19372}, {6767,10060}, {7051,11243}, {10571,22341}, {11216,19369}, {11244,19373}, {18435,18447}, {18915,18950}, {19175,19209}, {19370,32070}, {19371,32071}, {24308,24806}

X(32065) = midpoint of X(7355) and X(11189)
X(32065) = reflection of X(i) in X(j) for these (i,j): (6285, 11189), (11189, 1)
X(32065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7355, 6285), (56, 221, 26888)


X(32066) = CENTROID OF THE APOLLONIUS TRIANGLE

Barycentrics
a^2*(3*(b+c)^2*a^8+4*(b+c)*(2*b^2+3*b*c+2*c^2)*a^7+(b^4+c^4+2*(5*b^2+11*b*c+5*c^2)*b*c)*a^6-10*(b^3+c^3)*(b+c)^2*a^5-(10*b^4+10*c^4+(17*b^2+6*b*c+17*c^2)*b*c)*b*c*a^4+2*(b^2+c^2)*(b+c)*(5*b^4-9*b^2*c^2+5*c^4)*a^3-(b^4+c^4+2*(5*b^2+8*b*c+5*c^2)*b*c)*(b^4+c^4)*a^2-2*(b+c)*(4*b^8+4*c^8+(7*b^6+7*c^6-(b^4+c^4+(5*b^2-2*b*c+5*c^2)*b*c)*b*c)*b*c)*a-(3*b^8+3*c^8+(2*b^6+2*c^6-(5*b^4+5*c^4+2*(b^2+c^2)*b*c)*b*c)*b*c)*(b+c)^2) : :

X(32066) lies on the line {970,5529}


X(32067) = CENTROID OF THE 4th CONWAY TRIANGLE

Barycentrics
3*b*c*a^7-(b+c)*(4*b^2+3*b*c+4*c^2)*a^6-2*(4*b^4+4*c^4+(10*b^2+7*b*c+10*c^2)*b*c)*a^5-6*(b+c)*(b^2+3*b*c+c^2)*b*c*a^4+(8*b^6+8*c^6+(11*b^4+11*c^4-2*(4*b^2+7*b*c+4*c^2)*b*c)*b*c)*a^3+(b+c)*(4*b^6+4*c^6+(9*b^2+22*b*c+9*c^2)*(b-c)^2*b*c)*a^2+6*(b+c)*(b^2-c^2)*(b^3-c^3)*b*c*a+2*(b^2-c^2)^2*(b+c)*b^2*c^2 : :

X(32067) lies on these lines: {1,11233}, {2,10439}, {3984,11679}


X(32068) = CENTROID OF THE 3rd HATZIPOLAKIS TRIANGLE

Barycentrics    2*a^6-4*(b^2+c^2)*a^4+(3*b^4-8*b^2*c^2+3*c^4)*a^2-(b^4-c^4)*(b^2-c^2) : :
X(32068) = 5*X(389)+X(12605) = 5*X(6688)-4*X(13361) = 2*X(9826)+X(19481) = 2*X(10095)+X(18128) = X(10116)+5*X(15026) = 2*X(11695)+X(13292) = X(12022)+3*X(16226) = X(12241)+2*X(15012) = X(13142)+2*X(17704) = 5*X(13403)+X(18565) = X(31985)+2*X(32050)

X(32068) lies on these lines: {2,5965}, {5,15130}, {6,30771}, {51,29012}, {182,7494}, {389,12605}, {511,10691}, {539,13363}, {542,5943}, {575,13567}, {1209,15047}, {1368,5097}, {1853,5476}, {1899,19130}, {3060,19924}, {3448,12834}, {3564,6688}, {5422,21243}, {5644,10516}, {5946,18400}, {5972,13366}, {6388,14153}, {6677,12007}, {6723,15516}, {9826,19481}, {10095,18128}, {10116,15026}, {10601,24206}, {11427,22234}, {11695,13292}, {12022,16226}, {12241,15012}, {13142,17704}, {13403,18565}, {14561,18950}, {15004,18911}, {21849,29317}, {31985,32050}

X(32068) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 11225}, {5943, 11245}
X(32068) = {X(5422), X(21243)}-harmonic conjugate of X(25555)


X(32069) = CENTROID OF THE LEMOINE TRIANGLE

Barycentrics    (4*a^4+11*(b^2+c^2)*a^2-2*(b^2+3*b*c+c^2)*(b^2-3*b*c+c^2))*(4*a^2+b^2+c^2) : :
X(32069) = 2*X(8145)+X(31969)

X(32069) lies on these lines: {2,10183}, {8029,12073}, {8145,31969}

X(32069) = reflection of X(2) in X(10183)


X(32070) = CENTROID OF THE LUCAS ANTIPODAL TANGENTIAL TRIANGLE

Barycentrics    (SB+SC)*((12*R^2+6*SA+SW)*S^2-2*SB*SC*SW+S*(4*S^2+2*(SA+2*SW)*SA)) : :
X(32070) = 2*X(18980)+X(19500)

X(32070) lies on these lines: {51,19410}, {154,8939}, {1151,19442}, {1154,18939}, {2393,12590}, {2781,19507}, {2979,19406}, {3819,19422}, {5890,19414}, {5891,19428}, {6000,18980}, {6688,19448}, {8681,11198}, {9723,32071}, {10238,17842}, {10606,13021}, {11189,19434}, {11190,19432}, {11202,19440}, {11204,19454}, {11216,19426}, {11241,19436}, {11242,19439}, {11243,19450}, {11244,19452}, {11402,19358}, {18376,18414}, {18435,18462}, {18926,18950}, {19134,19153}, {19186,19209}, {19370,32065}, {19416,32062}, {19418,32063}, {19420,32064}, {23298,23332}

X(32070) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19358, 19404, 19408), (19446, 21642, 19410)


X(32071) = CENTROID OF THE LUCAS(-1) ANTIPODAL TANGENTIAL TRIANGLE

Barycentrics    (SB+SC)*((12*R^2+6*SA+SW)*S^2-2*SB*SC*SW-S*(4*S^2+2*(SA+2*SW)*SA)) : :
X(32071) = 2*X(18981)+X(19501)

X(32071) lies on these lines: {51,19411}, {154,8943}, {1152,19443}, {1154,18940}, {2393,12591}, {2781,19508}, {2979,19407}, {3819,19423}, {5890,19415}, {5891,19429}, {6000,18981}, {6688,19449}, {8681,32077}, {9723,32070}, {10240,17839}, {10606,13022}, {11189,19435}, {11190,19433}, {11202,19441}, {11204,19455}, {11216,19427}, {11241,19438}, {11242,19437}, {11243,19451}, {11244,19453}, {11402,19359}, {18376,18415}, {18435,18463}, {18927,18950}, {19135,19153}, {19187,19209}, {19371,32065}, {19417,32062}, {19419,32063}, {19421,32064}, {23299,23332}

X(32071) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19359, 19405, 19409), (19447, 21643, 19411)


X(32072) = CENTROID OF THE LUCAS INNER TRIANGLE

Barycentrics    (SB+SC)*(260*(3*SA+2*SW)*S^2+260*SA*SW^2+S*(1351*S^2+901*SA^2-900*SB*SC+150*SW^2)) : :

X(32072) lies on the Parry circle and the line {356,8496}


X(32073) = CENTROID OF THE LUCAS(-1) INNER TRIANGLE

Barycentrics    (SB+SC)*(260*(3*SA+2*SW)*S^2+260*SA*SW^2-S*(1351*S^2+901*SA^2-900*SB*SC+150*SW^2)) : :

X(32073) lies on the Parry circle and these lines: {}


X(32074) = CENTROID OF THE LUCAS(-1) TANGENTS TRIANGLE

Barycentrics    a^2*(-2*(6*a^4-6*(b^2+c^2)*a^2-3*c^4-3*b^4-14*b^2*c^2)*S+10*(b^2+c^2)*a^4-5*(3*b^4+5*b^2*c^2+3*c^4)*a^2+5*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)) : :
X(32074) = 2*X(1152)+X(31975)

X(32074) lies on the Parry circle and these lines: {23,6454}, {352,6481}, {1152,8156}, {11171,11199}


X(32075) = CENTROID OF THE 3rd MIXTILINEAR TRIANGLE

Barycentrics
a*(12*a^6-20*(b+c)*a^5-(24*b^2-97*b*c+24*c^2)*a^4+2*(b+c)*(19*b^2-45*b*c+19*c^2)*a^3+2*(5*b^4+5*c^4-4*(13*b^2-24*b*c+13*c^2)*b*c)*a^2-6*(b^2-c^2)*(b-c)*(3*b^2-7*b*c+3*c^2)*a+(b^2-c^2)^2*(2*b-c)*(b-2*c)) : :
X(32075) = 2*X(3)+X(31979)

X(32075) lies on these lines: {3,31979}, {1420,3924}


X(32076) = CENTROID OF THE 4th MIXTILINEAR TRIANGLE

Barycentrics
a*(12*a^8-28*(b+c)*a^7-(20*b^2-73*b*c+20*c^2)*a^6+6*(b+c)*(17*b^2-22*b*c+17*c^2)*a^5-(70*b^4+70*c^4+(91*b^2-162*b*c+91*c^2)*b*c)*a^4-8*(b^2-c^2)*(b-c)*(4*b^2-13*b*c+4*c^2)*a^3+3*(16*b^4+16*c^4+9*(b-c)^2*b*c)*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^3*(5*b^2+14*b*c+5*c^2)*a-(b+2*c)*(2*b+c)*(b-c)^6) : :
X(32076) = 2*X(3)+X(31980)

X(32076) lies on these lines: {3,31980}, {165,5011}


X(32077) = CENTROID OF THE LUCAS(-1) CENTRAL TRIANGLE

Barycentrics    a^2*(3*a^6-17*(b^2+c^2)*a^4+(21*b^4+26*b^2*c^2+21*c^4)*a^2+(12*a^4-8*(b^2+c^2)*a^2-4*b^4-40*b^2*c^2-4*c^4)*S-(b^2+c^2)*(7*b^4-18*b^2*c^2+7*c^4)) : :
X(32077) = 2*X(3)+X(10673) = 2*X(8156)+X(31973)

X(32077) lies on these lines: {3,494}, {5409,18940}, {8156,31973}, {8373,8400}, {8681,32071}, {8780,10133}

X(32077) = {X(3), X(11950)}-harmonic conjugate of X(26293)


X(32078) = CENTROID OF THE CEVIAN TRIANGLE OF X(3)

Barycentrics    a^2*(-a^2+b^2+c^2)*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2)*((b^2+c^2)*a^2-(b^2-c^2)^2) : :
X(32078) = 4*X(3)-X(31388), 4*X(140)-X(14978), 4*X(10184)-3*X(11197), X(10184)-3*X(12012), X(11197)-4*X(12012)

X(32078) lies on these lines: {2,10184}, {3,54}, {4,14635}, {5,14129}, {51,216}, {110,31626}, {140,14978}, {154,157}, {184,10979}, {233,3078}, {852,6688}, {2972,3819}, {2974,6676}, {3131,10632}, {3132,10633}, {3135,23635}, {6000,23719}, {6638,11451}, {7494,17008}, {7499,30737}, {7503,23709}, {10003,30506}, {13366,22052}, {18376,18416}, {18435,18464}, {20975,23195}, {23332,26905}, {26870,32064}, {26874,30258}

X(32078) = reflection of X(i) in X(j) for these (i,j): (2, 12012), (4, 14635), (11197, 2)
X(32078) = anticomplement of X(10184)
X(32078) = isogonal conjugate of the polar conjugate of X(233)
X(32078) = X(14635)-of-anti-Euler triangle
X(32078) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 233}, {5, 22052}, {97, 3078}, {140, 216}, {217, 1232}, {343, 13366}, {577, 14978}
X(32078) = barycentric quotient X(i)/X(j) for these (i,j): (3, 31617), (140, 276), (184, 288), (217, 1173), (233, 264), (418, 31626)
X(32078) = trilinear product X(i)*X(j) for these lines: {i,j}: {48, 233}, {216, 17438}, {217, 20879}
X(32078) = trilinear quotient X(i)/X(j) for these (i,j): (48, 288), (63, 31617), (233, 92)
X(32078) = {X(216), X(26907)}-harmonic conjugate of X(418)


X(32079) = CENTROID OF THE SODDY TRIANGLE

Barycentrics    (a+b-c)*(a-b+c)*(7*a^4-4*(b+c)*a^3-14*(b-c)^2*a^2+12*(b^2-c^2)*(b-c)*a-(b^2+14*b*c+c^2)*(b-c)^2) : :
X(32079) = X(7)+2*X(15913) = X(7)-4*X(17113) = X(15913)+2*X(17113)

X(32079) lies on these lines: {7,1699}, {479,17728}, {658,9778}, {3160,10164}, {10004,10171}

X(32079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9533, 15511, 10136), (15913, 17113, 7)


X(32080) = CENTROID OF THE INNER-SODDY TRIANGLE

Barycentrics
(a+b-c)*(a-b+c)*(-2*(6*a^4-32*(b+c)*a^3+(43*b^2+24*b*c+43*c^2)*a^2-14*(b^2-c^2)*(b-c)*a-3*(b^2+4*b*c+c^2)*(b-c)^2)*S+5*(-a+b+c)*(2*a^5+(b+c)*a^4-2*(4*b^2+3*b*c+4*c^2)*a^3+4*(b^2-c^2)*(b-c)*a^2+2*(b^2+5*b*c+c^2)*(b-c)^2*a-(b^2-c^2)*(b-c)^3)) : :

X(32080) lies on these lines: {}


X(32081) = CENTROID OF THE OUTER-SODDY TRIANGLE

Barycentrics
(a+b-c)*(a-b+c)*(2*(6*a^4-32*(b+c)*a^3+(43*b^2+24*b*c+43*c^2)*a^2-14*(b^2-c^2)*(b-c)*a-3*(b^2+4*b*c+c^2)*(b-c)^2)*S+5*(-a+b+c)*(2*a^5+(b+c)*a^4-2*(4*b^2+3*b*c+4*c^2)*a^3+4*(b^2-c^2)*(b-c)*a^2+2*(b^2+5*b*c+c^2)*(b-c)^2*a-(b^2-c^2)*(b-c)^3)) : :

X(32081) lies on the line {175,16214}


X(32082) = CENTROID OF THE 2nd INNER-SODDY TRIANGLE

Barycentrics    a^3-6*S*a-3*(b+c)*a^2+(b-c)^2*a+(b^2-c^2)*(b-c) : :
X(32082) = 2*X(1)+X(31533) = X(482)+2*X(32057)

X(32082) lies on these lines: {1,4}, {55,31538}, {176,9778}, {482,11246}, {1371,3474}, {5393,17728}, {10164,13389}, {13388,31570}, {16213,31535}

X(32082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3475, 32083), (176, 16663, 10134)


X(32083) = CENTROID OF THE 2nd OUTER-SODDY TRIANGLE

Barycentrics    a^3+6*S*a-3*(b+c)*a^2+(b-c)^2*a+(b^2-c^2)*(b-c) : :
X(32083) = 2*X(1)+X(31532) = X(481)+2*X(32058)

X(32083) lies on these lines: {1,4}, {55,31539}, {175,9778}, {481,11246}, {1372,3474}, {5405,17728}, {10164,13388}, {13389,31569}, {16214,31534}

X(32083) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3475, 32082), (175, 16662, 10135)


X(32084) = CENTROID OF THE YIU TRIANGLE

Barycentrics
a^16-5*(b^2+c^2)*a^14+3*(3*b^4+4*b^2*c^2+3*c^4)*a^12-2*(b^2+c^2)*(3*b^4+b^2*c^2+3*c^4)*a^10+(2*b^4-3*b^2*c^2+2*c^4)*b^2*c^2*a^8-(b^2+c^2)*(b^8+c^8-(4*b^4-3*b^2*c^2+4*c^4)*b^2*c^2)*a^6+(b^2-c^2)^2*(5*b^8+5*c^8-2*(3*b^4+b^2*c^2+3*c^4)*b^2*c^2)*a^4-2*(b^4-c^4)*(b^2-c^2)^3*(2*b^4-3*b^2*c^2+2*c^4)*a^2+(b^4+c^4)*(b^2-c^2)^6 : :
X(32084) = 2*X(8154)+X(31991)

X(32084) lies on these lines: {5,30529}, {381,9143}, {1989,14643}, {5663,30685}, {8154,31991}


X(32085) = ISOGONAL CONJUGATE OF X(3917)

Barycentrics    (a^2 + b^2) (a^2 + b^2 - c^2) (a^2 + c^2) (a^2 - b^2 + c^2) : :
Barycentrics    (4 R^2 SB + 4 R^2 SC + SB SC + 4 R^2 SW - SB SW - SC SW - SW^2)S^2 + 2 SB SC SW^2 : :
Barycentrics    SB SC (SB + SW) (SC + SW) : : (Peter Moses, April 14, 2019)
Barycentrics    (tan A)/(b^2 + c^2) : : (Randy Hutson, June 7, 2019)
Trilinears    tan A csc(A + ω) : : (Randy Hutson, June 7, 2019)
Trilinears    1/(2 b c - a b cos B - a c cos C) : : (Randy Hutson, June 7, 2019)

See Kadir Altintas and Ercole Suppa, Hyacinthos 28982.

Let (PA) be the pedal circle of the A-vertex of the anticomplementary triangle (and of the A-vertex of the tangential triangle), and define (PB) and (PC) cyclically. Let RA be the radical center of (O), (PB), (PC) (where (O) is the circumcircle). Define RB and RC cyclically. The lines ARA, BRB, CRC concur in X(32085). (Randy Hutson, June 7, 2019)

Generalization: Let X = x : y : z and X' = 1/x : 1/y : 1/z (trilinears) be two isogonal conjugate points. Let (PA) be the pedal circle of the A-vertex of the anticevian triangle of X (and of the A-vertex of the anticevian triangle of X'), and define (PB) and (PC) cyclically. Let RA be the radical center of (O), (PB), (PC). Define RB and RC cyclically. The lines ARA, BRB, CRC concur in the polar conjugate of the isotomic conjugate of the cevapoint of X and X', with trilinears 1/(x (y^2 + z^2) (a^2 - b^2 - c^2)) : :. (Randy Hutson, June 7, 2019)

X(32085) lies on the circumhyperbola {{A,B,C,X(4),X(93)}} (with center X(136)) and on these lines {2,8801}, {4,83}, {20,26224}, {25,183}, {53,6531}, {82,225}, {95,237}, {107,9076}, {235,14860}, {242,4222}, {251,393}, {297,16890}, {317,20022}, {458,18092}, {648,1843}, {689,2374}, {827,1300}, {847,10594}, {1093,1598}, {1105,3575}, {1217,7487}, {1596,16264}, {1826,2201}, {2052,16277}, {3089,18855}, {4194,27067}, {4200,27005}, {4232,10130}, {6530,6756}, {7716,9308}, {8793,11547}, {9755,14486}, {10002,10548}, {10301,17983}, {12110,14575}, {12122,22078}, {12173,18848}, {14018,29568}, {15424,26863}, {16230,18010}, {16263,18494}, {18105,23290}

X(32085) = isogonal conjugate of X(3917)
X(32085) = isotomic conjugate of X(3933)
X(32085) = cevapoint of X(i) and X(j) for these (i,j): {2, 7754}, {4, 25}, {6620, 9755}, {18101, 18108}
X(32085) = crosssum of X(3) and X(22138)
X(32085) = trilinear pole of line {419, 2501}
X(32085) = polar conjugate of X(141)
X(32085) = isogonal conjugate of the anticomplement of X(5943)
X(32085) = isogonal conjugate of the complement of X(3060)
X(32085) = isotomic conjugate of the anticomplement of X(5305)
X(32085) = isotomic conjugate of the complement of X(7754)
X(32085) = polar conjugate of the isotomic of X(83)
X(32085) = polar conjugate of the isogonal of X(251)
X(32085) = X(i)-cross conjugate of X(j) for these (i,j): {251, 83}, {428, 4}, {2489, 648}, {5305, 2}, {14618, 107}, {17922, 1897}
X(32085) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3917}, {2, 4020}, {3, 38}, {31, 3933}, {39, 63}, {48, 141}, {69, 1964}, {71, 16696}, {72, 17187}, {75, 20775}, {77, 3688}, {78, 1401}, {163, 2525}, {184, 1930}, {212, 3665}, {228, 16887}, {255, 427}, {304, 3051}, {305, 1923}, {326, 1843}, {394, 17442}, {577, 20883}, {603, 3703}, {656, 1634}, {810, 4576}, {826, 4575}, {906, 16892}, {1331, 2530}, {1332, 21123}, {1437, 15523}, {1444, 21035}, {1459, 4553}, {1790, 3954}, {2084, 4563}, {2200, 16703}, {3005, 4592}, {3990, 17171}, {4055, 16747}, {4558, 8061}, {4568, 22383}, {6507, 27376}, {7116, 16720}, {8024, 9247}, {17206, 21814}, {18604, 21016}, {19215, 26347}, {22367, 32010}
X(32085) = barycentric product of X(i)*X(j) for these lines: {i,j}: {4,83}, {19,3112}, {25,308}, {27,18082}, {29,18097}, {82,92}, {107,4580}, {162,18070}, {251,264}, {275,17500}, {286,18098}, {393,1799}, {419,14970}, {689,2489}, {733,17984}, {827,14618}, {1093,28724}, {1176,2052}, {1897,10566}, {1973,18833}, {2373,21459}, {2501,4577}, {4599,24006}, {6330,21458}, {6331,18105}, {6335,18108}, {6531,20022}, {10547,18027}, {10548,14860}, {16277,17907}
X(32085) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {2,3933}, {4,141}, {6,3917}, {19,38}, {25,39}, {27,16887}, {28,16696}, {31,4020}, {32,20775}, {82,63}, {83,69}, {92,1930}, {112,1634}, {141,4175}, {158,20883}, {251,3}, {264,8024}, {278,3665}, {281,3703}, {286,16703}, {308,305}, {393,427}, {419,732}, {427,7794}, {428,6292}, {458,14994}, {468,7813}, {523,2525}, {607,3688}, {608,1401}, {648,4576}, {827,4558}, {1096,17442}, {1176,394}, {1194,22424}, {1474,17187}, {1783,4553}, {1799,3926}, {1824,3954}, {1826,15523}, {1843,8041}, {1897,4568}, {1973,1964}, {1974,3051}, {2052,1235}, {2207,1843}, {2333,21035}, {2489,3005}, {2501,826}, {3112,304}, {4577,4563}, {4580,3265}, {4599,4592}, {4628,1331}, {5007,22078}, {6524,27376}, {6531,20021}, {6591,2530}, {6995,8362}, {7009,16720}, {7649,16892}, {8743,3313}, {8744,9019}, {8747,17171}, {8793,23115}, {8882,16030}, {8948,26347}, {10311,14096}, {10547,577}, {10549,21243}, {10551,22416}, {10566,4025}, {14273,14424}, {14569,27371}, {14618,23285}, {14885,22138}, {16277,14376}, {16890,4121}, {17409,23208}, {17500,343}, {18070,14208}, {18082,306}, {18097,307}, {18098,72}, {18099,4019}, {18101,26932}, {18105,647}, {18108,905}, {19118,3787}, {20022,6393}, {21458,441}, {21459,858}, {22105,14417}, {28724,3964}
X(32085) = trilinear product of X(i)*X(j) for these lines: {i,j}: {4,82}, {19,83}, {19,83}, {25,3112}, {25,3112}, {27,18098}, {28,18082}, {28,18082}, {92,251}, {112,18070}, {158,1176}, {308,1973}, {308,1973}, {811,18105}, {827,24006}, {1096,1799}, {1096,1799}, {1172,18097}, {1172,18097}, {1783,10566}, {1897,18108}, {1974,18833}, {1974,18833}, {2190,17500}, {2190,17500}, {2216,10550}, {2489,4593}, {2489,4593}, {2501,4599}, {2501,4599}, {3405,6531}, {4580,24019}, {4628,17924}, {4628,17924}, {6520,28724}, {6520,28724}, {7012,18101}, {7012,18101}, {8767,21458}, {8767,21458}
X(32085) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {1,3917}, {6,4020}, {19,39}, {25,1964}, {28,17187}, {31,20775}, {33,3688}, {34,1401}, {75,3933}, {158,427}, {162,1634}, {273,3665}, {318,3703}, {393,17442}, {419,2236}, {428,17457}, {811,4576}, {827,4575}, {862,4093}, {1096,1843}, {1824,21035}, {1897,4553}, {1930,4175}, {1969,8024}, {1973,3051}, {2052,20883}, {2190,16030}, {2333,21814}, {2501,8061}, {4577,4592}, {6520,27376}, {6591,21123}, {16600,22077}, {17446,22424}, {17469,22078}, {20964,22367}
X(32085) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {4,17500,10550}, {1176,17500,83}

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Points V-Caph: X(32086)-X(32097)

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This preamble and centers X(32086)-X(32097) were contributed by Clark Kimberling and Peter Moses, April 19, 2019.

Suppose that P = p:q:r (barycentrics). The Point V-Caph of P is the point given by

qr + 2(p + q + r)p : rp + 2(p + q + r)q : pq + 2(p + q + r)r

The points in a Caph family of a point P all lie on the line PP*, where P* is the isotomic conjugate of P.


X(32086) = POINT V-CAPH OF X(7)

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

X(32086) lies on these lines: {2, 10481}, {7, 8}, {12, 24797}, {226, 8055}, {279, 3616}, {348, 5550}, {479, 17169}, {664, 5543}, {728, 4454}, {938, 1111}, {1119, 5342}, {1125, 21314}, {1323, 3622}, {1358, 3485}, {1698, 20121}, {2481, 5558}, {3160, 17079}, {3241, 9312}, {3598, 16823}, {3665, 5226}, {3673, 10580}, {4308, 7223}, {4323, 27818}, {4384, 10521}, {4452, 7274}, {4872, 10248}, {4888, 6738}, {6172, 32008}, {7196, 26103}, {7288, 24805}, {7960, 24774}, {9436, 9780}, {9812, 17170}, {10588, 24798}, {18230, 32024}, {20053, 25719}

X(32086) = {X(7),X(8)}-harmonic conjugate of X(32098)
X(32086) = {X(85),X(6604)}-harmonic conjugate of X(31994)


X(32087) = POINT V-CAPH OF X(8)

Barycentrics    -a^2 + b^2 + 6*b*c + c^2 : :
Trilinears    sec^2(A/2) + 2 csc^2(A/2) : :

X(32087) lies on these lines {1, 4460}, {2, 2321}, {6, 4371}, {7, 8}, {9, 4461}, {10, 3672}, {40, 28638}, {63, 9536}, {77, 4853}, {78, 7269}, {86, 3241}, {142, 4007}, {144, 3686}, {145, 10436}, {192, 5296}, {193, 17116}, {200, 7190}, {239, 5749}, {269, 4915}, {273, 7046}, {314, 7320}, {321, 18228}, {326, 4861}, {329, 14213}, {346, 4384}, {347, 4847}, {350, 26038}, {391, 3729}, {519, 3945}, {524, 7222}, {527, 4034}, {536, 966}, {594, 3763}, {938, 5295}, {962, 4647}, {1014, 12513}, {1058, 28644}, {1100, 4470}, {1213, 28635}, {1219, 7176}, {1266, 4678}, {1278, 17257}, {1442, 3872}, {1447, 7172}, {1654, 4740}, {1698, 4021}, {2345, 3589}, {3161, 17277}, {3187, 19825}, {3243, 4923}, {3475, 4046}, {3596, 4441}, {3616, 4360}, {3617, 4357}, {3620, 29615}, {3621, 3879}, {3622, 28626}, {3623, 4464}, {3626, 4346}, {3629, 4363}, {3632, 3664}, {3663, 3679}, {3687, 5226}, {3694, 24554}, {3706, 10580}, {3739, 5308}, {3883, 30332}, {3886, 8236}, {3932, 9780}, {3950, 16832}, {3966, 9812}, {3977, 5271}, {3986, 28313}, {4058, 17284}, {4060, 17296}, {4072, 31211}, {4328, 4882}, {4359, 34255}, {4373, 17274}, {4395, 17293}, {4398, 32025}, {4405, 7227}, {4416, 4454}, {4419, 4686}, {4445, 7263}, {4478, 7232}, {4546, 30181}, {4643, 4726}, {4644, 6144}, {4648, 4688}, {4651, 30946}, {4668, 4862}, {4677, 4888}, {4699, 17316}, {4739, 4851}, {4748, 17246}, {4764, 17256}, {4772, 6542}, {4816, 4896}, {4821, 6646}, {4859, 29594}, {4869, 17294}, {4873, 6666}, {4916, 17392}, {4971, 15668}, {4980, 5739}, {4986, 21290}, {5082, 21279}, {5435, 11679}, {5543, 20007}, {5550, 28653}, {5750, 17014}, {7319, 30479}, {11024, 28612}, {14552, 28610}, {16816, 26685}, {16833, 17355}, {17143, 30022}, {17163, 18697}, {17184, 19826}, {17233, 29627}, {17322, 19877}, {17331, 20073}, {17353, 24599}, {17377, 20053}, {17394, 20057}, {20054, 30712}, {20055, 26806}, {26626, 28604}, {27147, 29583}, {27304, 27544}

X(32087) = isotomic conjugate of X(5558)
X(32087) = anticomplement of X(3247)
X(32087) = {X(7),X(8)}-harmonic conjugate of X(32099)
X(32087) = {X(69),X(75)}-harmonic conjugate of X(31995)


X(32088) = POINT V-CAPH OF X(9)

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

X(32088) lies on these lines: {2, 32007}, {8, 4702}, {9, 85}, {44, 27253}, {220, 31269}, {6173, 32015}, {6604, 18230}, {17336, 20880}, {27065, 30854}

X(32088) = {X(9),X(85)}-harmonic conjugate of X(32100)


X(32089) = POINT V-CAPH OF X(10)

Barycentrics    a^2 + 5*a*b + 4*b^2 + 5*a*c + 9*b*c + 4*c^2 : :

X(32089) lies on these lines: {2, 4399}, {10, 86}, {75, 3992}, {594, 31248}, {1698, 4360}, {3632, 30598}, {3634, 5564}, {3828, 17322}, {3932, 9780}, {4389, 5936}, {4460, 19877}, {4464, 31253}, {6535, 30594}, {17271, 21296}, {17279, 29576}, {17285, 24603}, {17311, 29593}, {17332, 28604}, {17359, 31311}, {17380, 28635}, {17384, 28633}

X(32089) = {X(10),X(86)}-harmonic conjugate of X(32101)


X(32090) = POINT V-CAPH OF X(37)

Barycentrics    4*a^2*b^2 + 9*a^2*b*c + 5*a*b^2*c + 4*a^2*c^2 + 5*a*b*c^2 + b^2*c^2 : :

X(32090) lies on these lines: {1, 4753}, {37, 274}, {4687, 17143}, {4755, 16819}, {17264, 25512}, {18145, 27255}, {21830, 27268}

X(32090) = {X(37),X(274)}-harmonic conjugate of X(32102)


X(32091) = POINT V-CAPH OF X(44)

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

X(32091) lies on these lines: {44, 20568}


X(32092) = POINT V-CAPH OF X(75)

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

X(32092) lies on these lines: {1, 75}, {2, 3760}, {7, 9534}, {10, 3761}, {19, 16747}, {35, 16992}, {63, 169}, {76, 1698}, {85, 3339}, {192, 31996}, {194, 4699}, {213, 4363}, {239, 20893}, {310, 17210}, {321, 16831}, {330, 16829}, {350, 3624}, {609, 16915}, {980, 31993}, {1089, 30758}, {1107, 4688}, {1111, 28611}, {1125, 4441}, {1218, 2663}, {1268, 30596}, {1449, 20174}, {1909, 3679}, {1975, 5251}, {2176, 17118}, {3208, 29383}, {3294, 3729}, {3633, 25303}, {3634, 18135}, {3665, 7243}, {3673, 16832}, {3739, 5283}, {3925, 3933}, {3926, 19854}, {4000, 16818}, {4063, 23807}, {4253, 24592}, {4352, 19853}, {4358, 25585}, {4361, 20963}, {4410, 17251}, {4664, 32009}, {4668, 24524}, {4671, 29578}, {4687, 32026}, {4691, 25278}, {4726, 25130}, {4739, 16975}, {4980, 29597}, {5088, 16824}, {5271, 18206}, {5280, 11321}, {5299, 20172}, {6376, 19875}, {6381, 9780}, {6390, 24953}, {6533, 7264}, {7031, 16998}, {7176, 16821}, {11679, 21422}, {16502, 20181}, {16705, 19858}, {16748, 16887}, {16815, 30563}, {16826, 28605}, {16827, 17116}, {16830, 31130}, {16834, 21432}, {17135, 17169}, {17211, 17889}, {17303, 25499}, {17308, 20913}, {17321, 25512}, {17753, 20245}, {17754, 29433}, {17759, 27255}, {18044, 29757}, {18145, 19876}, {20911, 28612}, {21384, 29773}, {24199, 29960}, {25457, 25661}, {26035, 30107}, {26959, 27318}, {30035, 30038}

X(32092) = {X(1),X(75)}-harmonic conjugate of X(32104)


X(32093) = POINT V-CAPH OF X(145)

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

X(32093) lies on these lines: {2, 1743}, {7, 145}, {8, 4888}, {69, 3617}, {75, 31145}, {141, 4747}, {144, 17300}, {193, 24599}, {320, 1279}, {346, 17311}, {391, 4675}, {464, 9965}, {1122, 3873}, {3241, 4862}, {3244, 4902}, {3621, 4896}, {3623, 3663}, {3631, 4470}, {3672, 17378}, {3870, 7271}, {4454, 4851}, {4488, 29573}, {4644, 4869}, {4648, 17332}, {4678, 25590}, {4699, 11160}, {5059, 10442}, {5232, 17361}, {6646, 29624}, {7222, 17374}, {17014, 20090}, {17151, 20014}, {17316, 20059}, {17375, 29616}, {17778, 21454}, {20043, 26842}, {20080, 26806}, {29583, 31300}


X(32094) = POINT V-CAPH OF X(190)

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

X(32094) lies on these lines: {10, 24428}, {100, 2748}, {190, 514}, {519, 1757}, {644, 4568}, {660, 6005}, {1018, 4063}, {3218, 3912}, {3570, 4169}, {3693, 9321}, {3732, 30720}, {4422, 6547}, {4440, 31647}, {4553, 6004}, {4562, 32042}, {4760, 21821}, {6632, 10196}, {17262, 24281}, {21272, 30732}, {23891, 30731}, {24196, 24419}


X(32095) = POINT V-CAPH OF X(192)

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

X(32095) lies on these lines: {1, 87}, {2, 17144}, {37, 20168}, {42, 14823}, {75, 25130}, {220, 20180}, {239, 7308}, {274, 4740}, {385, 3303}, {519, 27269}, {551, 27318}, {1107, 4704}, {1278, 31997}, {1500, 7786}, {1655, 3241}, {2176, 4393}, {3058, 7823}, {3210, 29570}, {3304, 7783}, {3622, 17759}, {3623, 21226}, {3746, 7793}, {3913, 16999}, {3934, 30998}, {4309, 14712}, {4360, 16969}, {4479, 24656}, {4664, 14897}, {4699, 17143}, {7762, 15170}, {7787, 16785}, {9263, 20057}, {9331, 26959}, {16777, 20170}, {16826, 17490}, {17024, 31088}, {17242, 30038}, {17244, 20257}, {17383, 27248}, {19738, 31036}, {20081, 25303}, {21830, 27268}, {24620, 29595}, {24621, 29580}, {25107, 30963}


X(32096) = POINT V-CAPH OF X(239)

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

X(32096) lies on these lines: {2, 3722}, {190, 4686}, {239, 335}, {1086, 3629}, {1100, 27191}, {1279, 29607}, {4366, 4384}, {4402, 4440}, {4437, 29617}, {4974, 24715}, {6650, 28558}, {6653, 29590}, {16593, 29628}, {16816, 17755}, {16833, 17738}, {17367, 26582}, {17380, 25357}


X(32097) = POINT V-CAPH OF X(320)

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

X(32097) lies on these lines: {7, 21290}, {69, 1111}, {80, 320}, {668, 7321}, {4555, 26726}, {4986, 31995}, {17274, 24222}

leftri

Points VI-Caph: X(32098)-X(32109)

rightri

This preamble and centers X(32098)-X(32109) were contributed by Clark Kimberling and Peter Moses, April 19, 2019.

Suppose that P = p:q:r (barycentrics). The Point VI-Caph of P is the point given by

qr - 2(p + q + r)p : rp - 2(p + q + r)q : pq - 2(p + q + r)r

The points in a Caph family of a point P all lie on the line PP*, where P* is the isotomic conjugate of P.


X(32098) = POINT VI-CAPH OF X(7)

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

X(32098) lies on these lines: {7, 8}, {57, 29627}, {145, 10481}, {279, 3241}, {348, 5543}, {728, 4869}, {938, 7264}, {1323, 3623}, {1565, 5734}, {2099, 24797}, {2481, 5556}, {3160, 20057}, {3244, 21314}, {3616, 9436}, {3633, 20121}, {3665, 4323}, {3912, 21454}, {4373, 20008}, {4862, 6738}, {9312, 20050}, {9812, 17753}, {9965, 25935}, {17079, 25718}, {20059, 30625}

X(32098) = {X(7),X(8)}-harmonic conjugate of X(32086)


X(32099) = POINT VI-CAPH OF X(8)

Barycentrics    3*a^2 - 3*b^2 - 2*b*c - 3*c^2 : :
Barycentrics    b c + 3 SA : :
Trilinears    sec^2(A/2) - 2 csc^2(A/2) : :

X(32099) lies on these lines: {1, 5232}, {2, 1449}, {6, 29611}, {7, 8}, {9, 29616}, {10, 3945}, {77, 200}, {78, 1442}, {86, 9780}, {141, 5222}, {142, 4034}, {144, 2321}, {145, 4357}, {150, 4738}, {189, 26872}, {193, 3661}, {239, 3620}, {269, 4882}, {279, 6743}, {306, 5273}, {307, 3160}, {314, 7319}, {318, 32001}, {326, 4420}, {329, 2893}, {344, 17295}, {346, 4416}, {347, 6737}, {355, 31780}, {391, 3912}, {519, 3672}, {524, 2345}, {527, 4007}, {594, 4644}, {599, 4000}, {651, 3713}, {894, 20080}, {914, 5744}, {938, 5814}, {966, 4690}, {1014, 1376}, {1086, 4371}, {1264, 5423}, {1266, 20052}, {1654, 5296}, {1743, 29594}, {1943, 18624}, {1992, 17289}, {3161, 17233}, {3187, 19823}, {3241, 17271}, {3421, 21279}, {3474, 4046}, {3578, 17776}, {3596, 25278}, {3616, 4966}, {3617, 5936}, {3618, 17228}, {3619, 3759}, {3621, 3875}, {3624, 4909}, {3625, 4346}, {3626, 25590}, {3629, 17293}, {3630, 4363}, {3631, 4361}, {3632, 3663}, {3633, 4021}, {3662, 4402}, {3664, 3679}, {3687, 5435}, {3694, 24635}, {3705, 15589}, {3706, 9812}, {3751, 5772}, {3758, 11008}, {3763, 4969}, {3872, 7269}, {3883, 8236}, {3886, 30332}, {3949, 18161}, {3964, 7279}, {3966, 10580}, {3974, 4872}, {3986, 29602}, {4001, 28610}, {4005, 10978}, {4042, 14828}, {4060, 4659}, {4328, 4915}, {4344, 5847}, {4358, 5739}, {4360, 20050}, {4384, 4869}, {4389, 20053}, {4399, 7232}, {4419, 4718}, {4431, 4454}, {4452, 17274}, {4464, 20014}, {4488, 17347}, {4643, 4681}, {4648, 17275}, {4657, 4725}, {4665, 7222}, {4668, 4888}, {4677, 4862}, {4678, 4967}, {4704, 6542}, {4720, 8822}, {4748, 4916}, {4788, 6646}, {4816, 4887}, {4853, 7190}, {4856, 29598}, {4886, 18141}, {4971, 17255}, {5044, 28644}, {5081, 32000}, {5226, 11679}, {5227, 7291}, {5257, 29624}, {5550, 17394}, {5815, 21270}, {5932, 31527}, {6144, 17369}, {6381, 10449}, {7046, 7282}, {7172, 7179}, {7320, 30479}, {11160, 17364}, {14555, 30829}, {15533, 17365}, {16667, 29604}, {16706, 21356}, {16786, 17349}, {16833, 21255}, {17014, 17306}, {17135, 30946}, {17184, 19824}, {17230, 26685}, {17236, 20016}, {17238, 26626}, {17248, 29585}, {17250, 20057}, {17251, 17390}, {17252, 17389}, {17253, 17388}, {17256, 17386}, {17260, 29583}, {17277, 29627}, {17282, 24599}, {17283, 31189}, {17288, 29617}, {17309, 17332}, {17310, 17331}, {17311, 17330}, {17315, 17328}, {17376, 28634}, {17378, 32025}, {18623, 26942}, {20090, 29593}, {26038, 30962}, {26041, 27097}, {28780, 28795}

X(32099) = isotomic conjugate of X(5556)
X(32099) = anticomplement of X(1449)
X(32099) = {X(7),X(8)}-harmonic conjugate of X(32087)
X(32099) = {X(69),X(75)}-harmonic conjugate of X(21296)
X(32099) = {X(17287),X(17363)}-harmonic conjugate of X(2)


X(32100) = POINT VI-CAPH OF X(9)

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

X(32100) lies on these lines: {8, 15481}, {9, 85}, {144, 32007}, {220, 31169}, {3219, 30854}, {6172, 6604}, {10025, 31269}, {16814, 27253}, {17335, 20880}

X(32100) = {X(9),X(85)}-harmonic conjugate of X(32088)


X(32101) = POINT VI-CAPH OF X(10)

Barycentrics    a^2 - 3*a*b - 4*b^2 - 3*a*c - 7*b*c - 4*c^2 : :

X(32101) lies on these lines: {2, 4478}, {7, 11237}, {10, 86}, {594, 31144}, {1654, 7227}, {1698, 30598}, {3617, 3672}, {3626, 4464}, {3679, 4360}, {4021, 4691}, {4357, 4745}, {4668, 17393}, {4887, 4967}, {4888, 17270}, {5278, 30590}, {6542, 31248}, {6666, 17285}, {7277, 28604}, {9780, 17377}, {17228, 20195}, {17239, 17291}, {17268, 31311}, {17275, 17368}, {17277, 17293}, {17287, 28633}, {17295, 29576}, {17305, 28634}, {17307, 17366}, {17394, 19875}, {26842, 27790}

X(32101) = {X(10),X(86)}-harmonic conjugate of X(32089)


X(32102) = POINT VI-CAPH OF X(37)

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

X(32101) lies on these lines: {1, 17336}, {37, 274}, {4664, 17143}, {4681, 16819}, {4704, 5283}

X(32102) = {X(37),X(274)}-harmonic conjugate of X(32090)


X(32103) = POINT VI-CAPH OF X(44)

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

X(32103) lies on these lines: {44, 20568}


X(32104) = POINT VI-CAPH OF X(75)

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

X(32194) lies on these lines: {1, 75}, {8, 3761}, {9, 20174}, {10, 3760}, {76, 3679}, {85, 18421}, {192, 16819}, {194, 4740}, {213, 4361}, {239, 26223}, {312, 16832}, {321, 3294}, {350, 1698}, {536, 5283}, {668, 4668}, {1107, 4686}, {1269, 17270}, {1278, 25264}, {1909, 3632}, {1975, 5258}, {2176, 17119}, {2321, 17050}, {2345, 16818}, {2481, 4385}, {3501, 29433}, {3617, 6381}, {3644, 32026}, {3672, 19853}, {3729, 16552}, {3730, 24592}, {3746, 16992}, {3770, 4034}, {4050, 29699}, {4359, 16831}, {4363, 20963}, {4431, 29960}, {4461, 27304}, {4479, 18140}, {4494, 4665}, {4659, 21384}, {4669, 25278}, {4671, 16815}, {4677, 24524}, {4699, 31996}, {4714, 7264}, {4717, 24331}, {4726, 16975}, {4732, 21615}, {4751, 32009}, {4980, 16834}, {5280, 20172}, {7243, 30617}, {7773, 31159}, {7776, 31140}, {9331, 27255}, {11321, 16785}, {11520, 20880}, {11679, 20367}, {16549, 17026}, {16823, 31130}, {16828, 17321}, {17030, 17759}, {17294, 20913}, {17301, 25499}, {17320, 19871}, {17754, 29742}, {17866, 20895}, {21070, 29966}, {24170, 30942}, {24190, 31027}, {24790, 27248}, {26234, 28612}

X(32104) = {X(1),X(75)}-harmonic conjugate of X(32092)


X(32105) = POINT VI-CAPH OF X(145)

Barycentrics    -5*a^2 - 6*a*b - b^2 - 6*a*c + 14*b*c - c^2 : :

X(32105) lies on these lines: {2, 3950}, {7, 145}, {69, 20054}, {75, 3622}, {192, 24599}, {319, 31145}, {346, 17366}, {1278, 17014}, {3617, 3672}, {3621, 3663}, {3623, 30712}, {4000, 30833}, {4346, 17361}, {4402, 6666}, {4454, 4852}, {4461, 17368}, {4862, 20050}, {9797, 21314}, {17272, 20052}, {17484, 20043}, {20014, 21296}


X(32106) = POINT VI-CAPH OF X(190)

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

X(32106) lies on these lines: {2, 31647}, {190, 514}, {545, 6547}, {3912, 17484}, {4473, 6549}, {17496, 25267}


X(32107) = POINT VI-CAPH OF X(192)

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

X(32107) lies on these lines: {1, 87}, {39, 30998}, {239, 3929}, {274, 27268}, {385, 5217}, {498, 19570}, {1107, 1278}, {1479, 13571}, {1655, 9780}, {1909, 20105}, {2176, 25269}, {2276, 20081}, {3177, 11684}, {3210, 5278}, {3617, 17759}, {3621, 21226}, {3634, 27269}, {3644, 17448}, {4352, 17280}, {4699, 5283}, {4704, 31997}, {4788, 17144}, {5204, 7783}, {5225, 7774}, {5333, 29595}, {6284, 7837}, {7173, 7777}, {7779, 9598}, {7905, 9664}, {16666, 20168}, {16815, 17490}, {17129, 31448}, {17232, 24214}, {17242, 24215}, {17495, 30563}, {19862, 27318}, {20018, 20072}, {20036, 20073}, {20691, 21219}, {24621, 29578}


X(32108) = POINT VI-CAPH OF X(239)

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

X(32108) lies on these lines: {190, 4718}, {239, 335}, {1086, 3630}, {3759, 9055}, {4366, 16468}, {4393, 17755}, {4422, 17393}, {4437, 17367}, {4864, 17266}, {12630, 20533}, {15570, 29575}, {16593, 17389}, {17287, 27191}, {24715, 28498}, {26582, 29617}


X(32109) = POINT VI-CAPH OF X(320)

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

X(32109) lies on these lines: {69, 4738}, {80, 320}, {150, 21286}

leftri

Points on Walsmith rectangular hyperbola: X(32110)-X(32114) and X(32119)-X(32127)

rightri

Centers X(32110)-X(32114) and X(32119)-X(32127) were contributed by Peter Moses, April 20, 2019.

The centers X(32110)-X(32114) and X(32119)-X(32127) lie on the hyperbola denoted by H1 at K1091 (Walsmith Focal Cubic), here named the Walsmith rectangular hyperbola.

The center of the Walsmith rectangular hyperbola is X(468), and the hyperbola passes through the vertices of the Walsmith triangles and X(i) for these i: 6, 74, 110, 113, 125, 1495, 2574, 2575, 2931, 3569, 3580, 5000, 5001, 7699, 7703, 10117, 11472, 15904, 32110, 32111, 32112, 32113, 32114, 32119, 32120, 32121, 32122, 32123, 32124, 32125, 32126, 32127, 32226, 32263, 32282, 32316. The hyperbola also passes through the bicentric pair PU(4).

Peter Moses (March 31, 2020) showed that an equation for the Walsmith rectangular hyperbola is

f(a,b,c,x,y,z) + f(b,c,a,y,z,x) + f(c,a,b,z,x,y) = 0, where

f(a,b,c,x,y,z) = b^2*c^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)*x^2 + a^2*(b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^2 - b^2 + c^2)*y*z.


X(32110) = MIDPOINT OF X(23) AND X(74)

Barycentrics    a^2*(2*a^8 - 3*a^6*b^2 - 3*a^4*b^4 + 7*a^2*b^6 - 3*b^8 - 3*a^6*c^2 + 6*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 2*b^6*c^2 - 3*a^4*c^4 - 5*a^2*b^2*c^4 + 2*b^4*c^4 + 7*a^2*c^6 + 2*b^2*c^6 - 3*c^8) : :
X(32110) = {X[110] - 3 X[186],X[323] - 3 X[15035],3 X[2070] + X[10620],3 X[2072] - 4 X[6723],X[3292] - 4 X[18571],X[3830] - 3 X[15362],X[7464] - 3 X[15055],X[7574] - 3 X[15061],X[10296] - 3 X[14644],2 X[10297] - 3 X[23515],3 X[10540] - X[12308],X[10990] + 2 X[16619],4 X[11801] - 3 X[13851],2 X[12041] - 3 X[21663],5 X[15040] - 3 X[22115],5 X[15051] - X[23061],3 X[15055] + X[15107],3 X[16111] - 2 X[20725]

X(32110) lies on the Walsmith rectangular hyperbola and these lines: {2, 4549}, {3, 6}, {4, 7703}, {5, 1531}, {22, 8717}, {23, 74}, {24, 7689}, {25, 11472}, {26, 1204}, {30, 125}, {51, 18570}, {64, 9714}, {110, 186}, {113, 468}, {155, 15750}, {184, 18324}, {185, 1658}, {323, 15035}, {376, 15360}, {382, 23325}, {512, 19902}, {517, 10149}, {541, 7426}, {549, 13857}, {550, 18555}, {858, 6699}, {1154, 14708}, {1209, 31833}, {1216, 22467}, {1495, 5663}, {1503, 8262}, {1511, 3292}, {1533, 10990}, {1594, 20191}, {1995, 4550}, {2070, 6000}, {2071, 11692}, {2072, 6723}, {2393, 11579}, {2777, 11799}, {2931, 21284}, {3066, 9818}, {3146, 11468}, {3357, 7517}, {3431, 11422}, {3515, 10539}, {3518, 11440}, {3520, 5446}, {3530, 8254}, {3564, 30714}, {3569, 14696}, {3580, 10295}, {3830, 15362}, {4846, 7493}, {5447, 7691}, {5448, 10018}, {5449, 6240}, {5462, 14118}, {5642, 18579}, {5651, 5891}, {5889, 12038}, {5890, 10298}, {5892, 15053}, {6102, 13367}, {6696, 7553}, {6756, 18488}, {7464, 15055}, {7514, 22112}, {7542, 13568}, {7556, 15072}, {7574, 15061}, {7687, 18323}, {9909, 11820}, {10110, 14130}, {10226, 10263}, {10272, 22249}, {10296, 14644}, {10297, 23515}, {10540, 12308}, {10605, 14070}, {10606, 18534}, {10619, 12899}, {11202, 18445}, {11572, 13561}, {11645, 20126}, {12088, 14641}, {12106, 15030}, {12107, 13491}, {12112, 15054}, {12307, 15606}, {12367, 16010}, {13474, 18378}, {14002, 16261}, {14927, 18931}, {15040, 22115}, {15051, 23061}, {15139, 17835}, {15712, 31802}, {18325, 20127}, {18474, 18533}, {18559, 23293}, {18572, 20304}, {19506, 31726}, {20300, 23328}, {20417, 29012}, {23329, 31723}

X(32110) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 3581}, {23, 74}, {376, 15360}, {1533, 10990}, {3580, 10295}, {7464, 15107}, {12112, 15054}, {12367, 16010}, {15139, 17835}, {18325, 20127}
X(32110) = reflection of X(i) in X(j) for these lines: {i,j}: {113, 468}, {858, 6699}, {1495, 7575}, {1511, 18571}, {1531, 5}, {1533, 16619}, {3292, 1511}, {5642, 18579}, {10272, 22249}, {13857, 549}, {18323, 7687}, {18572, 20304}, {25641, 11657}
X(32110) = reflection of X(25641) in the Orthic axis
X(32110) = circumcircle-inverse of X(14687)
X(32110) = Brocard-circle-inverse of X(39242)
X(32110) = antipode of X(113) in Walsmith rectangular hyperbola
X(32110) = orthocenter of X(6)X(1495)X(3569)
X(32110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 568, 11430}, {3, 9786, 569}, {3, 11438, 9730}, {24, 7689, 12162}, {26, 1204, 10575}, {182, 1350, 9967}, {1379, 1380, 14687}, {1620, 17834, 3}, {3515, 12163, 10539}, {5889, 21844, 12038}, {5890, 10298, 18475}, {6102, 15331, 13367}, {13349, 13350, 22463}, {15055, 15107, 7464}


X(32111) = MIDPOINT OF X(23) AND X(146)

Barycentrics    3*a^8*b^2 - 8*a^6*b^4 + 6*a^4*b^6 - b^10 + 3*a^8*c^2 + 10*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 10*a^2*b^6*c^2 + 3*b^8*c^2 - 8*a^6*c^4 - 6*a^4*b^2*c^4 + 20*a^2*b^4*c^4 - 2*b^6*c^4 + 6*a^4*c^6 - 10*a^2*b^2*c^6 - 2*b^4*c^6 + 3*b^2*c^8 - c^10 : :
X(32111) = 2 X[125] - 3 X[403],5 X[125] - 3 X[13399],3 X[186] - X[12244],3 X[186] - 4 X[15448],3 X[376] - 2 X[20725],5 X[403] - 2 X[13399],2 X[1514] + X[12112],3 X[10540] - X[12121],X[10721] + 3 X[14157],X[12244] - 4 X[15448],X[12902] - 3 X[31726],X[13619] - 4 X[15152],3 X[14643] - 2 X[15122],3 X[14912] - 4 X[15471]

X(32111) lies on the Walsmith rectangular hyperbola and these lines: {2, 11472}, {4, 6}, {5, 7703}, {22, 4549}, {23, 146}, {24, 5878}, {30, 110}, {54, 13488}, {64, 7505}, {74, 468}, {113, 858}, {125, 403}, {186, 10117}, {235, 6241}, {376, 20725}, {381, 18911}, {399, 18325}, {427, 7699}, {511, 1533}, {541, 7426}, {550, 26882}, {1495, 2777}, {1499, 1513}, {1531, 29012}, {1539, 18323}, {1555, 2794}, {1594, 11381}, {1596, 5890}, {1614, 1885}, {1906, 3567}, {1995, 4846}, {3146, 22660}, {3147, 12250}, {3292, 6053}, {3357, 10018}, {3426, 5094}, {3520, 16252}, {3521, 31830}, {3542, 6225}, {3564, 14094}, {3580, 5663}, {3581, 16619}, {3628, 13623}, {4550, 7495}, {5133, 16194}, {5894, 21844}, {6001, 15904}, {6240, 22802}, {6247, 16868}, {6696, 14940}, {6759, 18560}, {6823, 15058}, {7464, 11064}, {7542, 15062}, {8718, 12362}, {9820, 12086}, {9919, 21284}, {10151, 25739}, {10257, 13445}, {10294, 13202}, {10564, 16534}, {10733, 12419}, {11440, 13383}, {11457, 12315}, {11585, 12279}, {11744, 15139}, {11745, 26863}, {11820, 31152}, {12174, 18912}, {12902, 31726}, {13367, 14862}, {13474, 15559}, {13596, 23292}, {13619, 15152}, {14389, 31861}, {14643, 15122}, {14677, 18571}, {15030, 24206}, {15305, 15760}, {15531, 21850}, {15761, 18439}, {18388, 32062}

X(32111) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 12112}, {23, 146}, {399, 18325}, {1533, 15063}, {11744, 15139}
X(32111) = reflection of X(i) in X(j) for these lines: {i,j}: {4, 1514}, {74, 468}, {858, 113}, {3292, 6053}, {3580, 11799}, {3581, 16619}, {7464, 11064}, {10295, 1495}, {10564, 16534}, {13445, 10257}, {14677, 18571}, {18323, 1539}, {25739, 10151}
X(32111) = reflection of X(477) in the Orthic axis
X(32111) = crossdifference of every pair of points on line {520, 5651}
X(32111) = antipode of X(74) in Walsmith rectangular hyperbola
X(32111) = orthocenter of X(6)X(3569)X(3580)
X(32111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5656, 11456}, {4, 11456, 12022}, {4, 15032, 16657}, {235, 6241, 26879}, {1515, 6530, 4}, {5893, 16655, 4}, {22802, 26883, 6240}


X(32112) = CROSSDIFFERENCE OF X(30) AND X(2420)

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

The trilinear polar of X(32112) passes through X(3569) and the complement of X(877). (Randy Hutson, June 7, 2019)

X(32112) lies on the curve Q101, the Walsmith rectangular hyperbola, and these lines: {6, 647}, {74, 512}, {110, 250}, {113, 525}, {125, 523}, {232, 3569}, {262, 2394}, {264, 850}, {325, 6333}, {511, 684}, {526, 1495}, {924, 3447}, {2931, 8673}, {3425, 8723}, {3580, 9033}, {6530, 16230}, {8552, 10564}, {9139, 9213}, {11472, 30209}

X(32112) = reflection of X(10564) in X(8552)
X(32112) = reflection of X(32119) in X(468)
X(32112) = X(i)-isoconjugate of X(j) for these (i,j): {248, 24001}, {293, 4240}, {336, 23347}, {1821, 2420}, {1910, 2407}, {2173, 2966}, {2715, 14206}
X(32112) = crossdifference of every pair of points on line {30, 2420}
X(32112) = intersection of Simson line of X(74) and trilinear polar of X(74)
X(32112) = antipode of X(32119) in Walsmith rectangular hyperbola
X(32112) = orthocenter of X(74)X(110)X(1495)
X(32112) = orthocenter of X(74)X(125)X(3580)
X(32112) = orthocenter of X(113)X(125)X(1495)
X(32112) = barycentric product X(i)*X(j) for these lines: {i,j}: {74, 2799}, {297, 14380}, {325, 2433}, {511, 2394}, {684, 16080}, {1494, 3569}, {2421, 12079}, {6333, 8749}, {14919, 16230}
X(32112) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {74, 2966}, {232, 4240}, {237, 2420}, {240, 24001}, {511, 2407}, {684, 11064}, {2211, 23347}, {2394, 290}, {2433, 98}, {2491, 1495}, {2799, 3260}, {3569, 30}, {8430, 9214}, {8749, 685}, {14380, 287}, {14919, 17932}, {16080, 22456}, {17994, 1990}, {18808, 16081}


X(32113) = MIDPOINT OF X(23) AND X(69)

Barycentrics    3*a^6*b^2 - a^4*b^4 - 3*a^2*b^6 + b^8 + 3*a^6*c^2 - 4*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - a^4*c^4 + 3*a^2*b^2*c^4 - 2*b^4*c^4 - 3*a^2*c^6 + c^8 : :
X(32113) = 3 X[186] - X[6776],3 X[403] - 2 X[5480],3 X[2070] + X[11898],3 X[2072] - 4 X[24206],7 X[3619] - 5 X[30745],5 X[3620] - X[5189],5 X[3763] - 4 X[5159],X[7464] - 3 X[10519],2 X[10297] - 3 X[10516],X[10989] - 3 X[21356],4 X[15448] - 3 X[18374]}

X(32113) lies on the Walsmith rectangular hyperbola and these lines:: {6, 468}, {23, 69}, {30, 599}, {67, 74}, {110, 524}, {113, 511}, {125, 2393}, {141, 858}, {159, 21284}, {186, 6776}, {373, 16511}, {403, 5480}, {523, 3569}, {1316, 16321}, {1594, 12061}, {2070, 11898}, {2072, 9967}, {2452, 16324}, {2854, 3580}, {2930, 2931}, {3589, 15826}, {3619, 30745}, {3620, 5189}, {3763, 5159}, {3818, 18323}, {5654, 11477}, {7464, 10519}, {8547, 18911}, {8550, 11464}, {10117, 19596}, {10297, 10516}, {10510, 11064}, {10989, 21356}, {11179, 18579}, {11645, 16111}, {11663, 13371}, {15068, 16619}, {16776, 20113}, {17710, 26156}, {18358, 18572}, {31959, 31983}

X(32113) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 69}, {67, 12367}
X(32113) = reflection of X(i) in X(j) for these lines: {i,j}: {6, 468}, {858, 141}, {1316, 16321}, {2452, 16324}, {2453, 16334}, {3580, 8262}, {10510, 11064}, {11179, 18579}, {15826, 3589}, {18323, 3818}, {18572, 18358}
X(32113) = reflection of X(2453) in the Orthic axis
X(32113) = {X(8263),X(16789)}-harmonic conjugate of X(599)
X(32113) = crossdifference of every pair of points on line {182, 30209}
X(32113) = antipode of X(6) in Walsmith rectangular hyperbola
X(32113) = orthocenter of X(74)X(3569)X(3580)
X(32113) = orthocenter of X(113)X(1495)X(3569)


X(32114) = REFLECTION OF X(125) IN X(5181)

Barycentrics    4*a^6*b^2 - a^4*b^4 - 4*a^2*b^6 + b^8 + 4*a^6*c^2 - 14*a^4*b^2*c^2 + 8*a^2*b^4*c^2 - a^4*c^4 + 8*a^2*b^2*c^4 - 2*b^4*c^4 - 4*a^2*c^6 + c^8 : :
X(32114) = X[6] - 3 X[5642],X[6] - 3 X[5648],5 X[69] - 3 X[13169],3 X[110] - X[193],5 X[110] - 3 X[25321],3 X[113] - 2 X[21850],3 X[125] - 4 X[141],7 X[125] - 8 X[6698],5 X[125] - 4 X[25328],2 X[141] - 3 X[5181],7 X[141] - 6 X[6698],5 X[141] - 3 X[25328],2 X[193] - 3 X[5095],5 X[193] - 9 X[25321],3 X[895] - 5 X[3618],5 X[2930] - X[25336],5 X[3618] - 6 X[5972],5 X[3620] - 3 X[9140],2 X[3629] - 3 X[15303],5 X[5095] - 6 X[25321],7 X[5181] - 4 X[6698],5 X[5181] - 2 X[25328],10 X[6698] - 7 X[25328],4 X[6723] - 3 X[25320],3 X[9143] + X[20080],3 X[10519] - 2 X[20417],3 X[14912] - 5 X[15034],5 X[24981] - 2 X[25336]

X(32114) lies on the Walsmith rectangular hyperbola and these lines:: {6, 5642}, {69, 74}, {110, 193}, {113, 1596}, {125, 126}, {159, 2930}, {511, 1533}, {524, 1495}, {526, 6131}, {895, 3618}, {1350, 10990}, {1351, 16534}, {2931, 19588}, {3448, 15812}, {3564, 30714}, {3569, 9033}, {3580, 8681}, {3620, 9140}, {3629, 15303}, {5486, 5651}, {5965, 25714}, {6053, 10752}, {6723, 25320}, {7699, 11188}, {7703, 12272}, {9143, 20080}, {10519, 20417}, {11472, 17702}, {11898, 23236}, {13202, 14982}, {14912, 15034}
X(32114) = midpoint of X(11898) and X(23236)
X(32114) = reflection of X(i) in X(j) for these lines: {i,j}: {125, 5181}, {895, 5972}, {1351, 16534}, {5095, 110}, {5642, 5648}, {10752, 6053}, {10990, 1350}, {13202, 14982}, {24981, 2930}
X(32114) = crossdifference of every pair of points on line {2780, 5622}
X(32114) = antipode of X(32127) in Walsmith rectangular hyperbola

leftri

Incenters of not-equilateral central triangles: X(32115)-X(32118)

rightri

This preamble and centers X(32115)-X(32118) were contributed by César Eliud Lozada, April 19, 2019.

The appearance of (T, n) in the following list means that the incenter of triangle T-of-ABC is X(n), for any ABC:

(ABC-X3 reflections, 40), (anti-Aquila, 1), (anti-Ara, 1829), (1st anti-Brocard, 1281), (5th anti-Brocard, 12194), (6th anti-Brocard, 32115), (2nd anti-circumperp-tangential, 65), (anti-Euler, 944), (anti-inner-Grebe, 18992), (anti-outer-Grebe, 18991), (anti-Mandart-incircle, 3), (anti-orthocentroidal, 6126), (1st anti-orthosymmedial, 32116), (anticomplementary, 8), (Aquila, 1), (Ara, 9798), (Ascella, 12443), (Atik, 12450), (1st Auriga, 55), (2nd Auriga, 55), (1st Brocard, 3923), (5th Brocard, 9941), (6th Brocard, 32117), (2nd circumperp tangential, 3), (1st circumperp, 12518), (2nd circumperp, 12523), (inner-Conway, 11691), (Conway, 12539), (2nd Conway, 9807), (3rd Conway, 12554), (Ehrmann-mid, 18480), (Euler, 946), (3rd Euler, 12614), (4th Euler, 12622), (excenters-reflections, 12656), (excentral, 164), (2nd extouch, 12694), (Feuerbach, 5960), (inner-Garcia, 8), (outer-Garcia, 8), (Gossard, 12438), (inner-Grebe, 3641), (outer-Grebe, 3640), (hexyl, 12844), (Honsberger, 7670), (inner-Hutson, 12879), (Hutson intouch, 8422), (outer-Hutson, 12884), (incircle-circles, 12908), (intouch, 177), (inverse-in-incircle, 5571), (Johnson, 355), (inner-Johnson, 355), (outer-Johnson, 355), (1st Johnson-Yff, 5252), (2nd Johnson-Yff, 1837), (Lucas central, 1151), (Lucas homothetic, 12440), (Lucas inner tangential, 6407), (Lucas(-1) homothetic, 12441), (Lucas(-1) inner tangential, 6408), (Malfatti, 483), (Mandart-incircle, 3057), (medial, 10), (5th mixtilinear, 1), (6th mixtilinear, 167), (orthocentroidal, 5902), (1st orthosymmedial, 32118), (2nd Pamfilos-Zhou, 13090), (1st Parry, 9810), (2nd Parry, 9811), (1st Sharygin, 13091), (2nd Sharygin, 13301), (tangential-midarc, 1), (2nd tangential-midarc, 1), (3rd tri-squares-central, 8983), (4th tri-squares-central, 13971), (Ursa-major, 17657), (Ursa-minor, 17641), (Wasat, 21633), (X3-ABC reflections, 1482), (Yff central, 13092), (inner-Yff, 1), (outer-Yff, 1), (inner-Yff tangents, 1), (outer-Yff tangents, 1), (2nd Zaniah, 18258)

For some triangles T-of-ABC, the incenter of T is a triangle center when ABC is acute but it is not when ABC is obtuse, as can be seen in the following table:

Triangle T-of-ABC Incenter of T-of-ABC when ABC is acute Incenter of T-of-ABC when ABC is obtuse and angles A ≤ B ≤ C (Barycentric coordinates)
anti-Ascella X(11414) -SB*SC*(SB+SC) : -SA*SC*(SC+SA) : (2*S^2+2*SC^2-SA*SB)*(SA+SB)
anti-Atik X(1593) 4*R^2-SA : 4*R^2-SB : -SC
1st anti-circumperp X(20) 1 : 1 : -1
anti-Conway X(578) SA*(SB+SC)^2 : SB*(SC+SA)^2 : (2*S^2-SA*SB+SC^2)*(SA+SB)
2nd anti-Conway X(389) (S^2+SB*SC)*(SB+SC) : (S^2+SA*SC)*(SC+SA) : -(SC^2-SA*SB)*(SA+SB)
3rd anti-Euler X(12111) (S^2-SA^2+2*SB*SC)*(SB+SC) : (S^2-SB^2+2*SA*SC)*(SC+SA) : -(3*S^2-2*SA*SB+5*SC^2)*(SA+SB)
4th anti-Euler X(6241) (SB+SC)*(2*S^4+SB*SC*(S^2-SA^2)) :
(SC+SA)*(2*S^4+SA*SC*(S^2-SB^2)) :
-(SA+SB)*(2*S^4-(SA*SB-4*SC^2)*S^2+SA*SB*SC^2)
anti-excenters-reflections X(4) SB*SC : SA*SC : SB*SA-S^2/2
2nd anti-extouch X(1181) S^2*(SB+SC) : S^2*(SC+SA) : (SA-SC)*S^2-(SB+SC)*SA^2
anti-Honsberger X(182) SB*(SB+SC)^2 : SA*(SC+SA)^2 : -(SA*SB+SW^2)*(SA+SB)
anti-Hutson intouch X(3) SB*(S^2+2*SA^2)*(SB+SC) : SA*(S^2+2*SB^2)*(SC+SA) : -S^2*(8*R^2-SW)*(SA+SB)
anti-incircle-circles X(3) SB*(2*S^2+SA^2)*(SB+SC) : SA*(2*S^2+SB^2)*(SC+SA) : -S^2*(4*R^2+SW)*(SA+SB)
anti-inverse-in-incircle X(4) SB*SW : SA*SW : -SW^2+(SB+SC)*(SA+SC)
6th anti-mixtilinear X(3) 1 : 1 : 0
1st anti-Sharygin X(8884) SB/(S^2+SB*SC) : SA/(S^2+SA*SC) : -S^2/(SC*S^2+SA*SB*SC)
anti-tangential-midarc X(1) (a^2-b^2+c^2)*(c+a-b)*(b-c+a)*a : (b^2+c^2-a^2)*(c-a+b)*(b-c+a)*b : -(c^2+a^2+2*a*b+b^2)*(c-a+b)*(c+a-b)*c
anti-Ursa minor X(5) (SA+SW)*SB : (SB+SW)*SA : S^2+SA*SB+SC^2-SW^2
anti-Wasat X(185) (S^2+SB*SC)*(SB+SC) : (S^2+SA*SC)*(SC+SA) : -SC*(SW+SC)*(SA+SB)
circumorthic X(4) SB*SC : SA*SC : SB*SA-2*S^2
Ehrmann-side X(3) S^2+3*SB*SC : S^2+3*SA*SC : -3*S^2+3*SA*SB
Ehrmann-vertex X(4) 4*SB*(3*R^2-SW)*S^2 : 4*SA*(3*R^2-SW)*S^2 : -S^4-(SC^2-SW^2)*S^2-3*SA^2*SB^2
2nd Ehrmann X(576) SB*(3*SA+SW)*(SB+SC) : SA*(3*SB+SW)*(SA+SC) : (3*SB*SA-SW^2)*(SA+SB)
2nd Euler X(3) S^2+SB*SC : S^2+SA*SC : -S^2+SA*SB
1st excosine X(1498) S^2*(SB+SC) : S^2*(SC+SA) : -(S^2+2*SC^2)*(SA+SB)
extangents X(40) (a^2-b^2+c^2)*(b+c+a)*a : (b^2+c^2-a^2)*(b+c+a)*b : -(c^3+(a+b)*c^2+(a+b)^2*c+(a^2-b^2)*(a-b))*c
1st Hyacinth X(12370) 4*SA*(S^4-(3*SB^2+4*SB*SC+7*SC^2)*S^2+SB^2*SC^2) :
4*SA*(S^4-(3*SC^2-4*SB*SC+7*SB^2)*S^2+SB^2*SC^2) :
-4*(SA+5*SB-3*SC)*S^4-4*(4*SA*SC-3*SB^2)*SA*S^2-4*(SB+SC)*SA^3*SB
intangents X(1) a*(c-a+b)*(a^2-b^2+c^2) : -(b-c-a)*(b^2+c^2-a^2)*b : (c-a-b)*(c^2+a^2-2*a*b+b^2)*c
1st Kenmotu diagonals X(371) SB*(S-SA)*(SB+SC) : SA*(S-SB)*(SC+SA) : -(S*SW+SA*SB)*(SA+SB)
2nd Kenmotu diagonals X(372) SB*(S+SA)*(SB+SC) : SA*(S+SB)*(SC+SA) : -(S*SW-SA*SB)*(SA+SB)
Kosnita X(3) SB*(S^2-SA^2)*(SB+SC) : SA*(S^2-SB^2)*(SC+SA) : 2*S^2*(2*R^2-SW)*(SA+SB)
orthic X(4) 0 : 0 : 1
submedial X(5) 1 : 1 : 2
tangential X(3) SB*(SB+SC) : SA*(SA+SC) : -SW*(SA+SB)
inner tri-equilateral X(15) (SA-sqrt(3)*S)*(SB+SC)*SB : (SB-sqrt(3)*S)*(SA+SC)*SA : (SA*SB+sqrt(3)*S*SW)*(SA+SB)
outer tri-equilateral X(16) (SA+sqrt(3)*S)*(SB+SC)*SB : (SB+sqrt(3)*S)*(SA+SC)*SA : (SA*SB-sqrt(3)*S*SW)*(SA+SB)

X(32115) = INCENTER OF THE 6th ANTI-BROCARD TRIANGLE

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

X(32115) lies on these lines: {10,98}, {58,99}, {83,11599}, {182,2783}, {239,1281}, {291,4586}, {519,8298}, {740,1691}, {2456,29057}, {2792,12177}, {2796,5182}, {3573,4368}, {4154,19561}, {4672,5038}, {5977,16825}, {5988,10352}, {5992,10353}, {10131,32117}, {10789,16834}, {12151,28558}, {13196,17768}, {13355,24728}, {27838,27950}

X(32115) = inverse of X(5150) in the 1st Lemoine circle


X(32116) = INCENTER OF THE 1st ANTI-ORTHOSYMMEDIAL TRIANGLE

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

X(32116) lies on these lines: {28,105}, {109,1297}, {251,32118}, {2794,15971}, {2831,3744}, {2844,9157}, {5078,10016}


X(32117) = INCENTER OF THE 6th BROCARD TRIANGLE

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

X(32117) lies on these lines: {1,7187}, {3,1281}, {8,3177}, {20,24280}, {55,17789}, {72,15310}, {75,20992}, {76,2795}, {194,740}, {304,3685}, {384,3923}, {516,17760}, {744,24696}, {956,29010}, {1975,5695}, {2783,11257}, {2792,9863}, {2796,7833}, {2896,4655}, {3705,25083}, {3821,7876}, {4019,21299}, {4201,9791}, {4451,25252}, {4672,7787}, {5025,5988}, {5992,6655}, {7081,7580}, {7750,17768}, {7791,24248}, {7893,17770}, {8680,24351}, {9873,29097}, {9939,28558}, {10131,32115}, {16895,24295}, {17135,25257}, {17688,24342}, {20065,24695}, {20432,23407}, {27549,32034}


X(32118) = INCENTER OF THE 1st ORTHOSYMMEDIAL TRIANGLE

Barycentrics    a*((b+c)*a^4+2*b*c*a^3+(b+c)*b*c*a^2-(b^2-c^2)*(b^3-c^3)) : :
X(32118) = 3*X(354)-2*X(4353) = 3*X(354)-X(12721) = X(3663)+2*X(21848) = 2*X(3821)-3*X(5883) = 3*X(5902)-X(24248) = 3*X(10176)-4*X(24295)

X(32118) lies on these lines: {1,572}, {3,25065}, {4,15314}, {21,16566}, {31,1726}, {33,57}, {46,24309}, {51,2844}, {58,3497}, {65,516}, {72,17355}, {226,12618}, {251,32116}, {354,4353}, {405,25081}, {517,12722}, {518,2321}, {527,24476}, {726,2901}, {758,3923}, {761,29044}, {942,3663}, {971,24471}, {984,3730}, {991,7146}, {1009,25078}, {1011,25080}, {1210,12610}, {1400,1736}, {1451,1825}, {1469,2801}, {1721,2955}, {1746,26000}, {1753,23052}, {1764,11031}, {1770,29050}, {1781,4223}, {1876,3668}, {2352,16577}, {2690,2711}, {2809,3751}, {2825,12294}, {2831,5480}, {2838,18907}, {3671,21629}, {3729,3868}, {3754,4660}, {3812,18252}, {3821,5883}, {4329,5807}, {4356,11997}, {4463,5294}, {5256,20243}, {5884,29057}, {5902,24248}, {8094,12728}, {9021,17351}, {9532,19161}, {10158,19744}, {10176,24295}, {10319,10382}, {10572,29024}, {11221,19732}, {11529,12717}, {12445,12727}, {12652,18421}, {17132,24473}, {18389,29069}

X(32118) = midpoint of X(i) and X(j) for these lines: {i,j}: {65, 12723}, {942, 21848}, {3729, 3868}
X(32118) = reflection of X(i) in X(j) for these (i,j): (72, 17355), (3663, 942), (4660, 3754), (12721, 4353), (18252, 3812)
X(32118) = {X(354), X(12721)}-harmonic conjugate of X(4353)


X(32119) = X(6)X(1637)∩X(74)X(98)

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

X(32119) lies on the Walsmith rectangular hyperbola and these lines: {6, 1637}, {74, 98}, {107, 110}, {113, 132}, {125, 526}, {520, 3580}, {523, 1495}, {542, 31953}, {684, 5972}, {2492, 6793}, {2777, 9409}, {2797, 16163}, {3569, 6103}, {7669, 10117}

X(32119) = reflection of X(i) in X(j) for these lines: {i,j}: {125, 6130}, {684, 5972}, {32112, 468}
X(32119) = crossdifference of every pair of points on line {1625, 3269}
X(32119) = antipode of X(32112) in Walsmith rectangular hyperbola
X(32119) = orthocenter of X(6)X(74)X(113)
X(32119) = orthocenter of X(74)X(1495)X(3580)


X(32120) = X(6)X(523)∩X(74)X(1499)

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

X(32120) lies on the Walsmith rectangular hyperbola and these lines:: {6, 523}, {74, 1499}, {110, 525}, {113, 30209}, {125, 512}, {468, 3569}, {520, 32114}, {526, 32112}, {690, 1495}, {858, 24284}, {2780, 32110}, {3566, 10117}, {3580, 9517}, {9033, 32113}, {14417, 18860}

X(32120) = reflection of X(i) in X(j) for these lines: {i,j}: {858, 24284}, {3569, 468}
X(32120) = antipode of X(3569) in Walsmith rectangular hyperbola
X(32120) = orthocenter of X(6)X(74)X(3580)
X(32120) = orthocenter of X(6)X(113)X(1495)
X(32120) = orthocenter of X(110)X(125)X(1495)


X(32121) = X(6)X(14273)∩X(74)X(2374)

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

X(32121) lies on the Walsmith rectangular hyperbola and these lines: {6, 14273}, {74, 2374}, {99, 110}, {113, 126}, {125, 5139}, {512, 3580}, {523, 32113}, {526, 6131}, {924, 32112}, {1495, 3566}, {1499, 32109}, {3569, 10418}, {7665, 9138}, {16316, 32111}, {20186, 32110}

X(32121) = reflection of X(32114) and X(6131)
X(32121) = crossdifference of every pair of points on line {3124, 14984}
X(32121) = orthocenter of X(6)X(110)X(113)
X(32121) = orthocenter of X(6)X(125)X(2931)
X(32121) = orthocenter of X(110)X(1495)X(3580)


X(32122) = X(6)X(9033)∩X(74)X(2373)

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

X(32122) lies on the Walsmith rectangular hyperbola and these lines: {6, 9033}, {74, 2373}, {110, 1289}, {125, 127}, {520, 32112}, {525, 1495}, {690, 10117}, {3580, 8673}, {8057, 32113}, {30209, 32110}

X(32122) = orthocenter of X(6)X(74)X(125)


X(32123) = X(5)X(6)∩X(74)X(858)

Barycentrics    (a^2 - b^2 - c^2)*(a^12*b^2 - 2*a^10*b^4 - a^8*b^6 + 4*a^6*b^8 - a^4*b^10 - 2*a^2*b^12 + b^14 + a^12*c^2 - 2*a^10*b^2*c^2 + 7*a^8*b^4*c^2 - 14*a^6*b^6*c^2 + 5*a^4*b^8*c^2 + 8*a^2*b^10*c^2 - 5*b^12*c^2 - 2*a^10*c^4 + 7*a^8*b^2*c^4 + 12*a^6*b^4*c^4 - 4*a^4*b^6*c^4 - 14*a^2*b^8*c^4 + 9*b^10*c^4 - a^8*c^6 - 14*a^6*b^2*c^6 - 4*a^4*b^4*c^6 + 16*a^2*b^6*c^6 - 5*b^8*c^6 + 4*a^6*c^8 + 5*a^4*b^2*c^8 - 14*a^2*b^4*c^8 - 5*b^6*c^8 - a^4*c^10 + 8*a^2*b^2*c^10 + 9*b^4*c^10 - 2*a^2*c^12 - 5*b^2*c^12 + c^14) : :
X(32123) = 5 X[5] - 4 X[15090],2 X[15123] - 3 X[23515]

X(32123) lies on the Walsmith rectangular hyperbola and these lines: {4, 9938}, {5, 6}, {23, 12319}, {24, 22661}, {30, 10117}, {74, 858}, {110, 403}, {125, 1568}, {235, 12293}, {427, 11472}, {468, 2931}, {912, 15904}, {1147, 10024}, {1368, 4549}, {1495, 11799}, {1503, 15133}, {1594, 7703}, {3167, 10254}, {5133, 7699}, {5448, 5576}, {6193, 16868}, {6622, 12318}, {7505, 9932}, {9820, 13160}, {10255, 12164}, {10564, 15115}, {11064, 15136}, {11459, 12359}, {11585, 12163}, {12118, 15761}, {14984, 32112}, {15123, 23515}, {18323, 19479}, {18404, 19908}, {20427, 23335}

X(32123) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 12319}, {68, 12364}
X(32123) = reflection of X(i) in X(j) for these lines: {i,j}: {858, 23306}, {2931, 468}, {10564, 15115}, {15136, 11064}, {18323, 19479}
X(32123) = antipode of X(2931) in Walsmith rectangular hyperbola
X(32123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 5654, 15068}, {235, 23307, 12293}


X(32124) = X(6)X(23)∩X(74)X(7575)

Barycentrics    a^2*(8*a^10 - 10*a^8*b^2 - 12*a^6*b^4 + 16*a^4*b^6 + 4*a^2*b^8 - 6*b^10 - 10*a^8*c^2 + 24*a^6*b^2*c^2 - 11*a^4*b^4*c^2 - 14*a^2*b^6*c^2 + 11*b^8*c^2 - 12*a^6*c^4 - 11*a^4*b^2*c^4 + 22*a^2*b^4*c^4 - 5*b^6*c^4 + 16*a^4*c^6 - 14*a^2*b^2*c^6 - 5*b^4*c^6 + 4*a^2*c^8 + 11*b^2*c^8 - 6*c^10) : :
X(32124) = 3 X[403] - 2 X[15432]

X(32124) lies on the Walsmith rectangular hyperbola and these lines: {6, 23}, {30, 7699}, {74, 7575}, {113, 10295}, {125, 7426}, {186, 11472}, {403, 15432}, {468, 7703}, {10546, 18571}

X(32124) = midpoint of X(23) and X(7712)
X(32124) = reflection of X(7703) and X(468)
X(32124) = antipode of X(7703) in Walsmith rectangular hyperbola


X(32125) = X(6)X(66)∩X(74)X(403)

Barycentrics    a^10*b^2 - a^8*b^4 - 2*a^6*b^6 + 2*a^4*b^8 + a^2*b^10 - b^12 + a^10*c^2 + 2*a^6*b^4*c^2 + 2*a^4*b^6*c^2 - 7*a^2*b^8*c^2 + 2*b^10*c^2 - a^8*c^4 + 2*a^6*b^2*c^4 - 8*a^4*b^4*c^4 + 6*a^2*b^6*c^4 + b^8*c^4 - 2*a^6*c^6 + 2*a^4*b^2*c^6 + 6*a^2*b^4*c^6 - 4*b^6*c^6 + 2*a^4*c^8 - 7*a^2*b^2*c^8 + b^4*c^8 + a^2*c^10 + 2*b^2*c^10 - c^12 : :
X(32125) = 2 X[1514] + X[12379], 2 X[11064] - 3 X[15131]

X(32125) lies on the Walsmith rectangular hyperbola and these lines: {5, 64}, {6, 66}, {23, 13203}, {30, 2931}, {74, 403}, {110, 858}, {113, 2072}, {125, 15126}, {154, 1368}, {159, 31152}, {161, 1370}, {235, 1192}, {468, 10117}, {1498, 11585}, {1594, 6241}, {1596, 31860}, {1619, 30771}, {2393, 32114}, {2450, 3566}, {2777, 11799}, {2781, 3580}, {2883, 15072}, {3357, 10024}, {3564, 17847}, {5133, 7703}, {5169, 20300}, {5576, 9730}, {5654, 13371}, {5894, 11454}, {6696, 13160}, {6823, 8567}, {7396, 28419}, {7495, 15578}, {9932, 14790}, {10192, 15080}, {10255, 13093}, {10564, 18400}, {10606, 15760}, {11206, 31101}, {12118, 23335}, {12250, 16868}, {13352, 18381}, {15138, 15142}, {15472, 25739}, {15559, 16657}, {15577, 16063}, {15761, 20427}, {17824, 18914}, {18323, 19506}, {18382, 31133}, {31074, 32064}

X(32125) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 13203}, {11744, 12379}
X(32125) = reflection of X(i) in X(j) for these lines: {i,j}: {125, 15126}, {858, 23315}, {10117, 468}, {11744, 1514}, {18323, 19506}
X(32125) = crosspoint of X(16080) and X(18018)
X(32125) = crosssum of X(206) and X(3284)
X(32125) = crossdifference of every pair of points on line {8673, 9306}
X(32125) = antipode of X(10117) in Walsmith rectangular hyperbola
X(32125) = orthocenter of X(110)X(3569)X(3580)


X(32126) = X(6)X(5089)∩X(74)X(2766)

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

X(32126) lies on the Walsmith rectangular hyperbola and these lines: {6, 5089}, {40, 5692}, {72, 20989}, {74, 2766}, {110, 518}, {113, 517}, {125, 3827}, {468, 15904}, {650, 3569}, {910, 21873}, {912, 2931}, {2771, 32109}, {2778, 32110}, {2836, 3580}, {3740, 7703}, {7686, 7699}, {9004, 32114}

X(32126) = reflection of X(15904) and X(468)
X(32126) = antipode of X(15904) in Walsmith rectangular hyperbola


X(32127) = REFLECTION OF X(3292) IN X(6)

Barycentrics    a^2*(2*a^6 - 3*a^4*b^2 - 2*a^2*b^4 + 3*b^6 - 3*a^4*c^2 + 16*a^2*b^2*c^2 - 7*b^4*c^2 - 2*a^2*c^4 - 7*b^2*c^4 + 3*c^6) : :
X(32127) = 2 X[1350] - 3 X[21663]

X(32127) lies on the Walsmith rectangular hyperbola and these lines: {6, 373}, {74, 511}, {110, 8681}, {113, 3564}, {125, 524}, {193, 7703}, {520, 2451}, {538, 2452}, {576, 15030}, {1350, 10602}, {1351, 1597}, {1352, 1992}, {1495, 2854}, {1974, 6391}, {2030, 10765}, {2080, 22143}, {2393, 10117}, {2987, 9190}, {3003, 9145}, {6467, 8547}, {8548, 13352}, {9004, 15904}, {11003, 15531}, {18860, 20975}

X(32127) = reflection of X(3292) in X(6)
X(32127) = {X(6),X(8542)}-harmonic conjugate of X(373)
X(32127) = crossdifference of every pair of points on line {1499, 6776}
X(32127) = antipode of X(32114) in Walsmith rectangular hyperbola
X(32127) = orthocenter of X(74)X(1495)X(3569)


X(32128) = X(3)X(8)∩X(4)X(93)

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

See J.L. Ayme and Ercole Suppa, Hyacinthos 28984.

X(32128) lies on these lines: {3,8}, {4,93}, {498,2594}, {6928,10449}, {10441,10526}


X(32129) = CENTROID OF GEMINI TRIANGLE 104

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

X(32129) lies on these lines: {1, 32044}, {2, 3761}, {1978, 4664}, {4364, 30629}, {17237, 25378}, {26738, 30990}, {30967, 30991}


X(32130) = (name pending)

Barycentrics    (a^2+b^2-5 c^2) (a^2-5 b^2+c^2) (a^4-16 a^2 b^2+7 b^4+14 a^2 c^2-16 b^2 c^2+c^4) (a^4+14 a^2 b^2+b^4-16 a^2 c^2-16 b^2 c^2+7 c^4) : :
Barycentrics    (108 R^2 S^2+18 S^2 SB-21 S^2 SW-4 SW^3) (108 R^2 S^2+18 S^2 SC-21 S^2 SW-4 SW^3) : :

See Kadir Altintas and Ercole Suppa, Hyacinthos 28987.

X(32130) lies on Kiepert hyperbola and this line: {4,17952}

X(32130) = isogonal conjugate of X(32131)
X(32130) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {5485, 9741}

X(32131) = (name pending)

Barycentrics    a^2 (5 a^2-b^2-c^2) (7 a^4-16 a^2 b^2+b^4-16 a^2 c^2+14 b^2 c^2+c^4) : :
Barycentrics    18 S^4 + (108 R^2 SB+108 R^2 SC-18 SB SC-21 SB SW-21 SC SW)S^2 -4 SB SW^3-4 SC SW^3 : :

See Kadir Altintas and Ercole Suppa, Hyacinthos 28987.

X(32131) lies on this line: {3,6}

X(32131) = isogonal conjugate of X(32130)
X(32131) = barycentric product of X(i) and X(j) for these lines: {i,j}: {1384, 9741}

X(32132) = X(2)X(254)∩X(3)X(2165)

Barycentrics    (a^2-b^2-c^2) (a^4-2 a^2 b^2+b^4-2 b^2 c^2+c^4) (a^4+b^4-2 a^2 c^2-2 b^2 c^2+c^4) (a^6-a^4 b^2-a^2 b^4+b^6-3 a^4 c^2+2 a^2 b^2 c^2-3 b^4 c^2+3 a^2 c^4+3 b^2 c^4-c^6) (a^6-3 a^4 b^2+3 a^2 b^4-b^6-a^4 c^2+2 a^2 b^2 c^2+3 b^4 c^2-a^2 c^4-3 b^2 c^4+c^6) : :
Barycentrics    (6 R^2-SW)S^4 + (-8 R^6+8 R^4 SB+8 R^4 SC+2 R^2 SB SC+8 R^4 SW-6 R^2 SB SW-6 R^2 SC SW-SB SC SW-2 R^2 SW^2+SB SW^2+SC SW^2)S^2 + 8 R^6 SB SC-8 R^4 SB SC SW+2 R^2 SB SC SW^2 : :

See Kadir Altintas and Ercole Suppa, Hyacinthos 28987.

Let A'B'C' be the Schroeter triangle. Let P be a point on the nine-point circle. Let A" be the intersection, other than P, of the nine-point circle and line A'P; define B" and C" cyclically. Triangle A"B"C" is perspective to ABC for all P. If P = X(135), the perspector is X(32132). (Randy Hutson, June 7, 2019)

X(32132) lies on these lines: {2,254}, {3,2165}, {24,16172}, {68,394}, {96,97}, {925,3147}, {3546,5392}, {3926,20563}, {6642,14593}

X(32132) = isogonal conjugate of X(35603)
X(32132) = barycentric product of X(i) and X(j) for these lines: {i,j}: {68,6504}, {5392,15316)
X(32132) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {68,6515}, {115,135}, {254,11547}, {921,1748}, {1820,920}, {2165,3542}, {2351,1609}, {6504,317}, {8800,467}, {15316,1993}, {16391,6503}
X(32132) = trilinear product of X(i) and X(j) for these lines: {i,j}: {68, 921}, {68, 921}, {91, 15316}, {1820, 6504}, {1820, 6504}
X(32132) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {68,920}, {91,3542}

X(32133) = X(2)X(12505)∩X(67)X(10354)

Barycentrics    (a^2+b^2-5 c^2) (a^2-5 b^2+c^2) (a^4-4 a^2 b^2+b^4-c^4) (a^4-b^4-4 a^2 c^2+c^4) : :
Barycentrics    (648 R^4-162 R^2 SW+9 SW^2)S^4 + (-54 R^2 SB SC SW+9 SB SC SW^2-24 R^2 SW^3-3 SB SW^3-3 SC SW^3+6 SW^4)S^2 + 2 SB SC SW^4 : :

See Kadir Altintas and Ercole Suppa, Hyacinthos 28988.

X(32133) lies on these lines: {2,12505}, {67,10354}, {599,5486}, {858,14262}, {1296,16063}, {5094,21448}, {5485,16051}

X(32133) = barycentric product of X(i) and X(j) for these lines: {i,j}: {338,15406}, {5485,5486}
X(32133) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {115,5512}, {5485,11185}, {5486,1992}, {15406,249}, {21448,1995}

X(32133) = trilinear product of X(i) and X(j) for these lines: {i,j}: {1109,15406}, {1109,15406}
X(32133) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {1109, 5512}

leftri

X(5)-of-central (not equilateral) triangles: X(32134)-X(32215)

rightri

This preamble and centers X(32134)-X(32215) were contributed by César Eliud Lozada, April 23, 2019.

The appearance of (T, n) in the following list means that X(5)-of-triangle-T is X(n):

(ABC, 5), (ABC-X3 reflections, 550), (anti-Aquila, 5901), (anti-Ara, 6756), (anti-Artzt, 597), (anti-Ascella, 12161), (anti-Atik, 18952), (1st anti-Brocard, 114), (4th anti-Brocard, 14650), (5th anti-Brocard, 32134), (6th anti-Brocard, 32135), (2nd anti-circumperp-tangential, 18990), (1st anti-circumperp, 6101), (anti-Conway, 32136), (2nd anti-Conway, 10095), (anti-Euler, 3), (3rd anti-Euler, 3), (4th anti-Euler, 3), (anti-excenters-reflections, 32137), (2nd anti-extouch, 32046), (anti-inner-Grebe, 19116), (anti-outer-Grebe, 19117), (anti-Honsberger, 19155), (anti-Hutson intouch, 32138), (anti-incircle-circles, 32139), (anti-inverse-in-incircle, 32140), (anti-Mandart-incircle, 32141), (anti-McCay, 2482), (6th anti-mixtilinear, 32142), (anti-orthocentroidal, 1511), (1st anti-orthosymmedial, 19165), (1st anti-Sharygin, 19211), (anti-tangential-midarc, 32143), (anti-Ursa minor, 13561), (anti-Wasat, 5), (antiAOA, 13371), (anticomplementary, 3), (AOA, 32144), (Aquila, 355), (Ara, 26), (Aries, 32145), (Artzt, 9771), (Ascella, 9940), (Atik, 9947), (1st Auriga, 32146), (2nd Auriga, 32147), (Ayme, 32148), (1st Brocard-reflected, 32149), (1st Brocard, 24206), (2nd Brocard, 32150), (4th Brocard, 31840), (5th Brocard, 32151), (6th Brocard, 32152), (circummedial, 31744), (circumorthic, 6102), (2nd circumperp tangential, 32153), (1st circumperp, 3579), (2nd circumperp, 1385), (circumsymmedial, 31727), (inner-Conway, 72), (Conway, 1071), (2nd Conway, 4), (3rd Conway, 10441), (Ehrmann-cross, 30), (Ehrmann-mid, 546), (Ehrmann-side, 5876), (Ehrmann-vertex, 18379), (1st Ehrmann, 32154), (2nd Ehrmann, 32155), (Euler, 546), (2nd Euler, 11591), (3rd Euler, 9955), (4th Euler, 9956), (5th Euler, 32156), (excenters-midpoints, 32157), (excenters-reflections, 1482), (excentral, 3), (1st excosine, 26), (extangents, 32158), (extouch, 32159), (2nd extouch, 5777), (3rd extouch, 32160), (inner-Fermat, 18), (outer-Fermat, 17), (Feuerbach, 32161), (Fuhrmann, 5), (2nd Fuhrmann, 16160), (inner-Garcia, 5694), (outer-Garcia, 5690), (Garcia-reflection, 13463), (Gossard, 32162), (inner-Grebe, 5875), (outer-Grebe, 5874), (3rd Hatzipolakis, 32163), (hexyl, 3), (Honsberger, 5728), (Hutson extouch, 32164), (inner-Hutson, 12488), (Hutson intouch, 9957), (outer-Hutson, 12489), (1st Hyacinth, 32165), (2nd Hyacinth, 32166), (incentral, 32167), (incircle-circles, 5045), (intangents, 32168), (intouch, 942), (inverse-in-incircle, 5045), (Johnson, 5), (inner-Johnson, 10943), (outer-Johnson, 10942), (1st Johnson-Yff, 495), (2nd Johnson-Yff, 496), (K798e, 10021), (K798i, 140), (1st Kenmotu diagonals, 32169), (2nd Kenmotu diagonals, 32170), (Kosnita, 32171), (Lemoine, 32172), (Lucas antipodal, 32173), (Lucas central, 32175), (Lucas homothetic, 32177), (Lucas tangents, 32179), (Lucas(-1) antipodal, 32174), (Lucas(-1) central, 32176), (Lucas(-1) homothetic, 32178), (Lucas(-1) tangents, 32180), (Macbeath, 32181), (Mandart-excircles, 32182), (Mandart-incircle, 15171), (McCay, 7619), (medial, 140), (midarc, 12908), (2nd midarc, 32183), (midheight, 32184), (mixtilinear, 32185), (2nd mixtilinear, 32186), (3rd mixtilinear, 32187), (4th mixtilinear, 32188), (5th mixtilinear, 1483), (6th mixtilinear, 40), (1st Neuberg, 32189), (2nd Neuberg, 32190), (orthic, 143), (orthocentroidal, 5946), (1st orthosymmedial, 32191), (2nd orthosymmedial, 32192), (2nd Pamfilos-Zhou, 12490), (1st Parry, 14610), (2nd Parry, 32193), (3rd Parry, 32194), (Pelletier, 32195), (reflection, 32196), (1st Schiffler, 32197), (2nd Schiffler, 32198), (Schroeter, 10280), (1st Sharygin, 9959), (2nd Sharygin, 9508), (Soddy, 32199), (2nd inner-Soddy, 32200), (2nd outer-Soddy, 32201), (inner-squares, 32202), (outer-squares, 32203), (Steiner, 32204), (submedial, 32205), (symmedial, 32206), (tangential, 156), (tangential-midarc, 8099), (2nd tangential-midarc, 8100), (inner tri-equilateral, 32207), (outer tri-equilateral, 32208), (1st tri-squares-central, 13721), (2nd tri-squares-central, 13844), (3rd tri-squares-central, 13925), (4th tri-squares-central, 13993), (1st tri-squares, 13664), (2nd tri-squares, 13784), (3rd tri-squares, 13924), (4th tri-squares, 32209), (Trinh, 32210), (Ursa-major, 355), (Ursa-minor, 1), (inner-Vecten, 6119), (outer-Vecten, 6118), (Wasat, 5), (X-parabola-tangential, 32211), (X3-ABC reflections, 4), (Yff central, 12491), (Yff contact, 32212), (inner-Yff, 495), (outer-Yff, 496), (inner-Yff tangents, 32213), (outer-Yff tangents, 32214), (Yiu, 32215), (1st Zaniah, 18260), (2nd Zaniah, 5044)

X(32134) = X(5)-OF-5th ANTI-BROCARD TRIANGLE

Barycentrics    2*a^8-4*(b^2+c^2)*a^6+(-4*b^2*c^2+(b^2-c^2)^2)*a^4+(b^2-c^2)^2*b^2*c^2+(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2 : :
X(32134) = X(384)+3*X(22521) = X(3398)-3*X(12150) = X(12110)+3*X(12150)

X(32134) lies on these lines: {3,3329}, {4,11842}, {5,32}, {26,10790}, {30,3398}, {83,140}, {98,546}, {182,550}, {187,11272}, {355,10789}, {384,22521}, {495,10797}, {496,10798}, {548,12054}, {549,5171}, {632,7808}, {952,12194}, {1078,3628}, {1353,5039}, {1483,10800}, {1506,10631}, {1656,7793}, {1691,18583}, {2782,5007}, {3095,3972}, {3564,12193}, {3627,14880}, {4027,19687}, {5008,6248}, {5097,7816}, {5188,15870}, {5690,10791}, {5844,12195}, {5874,10793}, {5875,10792}, {5901,11364}, {5999,13111}, {6179,7697}, {6249,10991}, {6661,10333}, {6756,11380}, {7766,13108}, {7781,15520}, {7819,10350}, {7830,25555}, {7839,13188}, {7858,15561}, {7878,11171}, {8369,10349}, {8722,15712}, {9301,10346}, {9821,10348}, {10794,10943}, {10795,10942}, {10799,15171}, {10803,32213}, {10804,32214}, {11490,32141}, {11837,32146}, {11838,32147}, {11839,32162}, {11840,32177}, {11841,32178}, {12176,12206}, {12197,28174}, {12201,12208}, {12204,22523}, {12205,22522}, {12835,18990}, {13335,14881}, {13885,13925}, {13938,13993}, {18993,19116}, {18994,19117}, {22330,32135}, {22520,32153}

X(32134) = midpoint of X(i) and X(j) for these lines: {i,j}: {3398, 12110}, {12201, 13193}
X(32134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7787, 10788, 3), (11842, 18501, 4), (12210, 12211, 12212)


X(32135) = X(5)-OF-6th ANTI-BROCARD TRIANGLE

Barycentrics    2*a^10-6*(b^2+c^2)*a^8+6*(b^4+c^4)*a^6-(b^2+c^2)*(3*b^4-8*b^2*c^2+3*c^4)*a^4+(b^4+c^4)*(b^4-5*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(32135) = 3*X(6)+X(13188) = X(98)-3*X(182) = X(98)-9*X(5182) = X(98)+3*X(12177) = X(114)+3*X(18800) = 5*X(114)-3*X(25562) = X(147)+3*X(11179) = X(182)-3*X(5182) = X(2080)+3*X(12151) = 3*X(5055)+X(10488) = 3*X(5182)+X(12177) = 3*X(5476)-X(6321) = 2*X(6036)-3*X(10168) = 4*X(6721)-3*X(24206) = X(10754)-3*X(15520) = X(11676)+3*X(22525) = X(13172)+3*X(20423) = 5*X(18800)+X(25562) = 5*X(22234)+X(23235)

X(32135) lies on these lines: {2,98}, {6,1569}, {99,576}, {115,5038}, {262,8289}, {511,5026}, {543,10796}, {575,2782}, {690,25556}, {1691,5477}, {2030,12829}, {2080,2482}, {2456,29012}, {3098,10753}, {3398,14981}, {5055,10488}, {5095,14590}, {5097,5969}, {5476,6321}, {7697,10485}, {7787,22234}, {7808,20398}, {8590,8787}, {8724,11842}, {10104,20399}, {10131,32152}, {10351,11257}, {10754,15520}, {10991,12054}, {10992,12110}, {11645,22505}, {11676,22525}, {12042,20190}, {13172,20423}, {14159,25561}, {19120,19130}, {22330,32134}

X(32135) = midpoint of X(i) and X(j) for these lines: {i,j}: {99, 576}, {182, 12177}, {3098, 10753}, {8593, 11178}
X(32135) = reflection of X(i) in X(j) for these (i,j): (115, 25555), (12042, 20190)
X(32135) = {X(5182), X(12177)}-harmonic conjugate of X(182)


X(32136) = X(5)-OF-ANTI-CONWAY TRIANGLE

Barycentrics    a^2*(2*a^8-7*(b^2+c^2)*a^6+3*(3*b^4+2*b^2*c^2+3*c^4)*a^4-(b^2+c^2)*(5*b^4-9*b^2*c^2+5*c^4)*a^2+(b^4-b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(32136) = X(3)-9*X(11402) = 5*X(3)+3*X(12160) = X(3)+3*X(12161) = X(3)-3*X(32046) = X(3529)+3*X(31815) = X(3627)+3*X(31804) = 15*X(11402)+X(12160) = 3*X(11402)+X(12161) = 3*X(11402)-X(32046) = 5*X(11482)+3*X(19459) = X(12160)-5*X(12161) = X(12160)+5*X(32046) = X(15704)+3*X(31802) = X(24680)+3*X(31811)

X(32136) lies on these lines: {3,54}, {5,11264}, {6,156}, {22,13421}, {26,17809}, {49,1199}, {110,15026}, {143,184}, {155,14128}, {182,32142}, {265,3091}, {389,32171}, {546,12241}, {567,5876}, {568,5944}, {569,11591}, {575,3564}, {576,11536}, {578,5663}, {632,3292}, {1147,12006}, {1173,7545}, {1511,9545}, {1614,14627}, {1994,10263}, {2393,22330}, {2914,15101}, {2916,11477}, {3448,11702}, {3525,9716}, {3529,31815}, {3567,9704}, {3627,21659}, {5893,12102}, {6243,11003}, {6593,22234}, {8254,21243}, {8550,13371}, {9306,32205}, {9703,15043}, {9826,13358}, {10116,12242}, {10226,13382}, {10282,16881}, {10539,13364}, {11424,32137}, {11425,32138}, {11426,32139}, {11427,32140}, {11428,32158}, {11429,32168}, {11430,32210}, {11482,19459}, {11565,18569}, {11750,20424}, {12086,13491}, {12107,16625}, {12233,30522}, {13321,26882}, {13353,15067}, {13434,15060}, {13561,23292}, {14912,18952}, {15704,31802}, {17710,19150}, {18912,20304}, {19365,32143}, {24680,31811}

X(32136) = midpoint of X(12161) and X(32046)
X(32136) = X(140)-of-2nd anti-extouch triangle
X(32136) = X(3628)-of-anti-Ascella triangle
X(32136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 11422, 1493), (195, 5012, 6101), (11422, 11423, 3)


X(32137) = X(5)-OF-ANTI-EXCENTERS-REFLECTIONS TRIANGLE

Barycentrics    a^2*((b^2+c^2)*a^6-3*(b^2-c^2)^2*a^4+(b^2+c^2)*(3*b^4-5*b^2*c^2+3*c^4)*a^2-(b^4+7*b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(32137) = 3*X(2)-4*X(11017) = X(3)-5*X(11439) = X(3)+3*X(11455) = 7*X(4)-3*X(568) = 3*X(4)-X(6102) = 17*X(4)-9*X(11002) = 3*X(4)+X(18439) = 3*X(5)-X(10575) = X(5)-3*X(16194) = X(20)-3*X(15060) = 7*X(143)-6*X(568) = 3*X(143)-2*X(6102) = 17*X(143)-18*X(11002) = 3*X(143)+2*X(18439) = 9*X(568)-7*X(6102) = 9*X(568)+7*X(18439) = X(10575)+3*X(11381) = X(10575)-9*X(16194) = X(11381)+3*X(16194) = 5*X(11439)+3*X(11455) = 3*X(15060)-2*X(32142)

X(32137) lies on these lines: {2,11017}, {3,11439}, {4,94}, {5,10575}, {20,15060}, {24,32210}, {25,32138}, {26,11472}, {30,1216}, {33,32143}, {34,32168}, {49,13596}, {52,15687}, {64,13861}, {140,14915}, {156,1593}, {185,3845}, {195,14094}, {235,13561}, {376,11592}, {378,32171}, {381,10574}, {382,5876}, {389,3861}, {546,5462}, {550,14128}, {632,14855}, {1154,3627}, {1209,1533}, {1498,31861}, {1597,32139}, {1656,12279}, {1657,15058}, {1885,30522}, {2070,15062}, {3091,32205}, {3146,6101}, {3357,12106}, {3426,6642}, {3530,14641}, {3534,15056}, {3543,18436}, {3545,12046}, {3567,14269}, {3830,10263}, {3832,15026}, {3843,5946}, {3850,13363}, {3851,11465}, {3853,13754}, {3856,5943}, {3858,9730}, {4550,7525}, {4846,16620}, {5066,9729}, {5073,11459}, {5076,5889}, {5079,20791}, {5446,12102}, {5576,32111}, {5878,11818}, {5891,15704}, {5892,12811}, {5944,14130}, {6146,15807}, {6243,17578}, {7527,10610}, {7999,15681}, {10096,20191}, {10110,14893}, {10540,14865}, {11250,20773}, {11403,12161}, {11424,32136}, {11440,18378}, {11444,17800}, {11470,32155}, {11471,32158}, {11473,32169}, {11474,32170}, {11475,32207}, {11476,32208}, {11793,12103}, {11819,16654}, {12086,18350}, {12324,18952}, {12358,18565}, {12363,16658}, {13368,22584}, {13421,13598}, {13565,15760}, {15061,21451}, {15311,31830}, {17814,22334}, {18570,26883}, {19124,19155}, {19169,19211}, {20299,20304}, {20396,23294}, {28154,31752}, {28168,31751}

X(32137) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 11381}, {382, 5876}, {1539, 12292}, {3146, 6101}, {3627, 12162}, {6102, 18439}, {10263, 12111}, {12290, 13491}
X(32137) = reflection of X(i) in X(j) for these (i,j): (20, 32142), (143, 4), (185, 10095), (389, 3861), (550, 14128), (5446, 12102), (5889, 16982), (6146, 15807), (10627, 5907), (12103, 11793), (13421, 13598), (13491, 12006), (13630, 546), (14641, 3530)
X(32137) = anticomplement of the anticomplement of X(11017)
X(32137) = X(13491)-of-Ehrmann-mid triangle
X(32137) = X(32138)-of-anti-Ara triangle
X(32137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 18439, 6102), (11439, 11455, 3)


X(32138) = X(5)-OF-ANTI-HUTSON INTOUCH TRIANGLE

Barycentrics    a^2*(a^8-(b^2+c^2)*a^6-3*(b^2-c^2)^2*a^4+(b^2+c^2)*(5*b^4-9*b^2*c^2+5*c^4)*a^2-(b^2-c^2)^2*(b^2+2*c^2)*(2*b^2+c^2)) : :
X(32138) = 3*X(3)-X(32139) = 3*X(3)-2*X(32171) = X(155)-5*X(8567) = 3*X(156)-2*X(32139) = 3*X(156)-4*X(32171) = X(156)-4*X(32210) = X(1147)-3*X(11204) = X(1498)-3*X(18324) = 3*X(5085)-2*X(19155) = X(5878)-3*X(10201) = X(5925)+3*X(14852) = 2*X(10224)-3*X(23329) = 2*X(10226)-3*X(11204) = 3*X(10606)-X(12084) = 3*X(10606)+X(12163) = X(13093)+3*X(14070) = 2*X(18567)-3*X(23325) = X(22660)-3*X(23328) = 3*X(23328)-2*X(23336) = X(32139)-6*X(32210) = X(32171)-3*X(32210)

X(32138) lies on these lines: {3,74}, {4,13561}, {5,1204}, {20,30522}, {25,32137}, {26,64}, {30,3357}, {55,32143}, {56,32168}, {143,1593}, {146,14940}, {155,8567}, {185,18570}, {186,18439}, {378,6102}, {381,11704}, {382,18379}, {511,15579}, {541,20191}, {546,11438}, {568,14865}, {1147,10226}, {1151,32169}, {1152,32170}, {1154,10606}, {1192,11472}, {1498,18324}, {1657,13445}, {1658,6000}, {2070,12290}, {2071,18436}, {2777,5449}, {2883,10020}, {2904,13148}, {2937,12279}, {3146,3581}, {3516,12161}, {3532,17814}, {3534,7691}, {3628,4550}, {3851,15053}, {5020,11017}, {5085,19155}, {5448,25563}, {5584,32158}, {5878,10201}, {5890,14130}, {5895,15114}, {5925,14852}, {6101,11413}, {6243,12086}, {6696,13371}, {6759,15331}, {7502,10575}, {7526,10605}, {7575,26883}, {7728,16868}, {9544,23040}, {9786,10095}, {9818,12006}, {9833,15138}, {10224,23329}, {10539,15646}, {10540,21844}, {11250,13754}, {11264,18917}, {11270,18350}, {11381,32110}, {11412,18859}, {11425,32136}, {11455,18378}, {11477,32155}, {11479,32205}, {11480,32207}, {11481,32208}, {11750,13399}, {12085,13391}, {12162,21663}, {13093,14070}, {13406,22802}, {14915,17714}, {15060,17928}, {15311,15761}, {15704,20725}, {16003,21659}, {17702,18356}, {18377,20299}, {18403,23294}, {18435,22467}, {18562,25739}, {18567,23325}, {18913,18952}, {19172,19211}, {22660,23328}

X(32138) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 32140}, {26, 64}, {3357, 7689}, {5894, 12359}, {12084, 12163}, {15054, 15132}
X(32138) = reflection of X(i) in X(j) for these (i,j): (3, 32210), (4, 13561), (156, 3), (382, 18379), (1147, 10226), (2883, 10020), (5448, 25563), (6759, 15331), (11477, 32155), (13371, 6696), (18377, 20299), (22660, 23336), (22802, 13406), (32139, 32171)
X(32138) = X(156)-of-ABC-X3 reflections triangle
X(32138) = X(13561)-of-anti-Euler triangle
X(32138) = X(32137)-of-Ara triangle
X(32138) = X(32143)-of-anti-Mandart-incircle triangle
X(32138) = X(32168)-of-2nd circumperp tangential triangle
X(32138) = X(32210)-of-X3-ABC reflections triangle
X(32138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 11456, 5944), (11468, 12111, 3), (32139, 32171, 156)


X(32139) = X(5)-OF-ANTI-INCIRCLE-CIRCLES TRIANGLE

Barycentrics    a^2*(a^8-4*(b^2+c^2)*a^6+6*(b^4+c^4)*a^4-2*(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)^2) : :
Trilinears    3 cos A - 2 cos B cos C - 4 sin B sin C cos^2 A : :
X(32139) = 3*X(3)-2*X(32138) = 3*X(3)-4*X(32171) = 5*X(3)-4*X(32210) = 3*X(154)-2*X(1658) = 3*X(154)-X(12163) = 3*X(156)-X(32138) = 3*X(156)-2*X(32171) = 5*X(156)-2*X(32210) = 2*X(1498)+X(16266) = 5*X(1656)-4*X(13561) = 3*X(1853)-4*X(10224) = 3*X(3167)-X(12085) = 3*X(3167)+X(12315) = 5*X(3843)-4*X(18379) = 3*X(5050)-4*X(19155) = X(7387)-3*X(32063) = X(9925)+2*X(9968) = X(12164)+3*X(32063) = 5*X(32138)-6*X(32210) = 5*X(32171)-3*X(32210)

Let A'B'C' be the Kosnita triangle. Let A" be the circumcenter of triangle AB'C', and define B" and C" cyclically. Then X(32139) = X(20)-of-A"B"C". (Randy Hutson, June 7, 2019)

X(32139) lies on these lines: {3,74}, {4,1994}, {5,1181}, {6,546}, {22,18436}, {24,10540}, {25,6102}, {26,6759}, {30,155}, {49,378}, {52,7530}, {54,15305}, {64,11250}, {68,15761}, {140,17814}, {143,1598}, {154,1658}, {184,7526}, {185,6644}, {195,3830}, {323,3529}, {381,7592}, {382,1993}, {389,13861}, {394,550}, {403,25738}, {511,9925}, {542,8548}, {547,15805}, {568,10594}, {569,15030}, {578,31861}, {999,32143}, {1069,32047}, {1092,10575}, {1147,6000}, {1154,7387}, {1199,3832}, {1493,11403}, {1503,18569}, {1539,19504}, {1596,13292}, {1597,32137}, {1620,18571}, {1656,13561}, {1853,10224}, {2072,11457}, {2979,8718}, {3089,18951}, {3090,15052}, {3091,15032}, {3146,12112}, {3157,8144}, {3167,12085}, {3295,32168}, {3311,32169}, {3312,32170}, {3357,12038}, {3448,16868}, {3520,9544}, {3530,17811}, {3542,18917}, {3544,15018}, {3564,19149}, {3843,15087}, {3845,10982}, {3851,5422}, {3853,15811}, {5012,15058}, {5020,12006}, {5050,19155}, {5072,15037}, {5448,18381}, {5462,15011}, {5654,13371}, {5656,6193}, {5889,7517}, {5890,7506}, {5891,7516}, {5907,7514}, {5925,17847}, {5946,7529}, {6101,11414}, {6238,26888}, {6247,9820}, {6642,13630}, {6823,31831}, {7352,10535}, {7393,14128}, {7395,15060}, {7503,18435}, {7525,31834}, {7553,31815}, {7564,18388}, {7689,10282}, {7728,12419}, {8717,13348}, {8743,22146}, {9140,11704}, {9545,14865}, {9704,14130}, {9786,12106}, {9815,23410}, {9818,19347}, {10024,11442}, {10095,11432}, {10113,19456}, {10116,18390}, {10170,13154}, {10201,12359}, {10226,10606}, {10263,12160}, {10306,32158}, {10323,23039}, {10661,10676}, {10662,10675}, {10665,12970}, {10666,12964}, {11002,26863}, {11381,13352}, {11412,12083}, {11413,22115}, {11423,16261}, {11424,16194}, {11425,11472}, {11426,32136}, {11439,15033}, {11477,11663}, {11482,32155}, {11484,32205}, {11485,32207}, {11486,32208}, {11818,12233}, {11819,31383}, {12293,17824}, {12317,14940}, {13346,14915}, {13406,14852}, {13509,22120}, {14070,14530}, {14644,18504}, {15047,19709}, {15063,21659}, {15331,17821}, {15690,16936}, {16659,31723}, {16881,17810}, {17702,22802}, {17714,17834}, {17928,18350}, {18405,18567}, {18570,19357}, {19173,19211}, {20299,31283}, {31725,32111}

X(32139) = midpoint of X(i) and X(j) for these lines: {i,j}: {155, 1498}, {5878, 12118}, {7387, 12164}, {7728, 12419}, {12085, 12315}, {12308, 12412}
X(32139) = reflection of X(i) in X(j) for these (i,j): (3, 156), (26, 6759), (64, 11250), (68, 15761), (3357, 12038), (6247, 9820), (7689, 10282), (12084, 1147), (12163, 1658), (12359, 16252), (14216, 13371), (15132, 5609), (16266, 155), (17834, 17714), (18356, 13406), (18381, 5448), (18569, 22660), (32138, 32171), (32140, 5)
X(32139) = X(156)-of-X3-ABC reflections triangle
X(32139) = X(6102)-of-Ara triangle
X(32139) = X(32140)-of-Johnson triangle
X(32139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (399, 11456, 15068), (1614, 12111, 3), (11441, 11456, 3)


X(32140) = X(5)-OF-ANTI-INVERSE-IN-INCIRCLE TRIANGLE

Barycentrics    a^10-3*(b^2+c^2)*a^8+4*(b^4+c^4)*a^6-2*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^4+(b^2-c^2)^2*(3*b^4+4*b^2*c^2+3*c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(32140) = 3*X(2)-4*X(13561) = 3*X(4)-4*X(18379) = 3*X(154)-4*X(10020) = X(155)-3*X(1853) = 3*X(376)-4*X(32210) = 5*X(631)-4*X(32171) = 2*X(1147)-3*X(18281) = X(1498)-3*X(14852) = 3*X(1853)-2*X(13371) = 3*X(1992)-4*X(32155) = 5*X(3618)-4*X(19155) = 2*X(5448)-3*X(23325) = 4*X(5449)-3*X(10201) = 3*X(5654)-4*X(10224) = 2*X(6759)-3*X(10201) = X(11411)+3*X(32064) = X(14216)+2*X(18356) = X(14790)-3*X(32064) = 3*X(14852)-2*X(15761) = 3*X(18281)-4*X(20299)

X(32140) lies on these lines: {2,156}, {3,70}, {4,94}, {5,1181}, {20,30522}, {26,1503}, {30,64}, {52,11550}, {66,3564}, {69,10627}, {74,12278}, {110,6640}, {125,10539}, {140,1352}, {154,10020}, {155,1853}, {182,18128}, {185,18474}, {376,2888}, {381,18912}, {388,32143}, {389,11818}, {399,10255}, {427,12161}, {497,32168}, {511,14864}, {539,13346}, {542,1147}, {578,10116}, {631,3410}, {1154,11411}, {1199,5169}, {1204,16003}, {1209,10984}, {1368,31831}, {1370,6101}, {1498,14852}, {1593,12370}, {1594,18445}, {1595,13292}, {1614,6639}, {1656,18911}, {1658,9833}, {1992,32155}, {2072,11441}, {2550,32158}, {3068,32169}, {3069,32170}, {3088,11264}, {3098,17712}, {3357,17702}, {3519,13340}, {3538,11592}, {3546,5921}, {3580,7517}, {3581,31304}, {3618,19155}, {3796,7568}, {3818,5462}, {5448,23325}, {5449,6759}, {5562,14791}, {5576,7592}, {5596,19154}, {5609,15114}, {5654,10224}, {5876,18531}, {5889,31723}, {5946,7528}, {6000,9927}, {6143,9544}, {6146,7526}, {6243,7391}, {6247,12084}, {6515,10263}, {6642,18440}, {6643,11591}, {6644,12134}, {6776,32046}, {6816,15060}, {6997,15026}, {7386,32142}, {7392,32205}, {7401,12006}, {7403,11245}, {7505,10540}, {7506,26879}, {7529,26869}, {7530,16655}, {7564,12233}, {7689,18400}, {7706,13382}, {8144,10071}, {9140,26917}, {9786,31830}, {9820,23332}, {10024,11456}, {10055,32047}, {10095,11433}, {10264,26937}, {10516,15805}, {10620,18565}, {11202,20191}, {11250,12118}, {11424,18488}, {11427,32136}, {11440,12289}, {11488,32207}, {11489,32208}, {11585,15068}, {11695,18553}, {12038,23329}, {12085,12429}, {12106,16010}, {12111,18404}, {12241,31861}, {12290,31725}, {12419,15061}, {13364,18950}, {13367,18580}, {13567,13861}, {13630,18420}, {13754,18381}, {14449,31670}, {16172,20422}, {18383,18568}, {18570,19467}, {18918,22533}, {19139,23300}, {19174,19211}

X(32140) = midpoint of X(i) and X(j) for these lines: {i,j}: {64, 12293}, {68, 14216}, {11411, 14790}, {12085, 12429}
X(32140) = reflection of X(i) in X(j) for these (i,j): (20, 32138), (26, 12359), (68, 18356), (155, 13371), (156, 13561), (1147, 20299), (1498, 15761), (5596, 19154), (5609, 15114), (6759, 5449), (9833, 1658), (12084, 6247), (12118, 11250), (16266, 23335), (18569, 18381), (19139, 23300), (32139, 5)
X(32140) = anticomplement of X(156)
X(32140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (156, 13561, 2), (11442, 11457, 3)


X(32141) = X(5)-OF-ANTI-MANDART-INCIRCLE TRIANGLE

Barycentrics    a*(a^6-(b+c)*a^5-2*(b^2+c^2)*a^4+2*(b+c)*(b^2+c^2)*a^3+(b^4+c^4-(b+c)^2*b*c)*a^2-(b^2-c^2)^2*(b+c)*a+(b^2-c^2)^2*b*c) : :
X(32141) = 3*X(165)+X(5534) = 3*X(165)-X(24467) = 3*X(3158)+X(5709) = 3*X(4421)-X(11248) = 3*X(4421)+X(11500) = X(12338)+3*X(22556)

X(32141) lies on these lines: {1,6924}, {3,8}, {4,11849}, {5,55}, {21,5790}, {26,197}, {30,4421}, {35,355}, {40,14988}, {46,24475}, {56,1483}, {119,6284}, {140,1376}, {145,6942}, {149,6949}, {155,7074}, {156,692}, {165,5534}, {200,26921}, {227,32047}, {390,6944}, {404,10246}, {411,12702}, {474,16202}, {495,11501}, {496,11502}, {497,6959}, {499,1484}, {515,26285}, {517,6796}, {519,26286}, {546,11496}, {547,4428}, {550,10310}, {571,21855}, {632,4413}, {912,3579}, {958,7508}, {1001,3628}, {1012,18518}, {1058,6970}, {1385,5836}, {1388,10090}, {1478,14882}, {1482,3871}, {1486,13861}, {1621,1656}, {1771,5399}, {2077,18481}, {2098,10087}, {2886,31659}, {3085,6917}, {3149,10679}, {3158,5709}, {3198,8141}, {3293,5398}, {3295,5901}, {3303,10283}, {3434,6863}, {3560,18357}, {3564,12328}, {3617,6875}, {3740,18233}, {3746,5886}, {3753,24299}, {3913,5844}, {4188,7967}, {4294,6929}, {4302,11698}, {5010,5881}, {5070,5284}, {5082,6954}, {5172,10573}, {5217,22758}, {5218,6862}, {5248,9956}, {5264,5396}, {5281,6824}, {5432,26470}, {5450,26086}, {5541,11014}, {5552,6928}, {5560,5587}, {5693,12738}, {5697,6265}, {5762,6600}, {5763,6985}, {5779,7676}, {5818,7489}, {5840,18242}, {5843,11495}, {5874,11498}, {5875,11497}, {6154,15908}, {6326,11010}, {6756,11383}, {6825,17784}, {6834,20075}, {6868,7080}, {6883,9709}, {6906,18525}, {6915,18493}, {6921,10806}, {6923,10786}, {6934,10528}, {6941,10738}, {6950,26321}, {6958,12116}, {6960,20095}, {6971,27529}, {7491,17757}, {8273,15712}, {9778,16117}, {9897,15446}, {10525,13205}, {10902,26446}, {10944,14793}, {10993,11826}, {11490,32134}, {11492,32146}, {11493,32147}, {11494,32151}, {11503,32177}, {11504,32178}, {11509,18990}, {11510,15325}, {11517,31789}, {11729,26358}, {11848,32162}, {12114,28224}, {12178,12339}, {12255,12535}, {12334,12341}, {12336,22558}, {12337,22557}, {12338,22556}, {12514,31835}, {12515,15071}, {12737,21842}, {12775,18542}, {13887,13925}, {13940,13993}, {14795,18395}, {14798,24914}, {15624,29010}, {16203,16371}, {17522,24808}, {17714,20872}, {18999,19116}, {19000,19117}, {20986,32046}, {21740,25413}, {22457,23981}, {22935,30144}, {24680,25439}

X(32141) = midpoint of X(i) and X(j) for these lines: {i,j}: {3913, 11249}, {5534, 24467}, {6796, 8715}, {6985, 10306}, {11248, 11500}, {12334, 13204}
X(32141) = reflection of X(i) in X(j) for these (i,j): (5450, 26086), (10943, 140), (32153, 3)
X(32141) = X(156)-of-1st circumperp triangle
X(32141) = X(1483)-of-2nd circumperp tangential triangle
X(32141) = X(13561)-of-excentral triangle
X(32141) = X(26286)-of-inner-Garcia triangle
X(32141) = X(32138)-of-2nd circumperp triangle
X(32141) = X(32153)-of-ABC-X3 reflections triangle
X(32141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 5687, 5690), (3, 18526, 104), (100, 11491, 3)


X(32142) = X(5)-OF-6th ANTI-MIXTILINEAR TRIANGLE

Barycentrics    a^2*((b^2+c^2)*a^6-3*(b^2+c^2)^2*a^4+3*(b^4+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) : :
X(32142) = 3*X(2)+X(6101) = 9*X(2)-X(6243) = 9*X(2)-5*X(15026) = 3*X(3)+X(5876) = 9*X(3)-X(6241) = X(3)-9*X(7998) = X(3)+7*X(7999) = 3*X(3)+5*X(11444) = 5*X(3)+3*X(11459) = 7*X(3)+X(12111) = 5*X(3)-X(13491) = X(3)+3*X(15067) = 11*X(3)-3*X(15072) = 3*X(143)-X(6243) = 3*X(143)-5*X(15026) = 3*X(5876)+X(6241) = X(5876)-5*X(11444) = 5*X(5876)-9*X(11459) = X(5876)-3*X(11591) = X(5876)+6*X(11592) = 7*X(5876)-3*X(12111) = 5*X(5876)+3*X(13491) = X(5876)-9*X(15067) = 3*X(6101)+X(6243) = 3*X(6101)+5*X(15026) = X(6101)+2*X(32205) = X(6243)-5*X(15026) = X(6243)-6*X(32205) = 5*X(15026)-6*X(32205)

X(32142) lies on these lines: {2,143}, {3,74}, {4,11017}, {5,3917}, {6,13154}, {20,15060}, {26,17811}, {30,5447}, {51,13421}, {52,632}, {69,18952}, {95,19211}, {125,21230}, {140,389}, {141,12061}, {182,32136}, {185,15712}, {186,12300}, {323,1493}, {338,25043}, {394,7516}, {511,3628}, {546,10170}, {547,5446}, {548,5907}, {549,5562}, {550,5891}, {568,3525}, {599,15074}, {631,6102}, {1038,32143}, {1040,32168}, {1112,14940}, {1350,13861}, {1368,13561}, {1594,11576}, {1656,2979}, {1657,15056}, {3025,7144}, {3060,5070}, {3091,13340}, {3098,17714}, {3519,15108}, {3522,18435}, {3523,18436}, {3526,5946}, {3528,18439}, {3530,13754}, {3534,15058}, {3548,31807}, {5054,5889}, {5066,13598}, {5449,6698}, {5462,15606}, {5690,31849}, {5888,15037}, {5890,15720}, {5943,14449}, {5965,32165}, {6143,6242}, {6292,11675}, {6636,18350}, {7386,32140}, {7393,11426}, {7484,12161}, {7514,11425}, {7525,9306}, {7568,11064}, {7574,22804}, {8703,12162}, {9729,12108}, {9730,14869}, {10124,11695}, {10203,11702}, {10319,32158}, {10610,22115}, {10691,31831}, {11227,31836}, {11230,31737}, {11231,31738}, {11439,15681}, {11465,13321}, {11511,32155}, {11513,32169}, {11514,32170}, {11515,32207}, {11516,32208}, {11561,14448}, {11573,31835}, {11583,31376}, {12010,12900}, {12100,31834}, {12279,15688}, {12362,30522}, {13347,15083}, {13624,31752}, {14627,23061}, {14831,15713}, {15030,15704}, {15043,15694}, {15088,15465}, {15305,15696}, {15443,24470}, {18379,18531}, {19126,19155}, {26910,26915}, {26911,26914}, {31663,31751}

X(32142) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 11591}, {5, 10627}, {20, 32137}, {140, 1216}, {143, 6101}, {546, 15644}, {548, 5907}, {2979, 13364}, {5447, 11793}, {5462, 15606}, {5562, 13630}, {11573, 31835}, {13624, 31752}, {31663, 31751}
X(32142) = reflection of X(i) in X(j) for these (i,j): (3, 11592), (4, 11017), (143, 32205), (5446, 18874), (5462, 16239), (9729, 12108), (10095, 3628), (12006, 140), (14128, 11793), (16881, 11695), (16982, 10095)
X(32142) = complementary conjugate of X(31376)
X(32142) = anticomplement of X(32205)
X(32142) = complement of X(143)
X(32142) = X(11017)-of-anti-Euler triangle
X(32142) = X(11592)-of-X3-ABC reflections triangle
X(32142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 143, 32205), (2, 6101, 143), (6101, 15026, 6243)


X(32143) = X(5)-OF-ANTI-TANGENTIAL-MIDARC TRIANGLE

Barycentrics    a^2*((b+c)^2*a^6-(3*b^2-4*b*c+3*c^2)*(b+c)^2*a^4+(3*b^6+3*c^6-2*(b^4+c^4+(b-c)^2*b*c)*b*c)*a^2-(b^2-c^2)^2*(b^2-b*c+c^2)^2) : :
X(32143) = X(7352)+3*X(32065) = X(32047)-3*X(32065)

X(32143) lies on these lines: {1,3024}, {3,19367}, {5,1425}, {12,13561}, {26,221}, {33,32137}, {34,143}, {35,32210}, {36,32171}, {55,32138}, {56,156}, {65,32158}, {388,32140}, {1038,32142}, {1060,11591}, {1154,7352}, {1398,12161}, {1428,19155}, {1870,6102}, {2067,32169}, {3585,18379}, {4296,6101}, {5876,18447}, {6502,32170}, {7051,32207}, {7354,30522}, {7355,8144}, {9641,12279}, {9642,12290}, {9817,11017}, {10095,19366}, {13491,18455}, {18915,18952}, {19175,19211}, {19349,32046}, {19365,32136}, {19369,32155}, {19372,32205}, {19373,32208}

X(32143) = midpoint of X(i) and X(j) for these lines: {i,j}: {7352, 32047}, {7355, 8144}
X(32143) = reflection of X(32168) in X(1)
X(32143) = X(156)-of-2nd anti-circumperp-tangential triangle
X(32143) = X(32138)-of-Mandart-incircle triangle
X(32143) = X(32168)-of-5th mixtilinear triangle
X(32143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7352, 32065, 32047), (19367, 19368, 3)


X(32144) = X(5)-OF-AOA TRIANGLE

Barycentrics    2*a^10-7*(b^2+c^2)*a^8+2*(3*b^4+8*b^2*c^2+3*c^4)*a^6+4*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^4-8*(b^6-c^6)*(b^2-c^2)*a^2+3*(b^4-c^4)*(b^2-c^2)^3 : :
X(32144) = 9*X(2)-X(7387) = X(1147)+3*X(23332) = 3*X(15113)-X(15114) = 3*X(15113)+X(15115) = X(22660)+3*X(23329)

As a point on the Euler line, X(32144) has Shinagawa coefficients (E-10*F, -3*E-2*F).

X(32144) lies on these lines: {2,3}, {125,13292}, {1147,23332}, {3564,6697}, {5448,6696}, {5663,22967}, {6699,13568}, {6723,10110}, {9820,20299}, {11064,31831}, {11264,15129}, {11801,25487}, {12161,19360}, {13754,32184}, {15113,15114}, {15120,32165}, {15132,15142}, {22660,23329}

X(32144) = midpoint of X(i) and X(j) for these lines: {i,j}: {140, 13371}, {546, 11250}, {548, 18377}, {5448, 6696}, {9820, 20299}, {10224, 23336}, {11801, 25487}, {13383, 23335}, {15114, 15115}
X(32144) = reflection of X(i) in X(j) for these (i,j): (3530, 5498), (10020, 16239), (15330, 11540), (15331, 12108)
X(32144) = complement of X(13383)
X(32144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 1593, 546), (5, 3548, 140), (140, 546, 6644)


X(32145) = X(5)-OF-ARIES TRIANGLE

Barycentrics    SA*((4*R^2-2*SW)*S^2+(SB+SC)*(3*SW^2+2*R^4+(5*SA-13*SW)*R^2)) : :
X(32145) = 3*X(11206)+X(12420) = 3*X(11206)-X(32048)

X(32145) lies on these lines: {25,32166}, {3564,15580}, {5448,31804}, {6193,12087}, {11206,12420}

X(32145) = midpoint of X(12420) and X(32048)
X(32145) = X(32166)-of-Ara triangle
X(32145) = {X(11206), X(12420)}-harmonic conjugate of X(32048)


X(32146) = X(5)-OF-1st AURIGA TRIANGLE

Barycentrics    (2*a^4-2*(b+c)*a^3-(b^2-4*b*c+c^2)*a^2+2*(b^2-c^2)*(b-c)*a-(b^2-c^2)^2)*D+8*S^2*(-a+b+c)*a^2 : : , where D=4*S*sqrt(R*(4*R+r))

X(32146) lies on these lines: {3,5601}, {4,11875}, {5,5597}, {26,8190}, {30,9834}, {55,952}, {140,5599}, {145,11876}, {355,8186}, {495,11869}, {496,11871}, {546,8196}, {550,11822}, {1483,5598}, {3564,12415}, {5602,12645}, {5690,8197}, {5844,11253}, {5874,8199}, {5875,8198}, {5901,11366}, {6756,11384}, {8201,32177}, {8202,32178}, {9835,28224}, {10942,11867}, {10943,11865}, {11492,32141}, {11493,32153}, {11837,32134}, {11844,18526}, {11861,32151}, {11863,32162}, {11873,15171}, {11881,32213}, {11883,32214}, {12179,12476}, {12458,28174}, {12474,22668}, {13890,13925}, {13944,13993}, {18955,18990}, {19007,19116}, {19008,19117}

X(32146) = midpoint of X(11253) and X(12454)
X(32146) = reflection of X(32147) in X(55)
X(32146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5597, 8200, 5), (5601, 11843, 3)


X(32147) = X(5)-OF-2nd AURIGA TRIANGLE

Barycentrics    -(2*a^4-(2*(b+c))*a^3-(b^2-4*b*c+c^2)*a^2+(2*(b^2-c^2))*(b-c)*a-(b^2-c^2)^2)*D+8*S^2*(-a+b+c)*a^2 : : , where D=4*S*sqrt(R*(4*R+r))

X(32147) lies on these lines: {3,5602}, {4,11876}, {5,5598}, {26,8191}, {30,9835}, {55,952}, {140,5600}, {145,11875}, {355,8187}, {495,11870}, {496,11872}, {546,8203}, {550,11823}, {1483,5597}, {5601,12645}, {5690,8204}, {5844,11252}, {5874,8206}, {5875,8205}, {5901,11367}, {6756,11385}, {8208,32177}, {8209,32178}, {9834,28224}, {10942,11868}, {10943,11866}, {11492,32153}, {11493,32141}, {11838,32134}, {11843,18526}, {11862,32151}, {11874,15171}, {11882,32213}, {11884,32214}, {12180,12477}, {12459,28174}, {12475,22672}, {13891,13925}, {13945,13993}, {18956,18990}, {19009,19116}, {19010,19117}

X(32147) = midpoint of X(11252) and X(12455)
X(32147) = reflection of X(32146) in X(55)
X(32147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5598, 8207, 5), (5602, 11844, 3)


X(32148) = X(5)-OF-AYME TRIANGLE

Barycentrics
a*((b+c)*a^8-2*b*c*a^7-(b+c)*(2*b^2-b*c+2*c^2)*a^6+(5*b^2+8*b*c+5*c^2)*b*c*a^5-2*(b+c)*(3*b^2-b*c+3*c^2)*b*c*a^4-10*(b^2+c^2)*(b+c)^2*b*c*a^3+(b+c)*(2*b^6+2*c^6+(3*b^4+3*c^4-2*(4*b^2+7*b*c+4*c^2)*b*c)*b*c)*a^2+(b^2-c^2)^2*(7*b^2+12*b*c+7*c^2)*b*c*a-(b^2-c^2)^2*(b+c)^3*(b^2-4*b*c+c^2)) : :
X(32148) = X(9958)+3*X(11221) = 3*X(11221)-X(11259)

X(32148) lies on these lines: {5,10}, {612,32167}, {9958,11221}, {10618,30142}

X(32148) = midpoint of X(9958) and X(11259)
X(32148) = {X(9958), X(11221)}-harmonic conjugate of X(11259)


X(32149) = X(5)-OF-1st BROCARD-REFLECTED TRIANGLE

Barycentrics    3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6-15*(b^2+c^2)*b^2*c^2*a^4+(b^4+4*b^2*c^2+c^4)*(b^4-5*b^2*c^2+c^4)*a^2+2*(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(32149) = 3*X(2)+X(31958) = X(575)+2*X(3934) = X(6194)+3*X(14561) = X(6248)+2*X(20190) = X(14994)+2*X(15516)

X(32149) lies on these lines: {2,51}, {182,7697}, {538,7606}, {575,3934}, {620,24256}, {2782,10168}, {5969,7619}, {6248,20190}, {6683,8179}, {6704,25555}, {10347,22521}, {14994,15516}, {22681,29012}

X(32149) = midpoint of X(i) and X(j) for these lines: {i,j}: {182, 7697}, {5476, 22712}, {11261, 31958}
X(32149) = complement of X(11261)
X(32149) = {X(2), X(31958)}-harmonic conjugate of X(11261)


X(32150) = X(5)-OF-2nd BROCARD TRIANGLE

Barycentrics    (27*R^2*(SA+2*SW)-25*SW^2)*S^4+(SB*SC*(27*R^2+7*SW)+SW*(2*SA^2-3*SW^2))*SW*S^2-SB*SC*SW^4 : :
X(32150) = X(182)-3*X(10166) = 3*X(353)+X(1352) = 3*X(10166)+X(31959)

X(32150) lies on these lines: {141,31727}, {182,9169}, {353,1352}, {511,31608}, {542,31742}, {3098,14867}, {3818,31731}, {6719,10160}, {7619,9830}, {8705,18583}

X(32150) = midpoint of X(i) and X(j) for these lines: {i,j}: {141, 31727}, {182, 31959}, {3098, 14867}, {3818, 31731}
X(32150) = X(16776)-of-McCay triangle
X(32150) = X(31744)-of-1st Brocard triangle
X(32150) = X(32150)-of-circumsymmedial triangle
X(32150) = {X(10166), X(31959)}-harmonic conjugate of X(182)


X(32151) = X(5)-OF-5th BROCARD TRIANGLE

Barycentrics    2*a^8-3*(b^2+c^2)*a^6+2*(b^4+c^4)*a^4+3*(b^2+c^2)*b^2*c^2*a^2-(b^6-c^6)*(b^2-c^2) : :
X(32151) = 3*X(3)-5*X(7904) = 3*X(5)-2*X(7745) = 3*X(381)-X(7823) = 3*X(3095)-X(7877) = X(7756)-3*X(32152) = 3*X(7811)-X(9821) = 3*X(7811)+X(9873) = 5*X(7904)+3*X(9863) = X(9983)+3*X(22678)

X(32151) lies on these lines: {3,147}, {4,9301}, {5,32}, {26,10828}, {30,76}, {98,7911}, {140,3096}, {355,3099}, {381,7823}, {495,10038}, {496,10047}, {542,7830}, {546,9993}, {549,3788}, {550,1503}, {626,12042}, {632,7914}, {754,14881}, {952,9941}, {1078,6033}, {1352,2076}, {1483,9997}, {1656,10583}, {2782,7756}, {3094,3564}, {3095,7877}, {3104,9981}, {3398,7859}, {3406,10345}, {3628,7846}, {5690,9857}, {5844,12495}, {5874,9995}, {5875,9994}, {5901,11368}, {6287,12110}, {6655,12188}, {6756,11386}, {7502,15270}, {7575,16335}, {7761,14880}, {7801,8703}, {7831,12054}, {7870,12100}, {7883,14830}, {7915,13335}, {7916,9737}, {8362,10349}, {8782,13108}, {9983,22678}, {9985,12501}, {10346,11842}, {10871,10943}, {10872,10942}, {10875,32177}, {10876,32178}, {10877,15171}, {10878,32213}, {10879,32214}, {11494,32141}, {11861,32146}, {11862,32147}, {11885,32162}, {12497,28174}, {13892,13925}, {13946,13993}, {18957,18990}, {19011,19116}, {19012,19117}, {19780,22907}, {19781,22861}, {22744,32153}

X(32151) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 9863}, {9821, 9873}, {12501, 13210}
X(32151) = X(7823)-of-Ehrmann-mid triangle
X(32151) = X(19130)-of-6th Brocard triangle
X(32151) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2896, 9862, 3), (9301, 18503, 4), (9986, 9987, 3094)


X(32152) = X(5)-OF-6th BROCARD TRIANGLE

Barycentrics    2*a^8-4*(b^2+c^2)*a^6+(3*b^4+2*b^2*c^2+3*c^4)*a^4+2*(b^2+c^2)*b^2*c^2*a^2-(b^4+c^4)*(b^2-c^2)^2 : :
X(32152) = 3*X(262)-X(7823) = 3*X(7753)-4*X(11272) = X(7756)+2*X(32151) = 3*X(7811)-X(12251) = 3*X(7833)+X(9863) = 3*X(7833)-X(11257) = 5*X(7904)-3*X(22712) = 3*X(8356)-2*X(13334)

X(32152) lies on these lines: {3,114}, {4,1078}, {5,187}, {20,1352}, {30,5188}, {76,23698}, {98,6655}, {115,10104}, {140,7853}, {182,7791}, {194,5965}, {262,7823}, {315,9737}, {376,7883}, {384,24206}, {401,21243}, {491,9738}, {492,9739}, {511,7750}, {542,7833}, {543,13108}, {576,20065}, {631,7899}, {754,3095}, {1353,9607}, {1975,10992}, {2782,7756}, {3398,4045}, {5025,6036}, {6055,7841}, {6200,6290}, {6249,8150}, {6289,6396}, {6656,13335}, {6721,7907}, {6781,9996}, {7616,17578}, {7737,10358}, {7746,23514}, {7753,11272}, {7763,9734}, {7787,25555}, {7811,12251}, {7828,21445}, {7829,11842}, {7836,21166}, {7842,15980}, {7873,18860}, {7904,22712}, {8356,13334}, {10131,32135}, {10991,14880}, {11293,12975}, {11294,12974}, {12110,14712}

X(32152) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 7802}, {20, 9873}, {9863, 11257}
X(32152) = reflection of X(i) in X(j) for these (i,j): (3, 7830), (7747, 5)
X(32152) = inverse of X(19165) in the 2nd Brocard circle
X(32152) = X(7747)-of-Johnson triangle
X(32152) = X(7802)-of-Euler triangle
X(32152) = X(7830)-of-X3-ABC reflections triangle
X(32152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 14907, 5171), (7833, 9863, 11257)


X(32153) = X(5)-OF-2nd CIRCUMPERP TANGENTIAL TRIANGLE

Barycentrics    a*(a^6-(b+c)*a^5-2*(b-c)^2*a^4+2*(b^2-c^2)*(b-c)*a^3+(b^4+c^4-3*(b-c)^2*b*c)*a^2-(b^2-c^2)*(b-c)^3*a-(b^2-c^2)^2*b*c) : :
X(32153) = X(944)+3*X(5770) = X(5534)-5*X(7987) = 3*X(11194)-X(11249) = 3*X(11194)+X(12114) = 3*X(22680)+X(22779)

X(32153) lies on these lines: {1,1399}, {3,8}, {4,20067}, {5,56}, {21,10246}, {26,22654}, {30,10525}, {36,355}, {55,1483}, {119,5433}, {140,958}, {145,6950}, {153,6949}, {388,6862}, {392,24927}, {404,5790}, {405,16203}, {495,22759}, {496,22760}, {515,26286}, {517,5450}, {519,26285}, {546,18761}, {550,3428}, {912,960}, {997,31835}, {999,3485}, {1001,5843}, {1012,10680}, {1056,6892}, {1319,5887}, {1329,6713}, {1388,10074}, {1420,7330}, {1455,32047}, {1479,1484}, {1482,6906}, {1656,5253}, {1768,11014}, {2077,5288}, {2098,10058}, {3086,6929}, {3149,18519}, {3304,10283}, {3421,6961}, {3436,6958}, {3526,5260}, {3564,22595}, {3600,6824}, {3616,7489}, {3628,25524}, {3655,10902}, {3813,5840}, {3878,11715}, {4189,7967}, {4293,6917}, {4861,25413}, {5080,6971}, {5126,5777}, {5204,11499}, {5248,15178}, {5251,24954}, {5258,26446}, {5265,6944}, {5267,5882}, {5445,12751}, {5534,7987}, {5563,5886}, {5584,8703}, {5603,13743}, {5693,6265}, {5697,12737}, {5714,6913}, {5779,7677}, {5816,21773}, {5844,11248}, {5874,22757}, {5875,22756}, {5881,7280}, {5885,30147}, {6256,22775}, {6264,11010}, {6756,22479}, {6796,28204}, {6833,20076}, {6863,12115}, {6905,18525}, {6909,12702}, {6910,10805}, {6911,18357}, {6912,18493}, {6923,10527}, {6928,10785}, {6930,14986}, {6938,10529}, {6941,10742}, {6942,18524}, {6952,20060}, {6959,7288}, {6974,10597}, {6976,10586}, {6985,28186}, {7354,26470}, {7508,10267}, {8715,26086}, {10950,14793}, {10966,15171}, {11012,18481}, {11279,15175}, {11492,32147}, {11493,32146}, {11500,28224}, {11928,22938}, {12001,28444}, {13925,22763}, {13993,22764}, {14806,21855}, {16150,21669}, {16202,16370}, {19013,19116}, {19014,19117}, {19478,22586}, {21031,21154}, {22504,22780}, {22520,32134}, {22680,22779}, {22744,32151}, {22755,32162}, {22761,32177}, {22762,32178}, {22768,32213}, {22770,28174}, {22771,22773}, {22772,22774}, {22836,26287}, {23961,25440}

X(32153) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 24467}, {5450, 8666}, {11248, 12513}, {11249, 12114}, {19478, 22586}
X(32153) = reflection of X(i) in X(j) for these (i,j): (8715, 26086), (10942, 140), (22836, 26287), (32141, 3)
X(32153) = X(156)-of-2nd circumperp triangle
X(32153) = X(1483)-of-anti-Mandart-incircle triangle
X(32153) = X(13561)-of-hexyl triangle
X(32153) = X(24467)-of-anti-Aquila triangle
X(32153) = X(26285)-of-inner-Garcia triangle
X(32153) = X(32138)-of-1st circumperp triangle
X(32153) = X(32141)-of-ABC-X3 reflections triangle
X(32153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 12773, 944), (3, 18526, 11491), (104, 2975, 3)


X(32154) = X(5)-OF-1st EHRMANN TRIANGLE

Barycentrics    a^2*(2*a^6-(b^2+c^2)*a^4-2*(b^2+c^2)^2*a^2+(b^2+c^2)*((b^2+c^2)^2-9*b^2*c^2)) : :
X(32154) = 3*X(182)+X(8542) = 3*X(182)-X(8546) = X(8547)-5*X(12017) = 3*X(10168)-X(16511)

X(32154) lies on these lines: {2,67}, {3,9019}, {6,5888}, {23,16776}, {30,25488}, {140,524}, {141,3292}, {182,1511}, {187,30489}, {576,6101}, {597,13857}, {599,11422}, {1995,19127}, {2393,20190}, {2930,5012}, {3589,5159}, {5092,8705}, {5609,11178}, {7492,9971}, {7495,8262}, {7496,10510}, {7509,11477}, {7708,28662}, {7804,11594}, {8547,12017}, {9716,21356}, {10272,24206}, {10541,17928}, {11179,23236}, {12041,25489}, {13366,22165}, {16042,18374}

X(32154) = midpoint of X(i) and X(j) for these lines: {i,j}: {5092, 12039}, {8542, 8546}, {12041, 25489}
X(32154) = reflection of X(20113) in X(3589)
X(32154) = {X(182), X(8542)}-harmonic conjugate of X(8546)


X(32155) = X(5)-OF-2nd EHRMANN TRIANGLE

Barycentrics    (SB+SC)*((48*R^2-13*SW)*S^2+(2*R^2-3*SA+2*SW)*SA*SW) : :
X(32155) = 3*X(6)-X(156) = X(26)+3*X(17813) = 2*X(156)-3*X(19155) = 3*X(895)+X(15132) = 3*X(1992)+X(32140) = X(8548)+3*X(11216) = 3*X(10250)-X(11250) = 3*X(11216)-X(11255) = 5*X(11482)-X(32139) = X(13371)-3*X(23326) = X(18377)-3*X(23048)

X(32155) lies on these lines: {3,11443}, {5,21639}, {6,156}, {26,17813}, {143,8541}, {511,32210}, {524,13561}, {542,18379}, {575,32171}, {576,5663}, {895,15132}, {1154,8548}, {1353,11264}, {1493,15531}, {1992,32140}, {5876,18449}, {6101,11416}, {6102,8537}, {8538,11591}, {8539,32158}, {8540,32168}, {8550,30522}, {9813,32205}, {10250,11250}, {10602,32046}, {11405,12161}, {11470,32137}, {11477,32138}, {11482,32139}, {11511,32142}, {13371,23326}, {18377,23048}, {18919,18952}, {19178,19211}, {19369,32143}

X(32155) = midpoint of X(i) and X(j) for these lines: {i,j}: {8548, 11255}, {11477, 32138}
X(32155) = reflection of X(i) in X(j) for these (i,j): (19155, 6), (32171, 575)
X(32155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8548, 11216, 11255), (11443, 11458, 3)


X(32156) = X(5)-OF-5th EULER TRIANGLE

Barycentrics    6*(9*R^2-4*SW)*S^4+(27*R^2*SA*(SB+SC)+SW^2*(3*SA-4*SW))*S^2+SB*SC*SW^3 : :
X(32156) = X(3)+3*X(6032) = X(5)-3*X(10162) = 3*X(5)-X(14866) = 3*X(381)-X(31824) = 3*X(549)-X(31729) = 5*X(632)-3*X(10163) = 5*X(1656)-X(12505) = 11*X(3525)-3*X(6031) = 7*X(3526)-3*X(9829) = 2*X(3628)-3*X(10173) = 3*X(5055)+X(31961) = 3*X(5946)-X(31745) = 3*X(10162)+X(12506) = 9*X(10162)-X(14866) = 3*X(10173)-X(31606) = 3*X(11230)-X(31747) = 3*X(11231)-X(31746) = 3*X(12506)+X(14866) = 3*X(15067)-X(31736) = X(31744)+3*X(31840)

X(32156) lies on these lines: {2,31744}, {3,6032}, {5,9172}, {30,31749}, {140,3849}, {381,31824}, {517,31755}, {549,31729}, {575,20379}, {632,10163}, {1154,31753}, {1656,12505}, {3525,6031}, {3526,9829}, {3628,10173}, {5055,31961}, {5946,31745}, {8704,11272}, {11230,31747}, {11231,31746}, {15060,31743}, {15067,31736}, {30516,31727}

X(32156) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 31840}, {5, 12506}, {15060, 31743}, {31749, 31762}, {31753, 31763}, {31755, 31758}
X(32156) = reflection of X(31606) in X(3628)
X(32156) = complement of X(31744)
X(32156) = X(31824)-of-Ehrmann-mid triangle
X(32156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (10162, 12506, 5), (10173, 31606, 3628)


X(32157) = X(5)-OF-EXCENTERS-MIDPOINTS TRIANGLE

Barycentrics    2*a^4+2*(b+c)*a^3-(3*b^2+8*b*c+3*c^2)*a^2-2*(b+c)*(b^2-3*b*c+c^2)*a+(b^2-c^2)^2 : :
X(32157) = X(8)+3*X(4421) = 3*X(165)+X(32049) = 3*X(549)-X(22837) = 5*X(631)-X(10912) = 5*X(1698)-3*X(3829) = X(2136)+7*X(9588) = 3*X(3654)+X(3811) = X(3813)-3*X(26446) = X(3913)+3*X(5657) = X(6361)+3*X(11236) = 7*X(9780)-3*X(11235) = 3*X(10164)-X(11260) = 3*X(10164)+X(12640)

X(32157) lies on these lines: {2,13463}, {8,4421}, {10,528}, {21,13205}, {35,1145}, {40,12607}, {55,5554}, {100,32198}, {140,2802}, {165,32049}, {518,31787}, {519,12100}, {529,3579}, {549,22837}, {631,10912}, {952,26086}, {1329,5119}, {1376,27870}, {1385,5854}, {1697,3816}, {1698,3829}, {1706,3826}, {2136,9588}, {3035,3057}, {3036,10572}, {3058,25005}, {3654,3811}, {3679,5441}, {3813,26446}, {3880,6684}, {3885,5433}, {3895,24914}, {3913,5657}, {4640,6736}, {4642,17061}, {4861,13996}, {4999,10914}, {5086,6154}, {5123,10624}, {5176,15338}, {5204,12648}, {5221,11239}, {5250,9711}, {5428,5690}, {5541,24390}, {5559,15015}, {5836,6690}, {5855,11362}, {6361,11236}, {6667,12053}, {6691,9957}, {6940,22560}, {9780,11235}, {10107,13405}, {10164,11260}, {11010,17757}, {15813,26357}, {30337,31190}

X(32157) = midpoint of X(i) and X(j) for these lines: {i,j}: {40, 12607}, {100, 32198}, {3579, 10915}, {5690, 8715}, {11260, 12640}
X(32157) = complement of X(13463)
X(32157) = X(6247)-of-K798i triangle
X(32157) = X(32184)-of-excentral triangle
X(32157) = {X(10164), X(12640)}-harmonic conjugate of X(11260)


X(32158) = X(5)-OF-EXTANGENTS TRIANGLE

Barycentrics
a^2*((b+c)^2*a^9-(b^2-c^2)*(b-c)*a^8-2*(2*b^2-b*c+2*c^2)*(b+c)^2*a^7+2*(b^2-c^2)*(b-c)*(2*b^2+b*c+2*c^2)*a^6+(6*b^6+6*c^6+(6*b^4+6*c^4+(3*b^2+4*b*c+3*c^2)*b*c)*b*c)*a^5-(b+c)*(6*b^6+6*c^6-(6*b^4+6*c^4-(3*b^2-4*b*c+3*c^2)*b*c)*b*c)*a^4-2*(2*b^6+2*c^6-3*(b^4+c^4-(b^2-b*c+c^2)*b*c)*b*c)*(b+c)^2*a^3+2*(b^2-c^2)*(b-c)*(2*b^6+2*c^6+3*(b^4+c^4+(b^2+b*c+c^2)*b*c)*b*c)*a^2+(b^2-c^2)^2*(b+c)^2*(b^2-b*c+c^2)^2*a-(b^2-c^2)^3*(b-c)*(b^2+b*c+c^2)^2) : :
X(32158) = X(6237)+3*X(11190) = X(8141)-3*X(11190)

X(32158) lies on these lines: {3,11445}, {5,3611}, {19,143}, {26,3197}, {40,2940}, {55,156}, {65,32143}, {1154,6237}, {2550,32140}, {3101,6101}, {3925,13561}, {5415,32169}, {5416,32170}, {5584,32138}, {5876,18453}, {6102,6197}, {6243,9536}, {6253,30522}, {7688,32210}, {8251,11591}, {8539,32155}, {9537,18436}, {9816,32205}, {10095,11435}, {10306,32139}, {10319,32142}, {10636,32207}, {10637,32208}, {10902,32171}, {11406,12161}, {11428,32136}, {11471,32137}, {18379,18406}, {18921,18952}, {19133,19155}, {19181,19211}, {19350,32046}

X(32158) = reflection of X(32168) in X(156)
X(32158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6237, 11190, 8141), (11445, 11460, 3)


X(32159) = X(5)-OF-EXTOUCH TRIANGLE

Barycentrics
a*((b+c)*a^8-2*(b^2+b*c+c^2)*a^7-2*(b^2-c^2)*(b-c)*a^6+2*(b^2+b*c+c^2)*(3*b^2-2*b*c+3*c^2)*a^5-4*(b+c)*(2*b^2-b*c+2*c^2)*b*c*a^4-2*(b^2+c^2)*(3*b^2+5*b*c+3*c^2)*(b-c)^2*a^3+2*(b^2-c^2)*(b-c)*(b^4+c^4+4*(b^2+b*c+c^2)*b*c)*a^2+2*(b^2-c^2)^2*(b^4+c^4-(b+c)^2*b*c)*a-(b^2-c^2)^4*(b+c)) : :
X(32159) = 3*X(210)-X(1158) = 3*X(210)+X(18239) = 5*X(3697)-X(17649) = 3*X(3740)-X(18238) = 3*X(5657)+X(12666) = X(6245)-3*X(15064)

X(32159) lies on these lines: {2,18260}, {40,17615}, {72,6256}, {210,1158}, {515,960}, {518,12608}, {912,18242}, {956,6261}, {971,6796}, {2829,31837}, {3697,17649}, {3740,18238}, {3820,12616}, {3916,17661}, {4662,5690}, {5044,5450}, {5570,6941}, {5657,12666}, {6245,15064}, {12675,15325}

X(32159) = midpoint of X(i) and X(j) for these lines: {i,j}: {72, 6256}, {1158, 18239}, {6261, 14872}
X(32159) = reflection of X(5450) in X(5044)
X(32159) = anticomplement of X(18260)
X(32159) = {X(210), X(18239)}-harmonic conjugate of X(1158)


X(32160) = X(5)-OF-3rd EXTOUCH TRIANGLE

Barycentrics
a*((b+c)*a^14+2*(2*b^2+b*c+2*c^2)*a^13+(b^2-c^2)*(b-c)*a^12-8*(2*b^4+2*c^4+(b+c)^2*b*c)*a^11-(b+c)*(19*b^4+19*c^4-2*(4*b^2+b*c+4*c^2)*b*c)*a^10+2*(b^2+c^2)*(10*b^4+10*c^4+(5*b^2+2*b*c+5*c^2)*b*c)*a^9+(b+c)*(45*b^6+45*c^6-(10*b^4+10*c^4+(29*b^2-4*b*c+29*c^2)*b*c)*b*c)*a^8-16*(2*b^2-3*b*c+2*c^2)*(b+c)^2*b^2*c^2*a^7-3*(b^2-c^2)*(b-c)*(15*b^6+15*c^6+(30*b^4+30*c^4+(25*b^2+36*b*c+25*c^2)*b*c)*b*c)*a^6-2*(b^2-c^2)^2*(10*b^6+10*c^6+(5*b^4+5*c^4-6*(b^2-b*c+c^2)*b*c)*b*c)*a^5+(b^2-c^2)*(b-c)*(19*b^8+19*c^8+2*(24*b^6+24*c^6+(18*b^4+18*c^4+(32*b^2+25*b*c+32*c^2)*b*c)*b*c)*b*c)*a^4+8*(b^2-c^2)^2*(b-c)^2*(2*b^6+2*c^6+(5*b^4+5*c^4+2*(3*b^2+4*b*c+3*c^2)*b*c)*b*c)*a^3-(b^2-c^2)^3*(b-c)*(b^6+c^6+(10*b^4+10*c^4+(19*b^2+36*b*c+19*c^2)*b*c)*b*c)*a^2-2*(b^4-c^4)*(b^2-c^2)^3*(b+c)^2*(2*b^2-3*b*c+2*c^2)*a-(b^2-c^2)^7*(b-c)) : :

X(32160) lies on these lines: {5909,6684}, {11212,11254}

X(32160) = midpoint of X(11254) and X(31965)
X(32160) = {X(11212), X(31965)}-harmonic conjugate of X(11254)


X(32161) = X(5)-OF-FEUERBACH TRIANGLE

Barycentrics
2*(b^2+b*c+c^2)*a^11+2*(b+c)*(b^2+b*c+c^2)*a^10-(10*b^4+10*c^4+(9*b^2+8*b*c+9*c^2)*b*c)*a^9-2*(b+c)*(5*b^4+5*c^4+(5*b^2+6*b*c+5*c^2)*b*c)*a^8+2*(10*b^6+10*c^6+(7*b^4+7*c^4-(b^2+3*b*c+c^2)*b*c)*b*c)*a^7+2*(b+c)*(2*b^2+b*c+2*c^2)*(5*b^4+5*c^4+(2*b^2-3*b*c+2*c^2)*b*c)*a^6-(20*b^8+20*c^8+(8*b^6+8*c^6-(34*b^4+34*c^4+(37*b^2+24*b*c+37*c^2)*b*c)*b*c)*b*c)*a^5-2*(b^2-c^2)*(b-c)*(10*b^6+10*c^6+(27*b^4+27*c^4+(36*b^2+37*b*c+36*c^2)*b*c)*b*c)*a^4+(b^2-c^2)^2*(10*b^6+10*c^6-(20*b^2+19*b*c+20*c^2)*b^2*c^2)*a^3+2*(b^2-c^2)^4*(b+c)*(5*b^2+2*b*c+5*c^2)*a^2-(b^2-c^2)^4*(b+c)^2*(2*b-c)*(b-2*c)*a-2*(b^2-c^2)^6*(b+c) : :

X(32161) lies on these lines: {5,5947}, {11,10281}, {30,31750}, {517,31756}, {952,10277}, {1154,31754}, {5499,10209}, {7951,10208}

X(32161) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 5948}, {5499, 10209}, {31750, 31764}, {31754, 31765}, {31756, 31759}
X(32161) = complement of X(5) wrt Feuerbach triangle
X(32161) = {X(5947), X(5948)}-harmonic conjugate of X(5)


X(32162) = X(5)-OF-GOSSARD TRIANGLE

Barycentrics    (S^2-3*SB*SC)*(5*S^2-2*R^2*(36*R^2+12*SA-19*SW)+6*SA^2-4*SB*SC-5*SW^2) : :
X(32162) = X(355)-3*X(11852) = X(1482)-3*X(16212) = 2*X(5901)-3*X(11831) = X(12794)+3*X(22698)

As a point on the Euler line, X(32162) has Shinagawa coefficients (11EF-34F2-2S2,3EF+30F2-2S2).

X(32162) lies on these lines: {2,3}, {355,11852}, {495,11905}, {496,11906}, {523,7740}, {952,12438}, {1482,16212}, {1483,11910}, {1511,9033}, {3564,12418}, {5690,11900}, {5844,12626}, {5874,11902}, {5875,11901}, {5901,11831}, {10942,11904}, {10943,11903}, {11839,32134}, {11848,32141}, {11885,32151}, {11907,32177}, {11908,32178}, {11914,32213}, {11915,32214}, {12181,12795}, {12696,28174}, {12790,12797}, {12792,22897}, {12793,22852}, {12794,22698}, {13894,13925}, {13948,13993}, {18958,18990}, {19017,19116}, {19018,19117}, {22755,32153}

X(32162) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 20128}, {3, 4240}, {4, 18508}, {402, 15774}, {11251, 12113}, {12790, 13212}
X(32162) = reflection of X(i) in X(j) for these (i,j): (5, 402), (1650, 140), (18507, 546)
X(32162) = X(18508)-of-Euler triangle
X(32162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1651, 12113, 11251), (11897, 18507, 546), (11911, 18508, 4)


X(32163) = X(5)-OF-3rd HATZIPOLAKIS TRIANGLE

Barycentrics    (512*R^6-R^4*(223*SA+79*SW)+12*R^2*SW*(-2*SW+7*SA)-4*SW^2*(-SW+2*SA))*S^2+4*(R^4*(64*R^2-53*SW)+SW^2*(13*R^2-SW))*SB*SC : :
X(32163) = X(31985)+3*X(32068)

X(32163) lies on the line {31985,32050}

X(32163) = midpoint of X(31985) and X(32050)
X(32163) = {X(31985), X(32068)}-harmonic conjugate of X(32050)


X(32164) = X(5)-OF-HUTSON EXTOUCH TRIANGLE

Barycentrics
a*((b+c)*a^11-(3*b^2-4*b*c+3*c^2)*a^10-(b+c)*(b^2+24*b*c+c^2)*a^9+(11*b^4+11*c^4+2*(8*b^2-23*b*c+8*c^2)*b*c)*a^8-2*(b+c)*(3*b^4+3*c^4-4*(8*b^2+9*b*c+8*c^2)*b*c)*a^7-2*(7*b^6+7*c^6+(36*b^4+36*c^4-(43*b^2+24*b*c+43*c^2)*b*c)*b*c)*a^6+2*(b+c)*(7*b^6+7*c^6-(24*b^4+24*c^4+(73*b^2-4*b*c+73*c^2)*b*c)*b*c)*a^5+2*(3*b^8+3*c^8+2*(20*b^6+20*c^6-(4*b^4+4*c^4+(16*b^2-29*b*c+16*c^2)*b*c)*b*c)*b*c)*a^4-(b^2-c^2)*(b-c)*(11*b^6+11*c^6+(22*b^4+22*c^4-(47*b^2+84*b*c+47*c^2)*b*c)*b*c)*a^3+(b^4-c^4)*(b^2-c^2)*(b^4+c^4-2*(14*b^2+13*b*c+14*c^2)*b*c)*a^2+(b^2-c^2)^3*(b-c)*(3*b^4+3*c^4+2*(7*b^2+13*b*c+7*c^2)*b*c)*a-(b^2-c^2)^6) : :
X(32164) = 3*X(5918)+X(31968) = 3*X(5918)-X(32051) = 3*X(10167)-X(12731)

X(32164) lies on these lines: {5918,31968}, {10167,12731}

X(32164) = midpoint of X(31968) and X(32051)
X(32164) = {X(5918), X(31968)}-harmonic conjugate of X(32051)


X(32165) = X(5)-OF-1st HYACINTH TRIANGLE

Barycentrics    (5*R^2-4*SA+2*SW)*S^2+(R^2-2*SW)*SB*SC : :
X(32165) = X(140)-3*X(11245) = X(143)-3*X(11225) = 3*X(143)-X(13419) = X(389)+3*X(11232) = 3*X(6102)+X(21659) = X(10116)+3*X(11225) = 3*X(10116)+X(13419) = 9*X(11225)-X(13419) = 3*X(11232)-X(11264) = 2*X(11745)-3*X(16881) = X(13142)-5*X(13292) = 3*X(13142)+5*X(18914) = 3*X(13292)+X(18914) = 3*X(32068)-2*X(32205)

X(32165) lies on these lines: {5,1199}, {6,18356}, {30,52}, {54,140}, {125,1493}, {143,10116}, {184,18282}, {265,546}, {389,6153}, {397,11600}, {539,12006}, {542,10095}, {575,3564}, {1154,27552}, {1353,13371}, {1594,2914}, {1614,25338}, {1658,18925}, {1885,7722}, {1994,15002}, {2888,15037}, {3448,14627}, {3850,18388}, {3861,18379}, {5663,19481}, {5965,32142}, {6515,7525}, {6748,15557}, {6776,17714}, {8254,13366}, {10112,13630}, {10224,12161}, {11250,18913}, {11536,25328}, {11745,16881}, {11801,25402}, {11898,13154}, {12107,31804}, {12134,13163}, {12899,13367}, {13391,18128}, {13392,16238}, {15114,15130}, {15120,32144}, {15330,19357}, {16982,29012}, {20424,25739}, {22249,32171}, {32068,32205}

X(32165) = midpoint of X(i) and X(j) for these lines: {i,j}: {143, 10116}, {389, 11264}, {10112, 13630}, {10114, 13358}
X(32165) = reflection of X(12134) in X(13163)
X(32165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (10116, 11225, 143), (13353, 21230, 140)


X(32166) = X(5)-OF-2nd HYACINTH TRIANGLE

Barycentrics    SA*(2*(6*R^2-SW)*S^2+(SB+SC)*(2*R^4-(3*SA+5*SW)*R^2+SW^2)) : :
X(32166) = X(1147)-3*X(11245) = 3*X(11245)+X(12421)

X(32166) lies on these lines: {25,32145}, {68,7592}, {575,3564}, {1147,11245}, {6776,32048}, {10116,12235}, {11264,13630}, {11433,12420}, {12241,13292}, {17702,18914}, {18951,19908}

X(32166) = midpoint of X(i) and X(j) for these lines: {i,j}: {1147, 12421}, {10116, 12235}
X(32166) = X(32145)-of-anti-Ara triangle
X(32166) = {X(11245), X(12421)}-harmonic conjugate of X(1147)


X(32167) = X(5)-OF-INCENTRAL TRIANGLE

Barycentrics    a*(3*(b+c)*a^5+(b^2+4*b*c+c^2)*a^4-(b+c)*(6*b^2-b*c+6*c^2)*a^3-2*(b^4+c^4+3*(b^2+b*c+c^2)*b*c)*a^2+(b^2-c^2)*(b-c)*(3*b^2+5*b*c+3*c^2)*a+(b^2-c^2)^2*(b+c)^2) : :
X(32167) = X(500)+3*X(1962) = 3*X(1962)-X(8143)

Let LA be the trilinear polar of A wrt BCX(1), and define LB and LC cyclically. Let LI be the trilinear polar of X(1) wrt ABC (the antiorthic axis). Then X(32167) = QL-P11 (Nine-point Center QL-Diagonal Triangle) of quadrilateral LALBLCLI. (Randy Hutson, June 7, 2019)

X(32167) lies on these lines: {1,3}, {81,22937}, {500,1962}, {612,32148}, {2771,3743}, {9955,15569}, {11230,24936}, {11231,24883}

X(32167) = midpoint of X(i) and X(j) for these lines: {i,j}: {500, 8143}, {3743, 5453}
X(32167) = reflection of X(1) in X(10618)
X(32167) = X(10618)-of-Aquila triangle
X(32167) = X(15557)-of-excentral triangle
X(32167) = {X(500), X(1962)}-harmonic conjugate of X(8143)
X(32167) = centroid of X(11)X(214)X(500)X(4065)
X(32167) = centroid of X(500) and the vertices of the incentral triangle
X(32167) = QA-P13 (Nine-point Center of the QA-Diagonal Triangle) of quadrangle ABCX(1)


X(32168) = X(5)-OF-INTANGENTS TRIANGLE

Barycentrics    a^2*((b-c)^2*a^6-(3*b^2+4*b*c+3*c^2)*(b-c)^2*a^4+(3*b^6+3*c^6+2*(b^4+c^4-(b+c)^2*b*c)*b*c)*a^2-(b^2-c^2)^2*(b^2+b*c+c^2)^2) : :
X(32168) = X(6238)+3*X(11189) = X(8144)-3*X(11189)

X(32168) lies on these lines: {1,3024}, {3,11446}, {5,3270}, {11,13561}, {26,2192}, {33,143}, {34,32137}, {35,32171}, {36,32210}, {55,156}, {56,32138}, {497,32140}, {1040,32142}, {1062,11591}, {1154,6238}, {1250,32208}, {2066,32169}, {2330,19155}, {3100,6101}, {3295,32139}, {3583,18379}, {5414,32170}, {5876,18455}, {5889,9642}, {5944,9638}, {6102,6198}, {6243,9539}, {6284,30522}, {6285,32047}, {7071,12161}, {8540,32155}, {9538,18436}, {9641,11412}, {9817,32205}, {10095,11436}, {10638,32207}, {11017,19372}, {11429,32136}, {13491,18447}, {18922,18952}, {19182,19211}

X(32168) = midpoint of X(i) and X(j) for these lines: {i,j}: {6238, 8144}, {6285, 32047}
X(32168) = reflection of X(32158) in X(156)
X(32168) = X(156)-of-Mandart-incircle triangle
X(32168) = X(32138)-of-2nd anti-circumperp-tangential triangle
X(32168) = X(32143)-of-5th mixtilinear triangle
X(32168) = reflection of X(32143) in X(1)
X(32168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6238, 11189, 8144), (11446, 11461, 3)


X(32169) = X(5)-OF-1st KENMOTU DIAGONALS TRIANGLE

Barycentrics    (SB+SC)*(S^2+4*(4*R^2-SW)*S-(2*R^2-3*SA+2*SW)*SA) : :
X(32169) = X(10665)+3*X(11241) = 3*X(11241)-X(11265)

X(32169) lies on these lines: {3,11447}, {5,21640}, {6,156}, {26,17819}, {143,5412}, {371,5663}, {372,32171}, {590,13561}, {1151,32138}, {1154,10665}, {2066,32168}, {2067,32143}, {3068,32140}, {3070,30522}, {3311,32139}, {5410,12161}, {5415,32158}, {5876,18457}, {5944,18459}, {6101,11417}, {6102,10880}, {6200,32210}, {6564,18379}, {10201,19061}, {10533,11266}, {10897,11591}, {10961,32205}, {11473,32137}, {11513,32142}, {13909,18356}, {18923,18952}, {19183,19211}, {19355,32046}

X(32169) = midpoint of X(10665) and X(11265)
X(32169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32170), (11447, 11462, 3)


X(32170) = X(5)-OF-2nd KENMOTU DIAGONALS TRIANGLE

Barycentrics    (SB+SC)*(S^2-4*(4*R^2-SW)*S-(2*R^2-3*SA+2*SW)*SA) : :
X(32170) = X(10666)+3*X(11242) = 3*X(11242)-X(11266)

X(32170) lies on these lines: {3,11448}, {5,21641}, {6,156}, {26,17820}, {143,5413}, {371,32171}, {372,5663}, {615,13561}, {1152,32138}, {1154,10666}, {3069,32140}, {3071,30522}, {3312,32139}, {5411,12161}, {5414,32168}, {5416,32158}, {5876,18459}, {5944,18457}, {6101,11418}, {6102,10881}, {6396,32210}, {6502,32143}, {6565,18379}, {10201,19062}, {10534,11265}, {10898,11591}, {10963,32205}, {11474,32137}, {11514,32142}, {13970,18356}, {18924,18952}, {19184,19211}, {19356,32046}

X(32170) = midpoint of X(10666) and X(11266)
X(32170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32169), (11448, 11463, 3)


X(32171) = X(5)-OF-KOSNITA TRIANGLE

Barycentrics    a^2*(2*a^8-5*(b^2+c^2)*a^6+3*(b^2+c^2)^2*a^4+(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2-(b^6-c^6)*(b^2-c^2)) : :
X(32171) = 3*X(3)-X(32138) = 3*X(3)+X(32139) = X(26)-5*X(17821) = 3*X(154)+X(12084) = X(155)+3*X(18324) = 3*X(156)+X(32138) = 3*X(156)-X(32139) = 2*X(156)+X(32210) = 5*X(631)-X(32140) = X(1147)+3*X(11202) = X(1658)-3*X(11202) = X(5449)-3*X(10182) = X(9833)+3*X(18281) = 2*X(10125)-3*X(10182) = 3*X(10192)-X(15761) = 3*X(10193)-4*X(10212) = 3*X(10201)+X(12118) = 5*X(15034)-X(15132) = 2*X(32138)-3*X(32210) = 2*X(32139)+3*X(32210)

Let NANBNC be the reflection triangle of X(5). Let OA be the circumcenter of ANBNC, and define OB and OC cyclically; then X(32171) is the circumcenter of OAOBOC. (Randy Hutson, June 7, 2019)

X(32171) lies on these lines: {2,6288}, {3,74}, {4,16665}, {5,13367}, {15,32208}, {16,32207}, {24,143}, {26,13391}, {30,5448}, {35,32168}, {36,32143}, {49,186}, {52,7575}, {54,5946}, {140,13561}, {154,12084}, {155,18324}, {184,13630}, {185,15646}, {265,14940}, {371,32170}, {372,32169}, {376,18442}, {378,32137}, {382,26882}, {389,32136}, {468,12370}, {511,12107}, {539,15330}, {542,20191}, {546,11430}, {567,15026}, {568,1493}, {569,9827}, {575,32155}, {578,10095}, {631,3410}, {1092,7502}, {1147,1154}, {1495,3627}, {1503,23336}, {1657,26881}, {2070,10263}, {3090,14805}, {3091,3431}, {3515,12161}, {3520,10540}, {5020,12046}, {5072,10546}, {5092,12108}, {5449,10125}, {5498,20299}, {5889,9703}, {5890,9704}, {6000,10226}, {6101,7488}, {6642,32205}, {6644,12006}, {6759,11250}, {7506,13364}, {7555,15644}, {7712,17538}, {9306,14128}, {9544,21844}, {9706,15087}, {9818,11017}, {9833,18281}, {10113,16868}, {10192,15761}, {10193,10212}, {10201,12118}, {10224,18400}, {10254,12278}, {10255,12289}, {10264,17701}, {10298,18436}, {10539,18570}, {10564,15704}, {10902,32158}, {11425,13861}, {13163,19130}, {13346,17714}, {13406,17702}, {13754,15331}, {14070,16266}, {15060,18350}, {15074,15462}, {15088,18396}, {15647,22802}, {15712,22352}, {15806,18388}, {16223,21660}, {18925,18952}, {19154,23041}, {19185,19211}, {19479,20773}, {22249,32165}, {23292,31830}

X(32171) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 156}, {1147, 1658}, {6759, 11250}, {10282, 12038}, {13346, 17714}, {15647, 25487}, {32138, 32139}
X(32171) = reflection of X(i) in X(j) for these (i,j): (5449, 10125), (13561, 140), (18379, 5), (20299, 5498), (32155, 575), (32210, 3)
X(32171) = X(18379)-of-Johnson triangle
X(32171) = X(32210)-of-ABC-X3 reflections triangle
X(32171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 399, 11440), (3, 1614, 13491), (3, 32139, 32138)


X(32172) = X(5)-OF-LEMOINE TRIANGLE

Barycentrics    9*(6*R^2-3*SA+7*SW)*S^4+3*(9*R^2*SA*(SB+SC)+SW*(21*SA^2-30*SA*SW+14*SW^2))*S^2+SB*SC*SW^3 : :
X(32172) = X(8145)-3*X(32069) = X(31969)+3*X(32069)

X(32172) lies on these lines: {5397,8523}, {8145,31969}

X(32172) = midpoint of X(8145) and X(31969)
X(32172) = {X(31969), X(32069)}-harmonic conjugate of X(8145)


X(32173) = X(5)-OF-LUCAS ANTIPODAL TRIANGLE

Barycentrics    4*(4*R^2-2*SA+SW)*S^4-(8*R^2*SA*(SB+SC)+SW*(2*SA^2-6*SA*SW+3*SW^2))*S^2+SB*SC*SW^3-S*(8*S^4+4*(2*(SB+SC)*R^2+SA*(5*SA-4*SW))*S^2-4*SB*SC*SW^2) : :

X(32173) lies on the line {31970,32052}

X(32173) = midpoint of X(31970) and X(32052)


X(32174) = X(5)-OF-LUCAS(-1) ANTIPODAL TRIANGLE

Barycentrics    4*(4*R^2-2*SA+SW)*S^4-(8*R^2*SA*(SB+SC)+SW*(2*SA^2-6*SA*SW+3*SW^2))*S^2+SB*SC*SW^3+S*(8*S^4+4*(2*(SB+SC)*R^2+SA*(5*SA-4*SW))*S^2-4*SB*SC*SW^2) : :

X(32174) lies on the line {31971,32053}

X(32174) = midpoint of X(31971) and X(32053)


X(32175) = X(5)-OF-LUCAS CENTRAL TRIANGLE

Barycentrics    (SB+SC)*(30*S^4-(4*R^2*SA-23*SA^2+17*SB*SC-3*SW^2)*S^2+SA*SW^3-S*((2*R^2-16*SA-13*SW)*S^2-3*(SA+2*SW)*SA*SW)) : :
X(32175) = X(8155)-3*X(11198)

X(32175) lies on these lines: {1151,7598}, {8155,11198}

X(32175) = midpoint of X(8155) and X(31972)
X(32175) = {X(11198), X(31972)}-harmonic conjugate of X(8155)


X(32176) = X(5)-OF-LUCAS(-1) CENTRAL TRIANGLE

Barycentrics    (SB+SC)*(30*S^4-(4*R^2*SA-23*SA^2+17*SB*SC-3*SW^2)*S^2+SA*SW^3+S*((2*R^2-16*SA-13*SW)*S^2-3*(SA+2*SW)*SA*SW)) : :
X(32176) = X(8156)-3*X(32077) = X(31973)+3*X(32077)

X(32176) lies on these lines: {1152,7599}, {8156,31973}

X(32176) = midpoint of X(8156) and X(31973)
X(32176) = {X(31973), X(32077)}-harmonic conjugate of X(8156)


X(32177) = X(5)-OF-LUCAS HOMOTHETIC TRIANGLE

Barycentrics    (4*SA^2-3*SW^2)*S^2+SB*SC*SW^2-4*S*((2*R^2+SB+SC)*S^2-2*R^2*SB*SC) : :
X(32177) = X(9838)+3*X(12152) = X(10669)-3*X(12152) = X(12992)+3*X(22709)

X(32177) lies on these lines: {3,6462}, {4,11949}, {5,493}, {26,8194}, {30,9838}, {140,8222}, {355,8188}, {495,11930}, {496,11932}, {546,8212}, {550,11828}, {952,12440}, {1483,8210}, {3564,12426}, {5690,8214}, {5844,12636}, {5874,8218}, {5875,8216}, {5901,11377}, {6461,32178}, {6756,11394}, {8201,32146}, {8208,32147}, {10875,32151}, {10942,10951}, {10943,10945}, {11503,32141}, {11840,32134}, {11907,32162}, {11947,15171}, {11955,32213}, {11957,32214}, {12186,12994}, {12894,12998}, {12988,22908}, {12990,22863}, {12992,22709}, {13899,13925}, {13956,13993}, {18963,18990}, {19031,19116}, {19032,19117}, {22761,32153}, {22841,28174}

X(32177) = midpoint of X(i) and X(j) for these lines: {i,j}: {9838, 10669}, {12894, 13215}
X(32177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (493, 8220, 5), (6462, 11846, 3)


X(32178) = X(5)-OF-LUCAS(-1) HOMOTHETIC TRIANGLE

Barycentrics    (4*SA^2-3*SW^2)*S^2+SB*SC*SW^2+4*S*((2*R^2+SB+SC)*S^2-2*R^2*SB*SC) : :
X(32178) = X(9839)+3*X(12153) = X(10673)-3*X(12153) = X(12993)+3*X(22710)

X(32178) lies on these lines: {3,6463}, {4,11950}, {5,494}, {26,8195}, {30,9839}, {140,8223}, {355,8189}, {495,11931}, {496,11933}, {546,8213}, {550,11829}, {952,12441}, {1483,8211}, {3564,12427}, {5690,8215}, {5844,12637}, {5874,8219}, {5875,8217}, {5901,11378}, {6461,32177}, {6756,11395}, {8202,32146}, {8209,32147}, {10876,32151}, {10942,10952}, {10943,10946}, {11504,32141}, {11841,32134}, {11908,32162}, {11948,15171}, {11956,32213}, {11958,32214}, {12187,12995}, {12895,12999}, {12989,22909}, {12991,22864}, {12993,22710}, {13900,13925}, {13957,13993}, {18964,18990}, {19033,19116}, {19034,19117}, {22762,32153}, {22842,28174}

X(32178) = midpoint of X(i) and X(j) for these lines: {i,j}: {9839, 10673}, {12895, 13216}
X(32178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (494, 8221, 5), (6463, 11847, 3)


X(32179) = X(5)-OF-LUCAS TANGENTS TRIANGLE

Barycentrics    (SB+SC)*(44*S^4+(4*R^2*SA+31*SA^2-33*SB*SC+11*SW^2)*S^2+3*SA*SW^3+S*((2*R^2+20*SA+37*SW)*S^2+(17*SA^2-18*SB*SC+2*SW^2)*SW)) : :
X(32179) = X(1151)-3*X(11199) = 3*X(11199)+X(31974)

X(32179) lies on the line {1151,8155}

X(32179) = midpoint of X(1151) and X(31974)
X(32179) = {X(11199), X(31974)}-harmonic conjugate of X(1151)


X(32180) = X(5)-OF-LUCAS(-1) TANGENTS TRIANGLE

Barycentrics    (SB+SC)*(44*S^4+(4*R^2*SA+31*SA^2-33*SB*SC+11*SW^2)*S^2+3*SA*SW^3-S*((2*R^2+20*SA+37*SW)*S^2+(17*SA^2-18*SB*SC+2*SW^2)*SW)) : :
X(32180) = X(1152)-3*X(32074) = X(31975)+3*X(32074)

X(32180) lies on these lines: {1152,8156}, {6398,31973}

X(32180) = midpoint of X(1152) and X(31975)
X(32180) = {X(31975), X(32074)}-harmonic conjugate of X(1152)


X(32181) = X(5)-OF-MACBEATH TRIANGLE

Barycentrics    3*S^4-(R^2*(7*SA-3*SW)-2*SA^2+SB*SC+SW^2)*S^2+(2*R^2-SW)*(16*R^2-5*SW)*SB*SC : :
X(32181) = X(8146)-3*X(11197) = 3*X(11197)+X(31976)

X(32181) lies on these lines: {5,10274}, {5576,14674}, {8146,11197}

X(32181) = midpoint of X(8146) and X(31976)
X(32181) = {X(11197), X(31976)}-harmonic conjugate of X(8146)


X(32182) = X(5)-OF-MANDART-EXCIRCLES TRIANGLE

Barycentrics
2*a^13-(7*b^2+4*b*c+7*c^2)*a^11-(b+c)*(b^2-8*b*c+c^2)*a^10+(7*b^2-2*b*c+7*c^2)*(b+c)^2*a^9+(b+c)*(3*b^4+3*c^4-2*(11*b^2-b*c+11*c^2)*b*c)*a^8+2*(b^6+c^6-(8*b^4+8*c^4-(b^2+8*b*c+c^2)*b*c)*b*c)*a^7-2*(b+c)*(b^2-8*b*c+c^2)*(b^2+c^2)^2*a^6-8*(b^6+c^6-(3*b^4+3*c^4-4*(b^2+c^2)*b*c)*b*c)*(b^2+b*c+c^2)*a^5-2*(-4*b^2*c^2+(b^2-c^2)^2)*(b+c)*(b^4+c^4-2*(b-c)^2*b*c)*a^4+(b^2-c^2)^2*(b-c)^2*(5*b^4+5*c^4-2*(b^2-7*b*c+c^2)*b*c)*a^3+(b^2-c^2)^3*(b-c)^3*(3*b^2+4*b*c+3*c^2)*a^2-(b^2-c^2)^4*(b-c)^4*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :
X(32182) = 3*X(11246)+X(31977) = 3*X(11246)-X(32054)

X(32182) lies on these lines: {4338,12659}, {11246,31977}

X(32182) = midpoint of X(31977) and X(32054)
X(32182) = {X(11246), X(31977)}-harmonic conjugate of X(32054)


X(32183) = X(5)-OF-2nd MIDARC TRIANGLE

Barycentrics    a*(6*(-a+b+c)*sin(A/2)*a*b*c-(a+b-c)*(a^2-4*c*a+c^2-b^2)*sin(C/2)*b-(a-b+c)*(a^2-4*b*a+b^2-c^2)*sin(B/2)*c) : :
X(32183) = 3*X(1)-X(177) = 5*X(1)-3*X(11191) = X(1)-3*X(11234) = X(177)+3*X(8422) = 3*X(3241)+X(11691) = 3*X(5919)+X(17641) = X(31767)+2*X(31796)

X(32183) lies on these lines: {1,167}, {3,31800}, {30,31734}, {164,31393}, {495,12614}, {496,12622}, {517,5571}, {519,18258}, {999,12518}, {1317,10501}, {1385,31790}, {3241,11691}, {3488,12694}, {5045,31768}, {5882,8100}, {5919,17641}, {8094,10968}, {11040,11528}, {12443,24929}, {15172,31769}, {31766,31792}

X(32183) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 8422}, {5571, 31767}, {31734, 31770}
X(32183) = reflection of X(i) in X(j) for these (i,j): (5571, 31796), (12908, 1), (31766, 31792), (31768, 5045), (31769, 15172), (31790, 1385), (31800, 3)
X(32183) = inverse of X(30423) in the incircle
X(32183) = X(40)-of-incircle-circles triangle
X(32183) = X(942)-of-2nd tangential-midarc triangle
X(32183) = X(1385)-of-Hutson intouch triangle
X(32183) = X(1902)-of-2nd circumperp triangle
X(32183) = X(8422)-of-anti-Aquila triangle
X(32183) = X(9955)-of-Ursa-minor triangle
X(32183) = X(12699)-of-inverse-in-incircle triangle
X(32183) = X(12908)-of-5th mixtilinear triangle
X(32183) = X(31800)-of-ABC-X3 reflections triangle
X(32183) = {X(8422), X(11234)}-harmonic conjugate of X(1)


X(32184) = X(5)-OF-MIDHEIGHT TRIANGLE

Barycentrics    (SB+SC)*((10*R^2-SA-3*SW)*S^2+(4*R^2*(16*R^2-5*SW)-SA^2+SB*SC+2*SW^2)*SA) : :
X(32184) = 3*X(51)+X(5894) = X(52)+3*X(23328) = X(64)+7*X(15043) = X(185)+3*X(23332) = X(1498)-9*X(15045) = 3*X(1853)+5*X(10574) = 3*X(3060)+5*X(8567) = 5*X(3091)+3*X(7729) = X(3357)+3*X(5946) = 5*X(3567)+3*X(10606) = 9*X(5640)-X(5895) = 3*X(5892)-X(16252) = X(5893)-3*X(5943) = X(5925)+7*X(9781) = 3*X(5943)+X(31978) = X(6102)+3*X(23329) = X(6247)+3*X(9730) = 3*X(10193)-X(10627) = X(10263)+3*X(11204) = X(10575)+3*X(23324)

X(32184) lies on these lines: {3,9972}, {5,22800}, {51,5894}, {52,23328}, {64,15043}, {185,23332}, {389,2781}, {974,1594}, {1154,25563}, {1192,10249}, {1498,15045}, {1503,9729}, {1620,6403}, {1853,10574}, {1885,11746}, {2393,17704}, {2777,10095}, {3060,8567}, {3091,7729}, {3357,5946}, {3567,10606}, {3574,23315}, {3850,6000}, {5462,15311}, {5640,5895}, {5890,12300}, {5892,16252}, {5893,5943}, {5925,9781}, {6102,23329}, {6247,7403}, {6746,21663}, {8991,12240}, {9786,32191}, {10193,10627}, {10263,11204}, {10575,23324}, {10628,30531}, {11598,14865}, {12239,13980}, {13358,25564}, {13491,23325}, {13630,20299}, {13754,32144}, {14644,22948}, {15026,22802}, {17845,20791}, {18381,22804}

X(32184) = midpoint of X(i) and X(j) for these lines: {i,j}: {389, 6696}, {5893, 31978}, {13358, 25564}, {13630, 20299}
X(32184) = {X(5943), X(31978)}-harmonic conjugate of X(5893)


X(32185) = X(5)-OF-MIXTILINEAR TRIANGLE

Barycentrics
4*(b+c)*a^7-(9*b^2+8*b*c+9*c^2)*a^6+24*(b+c)*b*c*a^5+(11*b^4+11*c^4-14*(2*b^2+b*c+2*c^2)*b*c)*a^4-4*(b^2-c^2)^2*(b+c)*a^3-(3*b^4+3*c^4-2*(b^2+9*b*c+c^2)*b*c)*(b-c)^2*a^2+8*(b^2-c^2)*(b-c)^3*b*c*a+(b^2-c^2)^2*(b-c)^4 : :
X(32185) = X(7961)+3*X(11200) = X(8147)-3*X(11200)

X(32185) lies on these lines: {1,32186}, {7961,8147}

X(32185) = midpoint of X(7961) and X(8147)
X(32185) = {X(7961), X(11200)}-harmonic conjugate of X(8147)


X(32186) = X(5)-OF-2nd MIXTILINEAR TRIANGLE

Barycentrics
4*(b+c)*a^9-(17*b^2+8*b*c+17*c^2)*a^8+22*(b+c)*(b^2+c^2)*a^7+2*(b^4+c^4-(41*b^2-24*b*c+41*c^2)*b*c)*a^6-2*(b+c)*(13*b^4+13*c^4-6*(12*b^2-17*b*c+12*c^2)*b*c)*a^5+2*(8*b^4+8*c^4-(5*b^2+54*b*c+5*c^2)*b*c)*(b-c)^2*a^4+2*(b^2-c^2)*(b-c)*(b^2-10*b*c+c^2)*(b^2-4*b*c+c^2)*a^3-2*(b^4+c^4-(b^2+8*b*c+c^2)*b*c)*(b-c)^4*a^2-2*(b^2-c^2)*(b-c)^7*a+(b^2-c^2)^2*(b-c)^6 : :
X(32186) = X(7960)+3*X(11201) = X(8159)-3*X(11201)

X(32186) lies on these lines: {1,32185}, {7960,8159}

X(32186) = midpoint of X(7960) and X(8159)
X(32186) = {X(7960), X(11201)}-harmonic conjugate of X(8159)


X(32187) = X(5)-OF-3rd MIXTILINEAR TRIANGLE

Barycentrics
a*(8*a^9-22*(b+c)*a^8-8*(b^2-14*b*c+c^2)*a^7+4*(b+c)*(16*b^2-47*b*c+16*c^2)*a^6-(24*b^4+24*c^4+(143*b^2-448*b*c+143*c^2)*b*c)*a^5-(b+c)*(60*b^4+60*c^4-(371*b^2-668*b*c+371*c^2)*b*c)*a^4+2*(20*b^6+20*c^6-(23*b^4+23*c^4+(173*b^2-380*b*c+173*c^2)*b*c)*b*c)*a^3+2*(b+c)*(8*b^6+8*c^6-(87*b^4+87*c^4-11*(27*b^2-40*b*c+27*c^2)*b*c)*b*c)*a^2-(b^2-c^2)^2*(16*b^4+16*c^4-7*(11*b^2-18*b*c+11*c^2)*b*c)*a+(b^2-c^2)^3*(b-c)*(2*b-c)*(b-2*c)) : :
X(32187) = X(3)-3*X(32075) = X(31979)+3*X(32075)

X(32187) lies on the line {3,31979}

X(32187) = midpoint of X(3) and X(31979)
X(32187) = {X(31979), X(32075)}-harmonic conjugate of X(3)


X(32188) = X(5)-OF-4th MIXTILINEAR TRIANGLE

Barycentrics
a*(8*a^9-10*(b+c)*a^8-8*(4*b^2-b*c+4*c^2)*a^7+4*(b+c)*(12*b^2-7*b*c+12*c^2)*a^6+(32*b^4+32*c^4-(7*b^2-48*b*c+7*c^2)*b*c)*a^5-(b+c)*(68*b^4+68*c^4-(31*b^2-36*b*c+31*c^2)*b*c)*a^4+2*(19*b^2+39*b*c+19*c^2)*(b-c)^2*b*c*a^3+2*(b^2-c^2)*(b-c)*(16*b^4+16*c^4+(11*b^2-15*b*c+11*c^2)*b*c)*a^2-(b^2-c^2)^2*(b-c)^2*(8*b^2+23*b*c+8*c^2)*a-(b^2-c^2)*(b-c)^5*(b+2*c)*(2*b+c)) : :
X(32188) = X(3)-3*X(32076) = X(31980)+3*X(32076)

X(32188) lies on the line {3,31980}

X(32188) = midpoint of X(3) and X(31980)
X(32188) = X(31744)-of-1st circumperp triangle
X(32188) = X(32156)-of-excentral triangle
X(32188) = {X(31980), X(32076)}-harmonic conjugate of X(3)


X(32189) = X(5)-OF-1st NEUBERG TRIANGLE

Barycentrics    (b^2+c^2)*a^6-(b^2+c^2)^2*a^4+(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2-2*b^4*c^4 : :
X(32189) = 3*X(2)+X(31981) = X(76)+3*X(13085) = 3*X(262)-X(7759) = X(6309)-5*X(7786) = X(7781)-3*X(11171) = X(18768)-5*X(31276)

X(32189) lies on these lines: {2,39}, {3,8150}, {5,736}, {140,698}, {230,18806}, {262,7759}, {511,7780}, {626,2023}, {732,7764}, {754,14881}, {1078,1916}, {2021,7816}, {3094,7815}, {3095,7751}, {3202,3506}, {5976,7749}, {6680,24256}, {7752,9983}, {7775,10356}, {7781,11171}, {7804,13357}, {7895,14994}, {9462,18573}, {9862,18769}, {10357,13086}

X(32189) = midpoint of X(i) and X(j) for these lines: {i,j}: {3095, 7751}, {8149, 31981}
X(32189) = reflection of X(7764) in X(11272)
X(32189) = complement of X(8149)
X(32189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 31981, 8149), (76, 7746, 3934), (76, 7786, 7836)


X(32190) = X(5)-OF-2nd NEUBERG TRIANGLE

Barycentrics    (3*b^4+8*b^2*c^2+3*c^4)*a^4-(b^2+c^2)*(b^4-8*b^2*c^2+c^4)*a^2-c^8-(b^2-c^2)^2*b^2*c^2-b^8 : :
X(32190) = 3*X(2)+X(31982) = X(6308)+3*X(9765) = X(6308)-5*X(31268) = 3*X(9765)+5*X(31268)

X(32190) lies on these lines: {2,32}, {39,9478}, {114,6287}, {732,7764}, {3788,24273}, {5031,6683}, {7697,8149}, {7769,8290}, {7771,9990}, {8177,25555}

X(32190) = midpoint of X(i) and X(j) for these lines: {i,j}: {2896, 18548}, {7775, 13086}, {8150, 31982}
X(32190) = complement of X(8150)
X(32190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 31982, 8150), (1506, 6292, 83), (9765, 31268, 6308)


X(32191) = X(5)-OF-1st ORTHOSYMMEDIAL TRIANGLE

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b^4+c^4)*a^6-5*(b^2+c^2)*b^2*c^2*a^4+2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a^2-(b^6+c^6)*(b^2-c^2)^2) : :
X(32191) = X(6)-5*X(3567) = 3*X(6)+X(6403) = 5*X(6)-X(15073) = 3*X(51)-X(5480) = 9*X(51)-X(12294) = 3*X(51)+X(19161) = X(182)-3*X(5946) = 3*X(568)+X(1352) = 3*X(597)-X(9967) = X(1350)+3*X(3060) = X(1351)-9*X(13321) = X(1352)-3*X(16776) = 15*X(3567)+X(6403) = X(3589)+2*X(21852) = 5*X(3763)-X(11412) = 3*X(5050)-X(17710) = 3*X(5085)-7*X(15043) = 3*X(5480)-X(12294) = 5*X(6403)+3*X(15073) = X(12294)+3*X(19161)

X(32191) lies on these lines: {4,15321}, {6,24}, {51,125}, {52,141}, {140,143}, {159,11432}, {182,5946}, {251,19165}, {389,1503}, {518,31760}, {524,10127}, {542,13358}, {568,1352}, {575,12107}, {576,22828}, {597,9967}, {1154,24206}, {1350,3060}, {1351,13321}, {1353,2854}, {1843,6746}, {2393,12007}, {3098,10263}, {3564,16881}, {3763,11412}, {3818,6102}, {5050,17710}, {5085,15043}, {5092,12006}, {5097,14984}, {5446,29181}, {5449,10095}, {5889,10516}, {5900,22336}, {5943,11548}, {6467,12061}, {6593,16222}, {6776,9971}, {7592,20987}, {7716,15581}, {9786,32184}, {9822,16625}, {9973,14912}, {10110,16198}, {10625,21167}, {10691,21849}, {11002,16063}, {11438,15578}, {11649,15516}, {13391,14810}, {13630,29012}, {16224,28343}, {17810,19149}, {20391,21851}

X(32191) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 141}, {389, 9969}, {568, 16776}, {1843, 8550}, {3098, 10263}, {3818, 6102}, {5462, 21852}, {5480, 19161}, {6467, 12061}, {9822, 16625}
X(32191) = reflection of X(i) in X(j) for these (i,j): (3589, 5462), (5092, 12006), (19130, 10095)
X(32191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (51, 19161, 5480), (5480, 13567, 20300)


X(32192) = X(5)-OF-2nd ORTHOSYMMEDIAL TRIANGLE

Barycentrics    (SB+SC)*(3*(6*R^2-7*SW)*(3*R^2-SW)*S^4-(9*R^2*SA*(12*R^2+3*SA-8*SW)+14*R^2*SW^2-SW*(9*SA^2-12*SA*SW+7*SW^2))*SW*S^2+(4*R^2+3*SA-4*SW)*SA*SW^4) : :
X(32192) = X(5480)-3*X(11226) = 3*X(11226)+X(31983)

X(32192) lies on these lines: {182,7575}, {2781,31771}, {5480,11226}

X(32192) = midpoint of X(5480) and X(31983)
X(32192) = X(31744)-of-1st orthosymmedial triangle
X(32192) = {X(11226), X(31983)}-harmonic conjugate of X(5480)


X(32193) = X(5)-OF-2nd PARRY TRIANGLE

Barycentrics    (3*a^4-(b^2+c^2)*a^2-b^4+b^2*c^2-c^4)*(b^2-c^2) : :
X(32193) = 5*X(351)-3*X(9123) = 3*X(351)-X(9131) = X(351)-3*X(9185) = 3*X(1637)-X(9134) = 2*X(5113)+X(14316) = 4*X(6587)-X(23301) = 9*X(9123)-5*X(9131) = X(9123)-5*X(9185) = 3*X(9123)+5*X(9979) = 6*X(9123)-5*X(14610) = X(9131)-9*X(9185) = X(9131)+3*X(9979) = 2*X(9131)-3*X(14610) = 2*X(9134)-3*X(10278) = 3*X(9185)+X(9979) = 6*X(9185)-X(14610) = 3*X(9189)-X(14417) = 2*X(9979)+X(14610) = X(13307)+3*X(22734) = 3*X(14420)+X(14424)

Let A'B'C' and A"B"C" be the cevian and anticevian triangles of X(6), resp. Let (OA) be the cevian circle of A". Let A* be the intersection, other than A', of (OA) and line BC. Define B* and C* cyclically. X(32193) is the centroid of triangle A*B*C*. (Randy Hutson, August 10, 2020)

X(32193) lies on these lines: {2,9479}, {111,9076}, {351,523}, {525,9208}, {526,14697}, {690,5461}, {804,1637}, {826,4142}, {900,9811}, {2450,3566}, {2799,10190}, {3124,7668}, {3800,5027}, {4977,9810}, {8029,9147}, {8704,32194}, {9007,13303}, {9138,13291}, {9148,10189}, {9189,14417}, {9200,22889}, {9201,22934}, {9512,20998}, {10276,14698}, {13250,28221}, {13251,28217}, {13307,22734}, {14272,14977}

X(32193) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 14420}, {351, 9979}, {8029, 9147}, {9138, 13291}, {14272, 14977}
X(32193) = reflection of X(i) in X(j) for these (i,j): (9148, 10189), (10190, 11176), (10278, 1637), (14610, 351)
X(32193) = complement of X(14424)
X(32193) = X(550)-of-1st Parry triangle
X(32193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9185, 9979, 351), (13319, 13320, 3569)


X(32194) = X(5)-OF-3rd PARRY TRIANGLE

Barycentrics    a^2*(10*a^8-29*(b^2+c^2)*a^6+3*(2*b^4+7*b^2*c^2+2*c^4)*a^4+(b^2+c^2)*(31*b^4-82*b^2*c^2+31*c^4)*a^2-14*b^8+(34*b^4+15*b^2*c^2+34*c^4)*b^2*c^2-14*c^8)*(b^2-c^2) : :
X(32194) = X(351)-3*X(11215) = X(31986)+3*X(11215)

X(32194) lies on these lines: {351,31986}, {523,31772}, {8704,32193}

X(32194) = midpoint of X(i) and X(j) for these lines: {i,j}: {351, 31986}, {31772, 31773}
X(32194) = {X(31986), X(11215)}-harmonic conjugate of X(351)


X(32195) = X(5)-OF-PELLETIER TRIANGLE

Barycentrics    a*(a^5-(b+c)*a^4-5*b*c*a^3+6*(b+c)*b*c*a^2-(b^2+c^2)*(b^2+b*c+c^2)*a+(b^2-c^2)^2*(b+c))*(b-c) : :
X(32195) = X(1)+3*X(11193) = 11*X(5550)-3*X(30613) = 3*X(11193)-X(11247)

X(32195) lies on these lines: {1,11193}, {513,5045}, {521,3813}, {650,3746}, {676,2775}, {885,1058}, {946,3309}, {2646,11934}, {3900,5044}, {5550,30613}, {6198,18344}, {8760,15178}, {9957,14077}

X(32195) = midpoint of X(1) and X(11247)
X(32195) = X(8151)-of-incircle-circles triangle
X(32195) = X(10280)-of-Ursa-minor triangle
X(32195) = X(11247)-of-anti-Aquila triangle
X(32195) = {X(1), X(11193)}-harmonic conjugate of X(11247)


X(32196) = X(5)-OF-REFLECTION TRIANGLE

Barycentrics    (SB+SC)*((17*R^2-2*SA-6*SW)*S^2+(2*SB*SC+4*SW^2-2*SA^2+2*R^4+(-10*SW+3*SA)*R^2)*SA) : :
X(32196) = 3*X(2)-4*X(13365) = X(3)-3*X(7730) = 3*X(51)-2*X(8254) = X(195)-3*X(3060) = 3*X(568)-X(12254) = 4*X(973)-3*X(5946) = 3*X(3060)+X(13423) = X(3519)+2*X(13421) = X(5876)-4*X(11576) = 3*X(5891)-4*X(20584) = 3*X(5946)-2*X(10610) = 2*X(6152)+X(10263) = 4*X(6689)-5*X(15026) = 4*X(10095)-X(12226) = 4*X(13565)-3*X(15067) = X(15801)-4*X(16982)

X(32196) lies on these lines: {2,13365}, {3,7730}, {4,93}, {5,11808}, {51,8254}, {54,143}, {156,195}, {206,576}, {511,6153}, {550,11802}, {568,12254}, {569,973}, {1112,11702}, {1209,6101}, {3518,11597}, {3574,13406}, {3627,10628}, {5446,11563}, {5609,14668}, {5891,20584}, {6102,10116}, {6145,15101}, {6639,12363}, {6689,15026}, {7530,17824}, {7691,13391}, {9019,9977}, {9707,12291}, {9920,12161}, {10095,12226}, {10203,15107}, {10254,12606}, {11441,12280}, {11805,22660}, {12134,14449}, {13565,15067}, {14652,15787}, {21660,22051}

X(32196) = midpoint of X(i) and X(j) for these lines: {i,j}: {195, 13423}, {2888, 6243}, {10263, 13368}, {12280, 12316}
X(32196) = reflection of X(i) in X(j) for these (i,j): (5, 11808), (54, 143), (550, 11802), (5876, 22804), (6101, 1209), (10610, 973), (11702, 1112), (13368, 6152), (15532, 1493), (20424, 5446), (21230, 6153), (21660, 22051), (22804, 11576)
X(32196) = anticomplement of the anticomplement of X(13365)
X(32196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (973, 10610, 5946), (3060, 13423, 195)


X(32197) = X(5)-OF-1st SCHIFFLER TRIANGLE

Barycentrics
2*(b+c)*a^12-5*(b^2+c^2)*a^11-(b+c)*(5*b^2+4*b*c+5*c^2)*a^10+(21*b^4+21*c^4-(5*b^2-34*b*c+5*c^2)*b*c)*a^9-(b+c)*(b^4+c^4-2*(11*b^2-3*b*c+11*c^2)*b*c)*a^8-(34*b^6+34*c^6-(18*b^4+18*c^4-(43*b^2-16*b*c+43*c^2)*b*c)*b*c)*a^7+(b+c)*(14*b^6+14*c^6-(46*b^4+46*c^4-(21*b^2-32*b*c+21*c^2)*b*c)*b*c)*a^6+(26*b^8+26*c^8-(24*b^6+24*c^6-(4*b^2+3*b*c+4*c^2)*(b^2-4*b*c+c^2)*b*c)*b*c)*a^5-2*(b+c)*(8*b^8+8*c^8-(23*b^6+23*c^6-(3*b^4+3*c^4+(14*b^2-3*b*c+14*c^2)*b*c)*b*c)*b*c)*a^4-(9*b^6+9*c^6-(14*b^4+14*c^4-(8*b^2-21*b*c+8*c^2)*b*c)*b*c)*(b^2-c^2)^2*a^3+(b^2-c^2)^3*(b-c)*(7*b^4+7*c^4-(8*b^2+11*b*c+8*c^2)*b*c)*a^2+(b^2-c^2)^3*(b-c)^3*(b^3+c^3)*a-(b^2-c^2)^5*(b-c)^3 : :
X(32197) = 3*X(11218)-X(32055)

X(32197) lies on the line {11218,32055}


X(32198) = X(5)-OF-2nd SCHIFFLER TRIANGLE

Barycentrics
2*(b+c)*a^6-(3*b^2+8*b*c+3*c^2)*a^5-(b+c)*(3*b^2-16*b*c+3*c^2)*a^4+(2*b-c)*(b-2*c)*(3*b^2+8*b*c+3*c^2)*a^3-2*(b+c)*(7*b^2-15*b*c+7*c^2)*b*c*a^2-(b^2-c^2)^2*(3*b^2-7*b*c+3*c^2)*a+(b^2-c^2)^3*(b-c) : :
X(32198) = 3*X(3829)-4*X(6702) = 3*X(4421)-X(6224) = 3*X(5657)-X(22560) = 3*X(11219)-X(11256) = 3*X(11219)+X(12641)

X(32198) lies on these lines: {8,13205}, {9,80}, {11,8256}, {100,32157}, {529,12515}, {952,5450}, {1329,12758}, {1387,10199}, {1484,2802}, {1737,17652}, {1768,32049}, {2771,10915}, {2800,12607}, {2932,12647}, {3035,12740}, {3816,15558}, {3829,6702}, {3880,10265}, {3913,12247}, {4421,6224}, {5657,22560}, {5854,12737}, {6735,17638}, {7701,12751}, {10944,17100}, {11219,11256}, {19914,25438}

X(32198) = midpoint of X(i) and X(j) for these lines: {i,j}: {8, 13205}, {1768, 32049}, {3913, 12247}, {11256, 12641}, {19914, 25438}
X(32198) = reflection of X(i) in X(j) for these (i,j): (100, 32157), (3813, 12619), (13463, 11)
X(32198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8256, 27870, 13463), (11219, 12641, 11256)


X(32199) = X(5)-OF-SODDY TRIANGLE

Barycentrics
7*a^7-5*(b+c)*a^6-2*(4*b^2-9*b*c+4*c^2)*a^5-8*(b^2-c^2)*(b-c)*a^4+(19*b^2+12*b*c+19*c^2)*(b-c)^2*a^3-(b^2-c^2)*(b-c)*(b^2+12*b*c+c^2)*a^2-2*(b^2+c^2)*(b-c)^4*a-2*(b^3+c^3)*(b-c)^4 : :
X(32199) = X(32056)-3*X(32079)

X(32199) lies on the line {32056,32079}


X(32200) = X(5)-OF-2nd INNER-SODDY TRIANGLE

Barycentrics
(a+b+c)*(22*(b+c)*a^8-(47*b^2+42*b*c+47*c^2)*a^7-(b+c)*(27*b^2+61*b*c+27*c^2)*a^6+(117*b^4+117*c^4+(123*b^2+136*b*c+123*c^2)*b*c)*a^5-(b+c)*(43*b^4+43*c^4-152*(b^2-b*c+c^2)*b*c)*a^4-(57*b^4+57*c^4+4*(55*b^2+57*b*c+55*c^2)*b*c)*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(35*b^4+35*c^4-(25*b^2+74*b*c+25*c^2)*b*c)*a^2+(3*b^4+3*c^4+(45*b^2+86*b*c+45*c^2)*b*c)*(b-c)^4*a-(b^2-c^2)*(b-c)^3*(b^2-3*c^2)*(3*b^2-c^2))+2*S*(6*a^8-6*(b+c)*a^7-6*(7*b^2+13*b*c+7*c^2)*a^6+5*(b+c)*(10*b^2-11*b*c+10*c^2)*a^5+2*(21*b^4+21*c^4+(109*b^2+82*b*c+109*c^2)*b*c)*a^4-2*(b+c)*(29*b^4+29*c^4-(15*b^2+61*b*c+15*c^2)*b*c)*a^3-2*(3*b^4+3*c^4+2*(29*b^2+61*b*c+29*c^2)*b*c)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(14*b^4+14*c^4+(9*b^2-68*b*c+9*c^2)*b*c)*a+8*(b^2-c^2)^2*(b-c)^2*b*c) : :

X(32200) lies on these lines: {176,31545}, {942,31541}


X(32201) = X(5)-OF-2nd OUTER-SODDY TRIANGLE

Barycentrics
(a+b+c)*(22*(b+c)*a^8-(47*b^2+42*b*c+47*c^2)*a^7-(b+c)*(27*b^2+61*b*c+27*c^2)*a^6+(117*b^4+117*c^4+(123*b^2+136*b*c+123*c^2)*b*c)*a^5-(b+c)*(43*b^4+43*c^4-152*(b^2-b*c+c^2)*b*c)*a^4-(57*b^4+57*c^4+4*(55*b^2+57*b*c+55*c^2)*b*c)*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(35*b^4+35*c^4-(25*b^2+74*b*c+25*c^2)*b*c)*a^2+(3*b^4+3*c^4+(45*b^2+86*b*c+45*c^2)*b*c)*(b-c)^4*a-(b^2-c^2)*(b-c)^3*(b^2-3*c^2)*(3*b^2-c^2))-2*S*(6*a^8-6*(b+c)*a^7-6*(7*b^2+13*b*c+7*c^2)*a^6+5*(b+c)*(10*b^2-11*b*c+10*c^2)*a^5+2*(21*b^4+21*c^4+(109*b^2+82*b*c+109*c^2)*b*c)*a^4-2*(b+c)*(29*b^4+29*c^4-(15*b^2+61*b*c+15*c^2)*b*c)*a^3-2*(3*b^4+3*c^4+2*(29*b^2+61*b*c+29*c^2)*b*c)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(14*b^4+14*c^4+(9*b^2-68*b*c+9*c^2)*b*c)*a+8*(b^2-c^2)^2*(b-c)^2*b*c) : :

X(32201) lies on these lines: {175,31544}, {13390,31555}


X(32202) = X(5)-OF-INNER-SQUARES TRIANGLE

Barycentrics    (16*R^2-5*SA+5*SW)*S^2-2*(8*R^2-3*SW)*SB*SC+S*(6*S^2-(SB+SC)*(SA-4*SW)) : :
X(32202) = 3*X(11209)+X(31987)

X(32202) lies on the line {11209,31987}

X(32202) = midpoint of X(31987) and X(32059)
X(32202) = {X(11209), X(31987)}-harmonic conjugate of X(32059)


X(32203) = X(5)-OF-OUTER-SQUARES TRIANGLE

Barycentrics    (16*R^2-5*SA+5*SW)*S^2-2*(8*R^2-3*SW)*SB*SC-S*(6*S^2-(SB+SC)*(SA-4*SW)) : :
X(32203) = 3*X(11210)+X(31988)

X(32203) lies on the line {11210,31988}

X(32203) = midpoint of X(31988) and X(32060)
X(32203) = {X(11210), X(31988)}-harmonic conjugate of X(32060)


X(32204) = X(5)-OF-STEINER TRIANGLE

Barycentrics    (3*a^8-8*(b^2+c^2)*a^6+(8*b^4+7*b^2*c^2+8*c^4)*a^4-(b^2+c^2)*(4*b^4-3*b^2*c^2+4*c^4)*a^2+(b^4+c^4)*(b^2-c^2)^2)*(b^2-c^2) : :
X(32204) = X(3)+3*X(11123) = X(4)-9*X(9168) = X(5)-3*X(10190) = 5*X(632)-3*X(10278) = 9*X(1649)-5*X(1656) = 7*X(3523)-3*X(16220) = 7*X(3526)-3*X(8029) = 17*X(3533)-9*X(5466) = X(8151)-3*X(11123) = 3*X(10189)-4*X(16239)

X(32204) lies on these lines: {2,10280}, {3,8151}, {4,9168}, {5,10190}, {140,523}, {195,30219}, {512,5447}, {525,1147}, {550,1499}, {632,10278}, {669,13564}, {1649,1656}, {2501,10018}, {3523,16220}, {3526,8029}, {3533,5466}, {5926,6563}, {10189,16239}

X(32204) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 8151}, {5926, 6563}
X(32204) = reflection of X(10279) in X(140)
X(32204) = anticomplement of X(10280)
X(32204) = {X(3), X(11123)}-harmonic conjugate of X(8151)


X(32205) = X(5)-OF-SUBMEDIAL TRIANGLE

Barycentrics    a^2*((b^2+c^2)*a^6-(3*b^4-2*b^2*c^2+3*c^4)*a^4+(b^2+c^2)*(3*b^4-13*b^2*c^2+3*c^4)*a^2-(b^4-5*b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(32205) = 3*X(2)+X(143) = 9*X(2)-X(6101) = 15*X(2)+X(6243) = 3*X(2)+5*X(15026) = X(3)+15*X(11451) = X(3)-17*X(11465) = X(3)+3*X(13364) = 7*X(5)+X(185) = X(5)-9*X(373) = 5*X(5)+3*X(9730) = 9*X(5)-X(12162) = X(5)+3*X(13363) = 3*X(5)+X(13630) = 11*X(5)-3*X(15030) = 3*X(143)+X(6101) = 5*X(143)-X(6243) = X(143)-5*X(15026) = 2*X(185)+7*X(11017) = X(185)-7*X(12006) = X(185)+14*X(12046) = 9*X(185)+7*X(12162) = 3*X(185)-7*X(13630) = 15*X(373)+X(9730) = 18*X(373)-X(11017) = 9*X(373)+X(12006) = 9*X(373)-2*X(12046) = 3*X(373)+X(13363) = 5*X(6101)+3*X(6243) = X(6101)+15*X(15026) = X(6101)-3*X(32142) = X(6243)+5*X(32142) = 5*X(11451)-X(13364) = 17*X(11465)+3*X(13364) = 5*X(15026)+X(32142)

X(32205) lies on these lines: {2,143}, {3,11451}, {5,113}, {26,17825}, {30,11695}, {49,15018}, {51,632}, {54,5643}, {110,15047}, {140,5446}, {156,5020}, {381,12279}, {389,547}, {511,16239}, {546,5892}, {568,5067}, {1112,6143}, {1154,3628}, {1511,13434}, {1614,15038}, {1656,5889}, {3090,6102}, {3091,32137}, {3411,11624}, {3412,11626}, {3526,5640}, {3530,10110}, {3544,18439}, {3567,5070}, {3589,10020}, {3627,14845}, {3819,14449}, {3845,27355}, {3850,9729}, {3851,11439}, {3853,16836}, {3856,14915}, {3857,10575}, {3859,13474}, {3917,13421}, {5054,9781}, {5055,5876}, {5056,15060}, {5072,10574}, {5079,5890}, {5447,10124}, {5544,7393}, {5562,15699}, {5907,12812}, {5972,8254}, {6000,12811}, {6241,19709}, {6642,32171}, {6689,13365}, {6746,14940}, {7392,32140}, {7486,18436}, {7999,13321}, {9306,32136}, {9813,32155}, {9817,32168}, {9818,32210}, {9825,30522}, {10545,18378}, {10601,32046}, {10625,11539}, {10643,32207}, {10644,32208}, {10961,32169}, {10963,32170}, {11284,12161}, {11444,15703}, {11479,32138}, {11484,32139}, {11812,13348}, {12045,15606}, {12100,13598}, {12834,14627}, {13403,15465}, {13565,14788}, {13861,15805}, {14641,14893}, {14984,25555}, {15022,18435}, {16042,18350}, {16105,30507}, {18379,18420}, {18928,18952}, {19137,19155}, {19188,19211}, {19372,32143}, {32068,32165}

X(32205) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 12006}, {140, 10095}, {143, 32142}, {389, 14128}, {3530, 10110}, {3628, 5462}, {3850, 9729}, {6689, 13365}, {10627, 16982}, {11793, 16881}
X(32205) = reflection of X(i) in X(j) for these (i,j): (5, 12046), (11017, 5), (11592, 140)
X(32205) = complement of X(32142)
X(32205) = X(11017)-of-Johnson triangle
X(32205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 143, 32142), (2, 15026, 143)


X(32206) = X(5)-OF-SYMMEDIAL TRIANGLE

Barycentrics    a^2*(3*(b^2+c^2)*a^6-6*(b^4+b^2*c^2+c^4)*a^4+(b^2+c^2)*(2*b^4-15*b^2*c^2+2*c^4)*a^2+(b^4+c^4)*(b^4-b^2*c^2+c^4)) : :
X(32206) = X(8152)-3*X(11205) = 3*X(11205)+X(31989)

X(32206) lies on these lines: {511,14133}, {1199,8718}, {8152,11205}

X(32206) = midpoint of X(8152) and X(31989)
X(32206) = {X(11205), X(31989)}-harmonic conjugate of X(8152)


X(32207) = X(5)-OF-INNER TRI-EQUILATERAL TRIANGLE

Barycentrics    (SB+SC)*(4*SA*SB*SC+sqrt(3)*S*(S^2+2*R^2*SA-SA^2-2*SB*SC)) : :
X(32207) = X(10661)+3*X(11243) = 3*X(11243)-X(11267)

X(32207) lies on these lines: {3,11452}, {5,21647}, {6,156}, {15,5663}, {16,32171}, {26,17826}, {143,10641}, {1154,10661}, {5318,30522}, {5876,18468}, {5944,18470}, {6101,11420}, {6102,10632}, {7051,32143}, {10634,11591}, {10636,32158}, {10638,32168}, {10643,32205}, {10645,32210}, {11268,30402}, {11408,12161}, {11475,32137}, {11480,32138}, {11485,32139}, {11488,32140}, {11515,32142}, {13561,23302}, {16808,18379}, {18929,18952}, {19190,19211}, {19363,32046}

X(32207) = midpoint of X(10661) and X(11267)
X(32207) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32208), (11452, 11466, 3)


X(32208) = X(5)-OF-OUTER TRI-EQUILATERAL TRIANGLE

Barycentrics    (SB+SC)*(4*SA*SB*SC-sqrt(3)*S*(S^2+2*R^2*SA-SA^2-2*SB*SC)) : :
X(32208) = X(10662)+3*X(11244) = 3*X(11244)-X(11268)

X(32208) lies on these lines: {3,11453}, {5,21648}, {6,156}, {15,32171}, {16,5663}, {26,17827}, {143,10642}, {1154,10662}, {1250,32168}, {5321,30522}, {5876,18470}, {5944,18468}, {6101,11421}, {6102,10633}, {10635,11591}, {10637,32158}, {10644,32205}, {10646,32210}, {11267,30403}, {11409,12161}, {11476,32137}, {11481,32138}, {11486,32139}, {11489,32140}, {11516,32142}, {13561,23303}, {16809,18379}, {18930,18952}, {19191,19211}, {19364,32046}, {19373,32143}

X(32208) = midpoint of X(10662) and X(11268)
X(32208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32207), (11453, 11467, 3)


X(32209) = X(5)-OF-4th TRI-SQUARES TRIANGLE

Barycentrics    2*a^4-15*(b^2+c^2)*a^2+(20*a^2+6*b^2+6*c^2)*S+5*(b^2-c^2)^2 : :
X(32209) = 3*X(13847)-X(13933) = 3*X(13847)+X(13934)

X(32209) lies on these lines: {20,486}, {615,640}, {642,3069}, {6251,13951}, {6290,13961}, {8184,13972}, {8252,13921}, {12123,13939}, {12787,13942}, {12963,13821}

X(32209) = midpoint of X(13933) and X(13934)
X(32209) = X(642)-of-4th tri-squares-central triangle
X(32209) = {X(13847), X(13934)}-harmonic conjugate of X(13933)


X(32210) = X(5)-OF-TRINH TRIANGLE

Barycentrics    a^2*(2*a^8-3*(b^2+c^2)*a^6-(b^2-3*c^2)*(3*b^2-c^2)*a^4+(b^2+c^2)*(7*b^4-13*b^2*c^2+7*c^4)*a^2-(3*b^4+7*b^2*c^2+3*c^4)*(b^2-c^2)^2) : :
X(32210) = 3*X(3)-X(156) = 5*X(3)-X(32139) = X(26)+3*X(10606) = X(64)+3*X(18324) = 3*X(74)+X(15132) = X(156)+3*X(32138) = 5*X(156)-3*X(32139) = 2*X(156)-3*X(32171) = 3*X(376)+X(32140) = X(5448)-3*X(10193) = 2*X(5498)-3*X(10193) = X(7689)+3*X(11204) = 3*X(7689)+X(13346) = 5*X(8567)-X(12084) = 15*X(8567)+X(17834) = 3*X(11204)-X(11250) = 9*X(11204)-X(13346) = 3*X(11250)-X(13346) = 3*X(12084)+X(17834) = 5*X(32138)+X(32139) = 2*X(32138)+X(32171) = 2*X(32139)-5*X(32171)

X(32210) lies on these lines: {2,3521}, {3,74}, {5,21663}, {24,32137}, {26,10606}, {30,5449}, {35,32143}, {36,32168}, {64,18324}, {143,378}, {343,550}, {376,2888}, {511,32155}, {569,1204}, {1154,7689}, {1192,31861}, {1539,16868}, {1620,11472}, {1658,3357}, {1994,3520}, {2071,6101}, {2777,13406}, {2937,13445}, {3581,12086}, {3627,32110}, {3631,14810}, {5012,18364}, {5092,19155}, {5448,5498}, {5621,15074}, {5894,15761}, {5946,14130}, {6000,15331}, {6200,32169}, {6396,32170}, {6642,11017}, {7526,10601}, {7527,15026}, {7555,14641}, {7575,11381}, {7688,32158}, {7728,14940}, {8567,12084}, {9818,32205}, {10020,15311}, {10095,11438}, {10201,20427}, {10224,25563}, {10226,13754}, {10249,11255}, {10264,21659}, {10540,17506}, {10605,32046}, {10645,32207}, {10646,32208}, {11410,12161}, {11430,32136}, {11479,12046}, {11598,19506}, {12107,14915}, {12162,15646}, {12226,13340}, {13371,23328}, {13567,15807}, {15060,22467}, {15332,18400}, {18377,23329}, {18439,21844}, {18562,23294}, {18565,23293}, {18931,18952}, {19192,19211}

X(32210) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32138}, {1658, 3357}, {5894, 15761}, {7689, 11250}
X(32210) = reflection of X(i) in X(j) for these (i,j): (5448, 5498), (10224, 25563), (13406, 20191), (18379, 13561), (19155, 5092), (32171, 3)
X(32210) = X(32171)-of-ABC-X3 reflections triangle
X(32210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 74, 13491), (3, 11468, 12041), (3, 12111, 1511)


X(32211) = X(5)-OF-X-PARABOLA-TANGENTIAL TRIANGLE

Barycentrics
2*a^16-6*(b^2+c^2)*a^14+3*(b^4+8*b^2*c^2+c^4)*a^12+5*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*a^10+(b^8+c^8-4*(6*b^4-19*b^2*c^2+6*c^4)*b^2*c^2)*a^8-2*(b^2+c^2)*(7*b^8+7*c^8-(34*b^4-57*b^2*c^2+34*c^4)*b^2*c^2)*a^6+(11*b^12+11*c^12-2*(13*b^8+13*c^8+(3*b^4-22*b^2*c^2+3*c^4)*b^2*c^2)*b^2*c^2)*a^4-(b^4-c^4)*(b^2-c^2)*(b^8+c^8+(5*b^4-13*b^2*c^2+5*c^4)*b^2*c^2)*a^2-(b^4-b^2*c^2+c^4)*(b^2-c^2)^6 : :
X(32211) = 3*X(8029)+X(31990) = 3*X(8029)-X(32061)

X(32211) lies on the line {8029,31990}

X(32211) = midpoint of X(31990) and X(32061)
X(32211) = {X(8029), X(31990)}-harmonic conjugate of X(32061)


X(32212) = X(5)-OF-YFF CONTACT TRIANGLE

Barycentrics    (a^3+2*(b+c)*a^2-(2*b^2+7*b*c+2*c^2)*a+(b+c)*(b^2+b*c+c^2))*(b-c) : :
X(32212) = X(1)-3*X(10196) = X(8)+3*X(6546) = X(145)-9*X(31992) = 5*X(1698)-3*X(21204) = 5*X(3616)-9*X(6544) = X(5592)-3*X(6546) = 3*X(6545)-7*X(9780) = 9*X(14475)-13*X(19877)

X(32212) lies on these lines: {1,10196}, {8,5592}, {10,514}, {40,3667}, {145,31992}, {513,4662}, {1698,21204}, {3239,19582}, {3616,6544}, {4528,28521}, {6545,9780}, {14077,31792}, {14475,19877}, {19963,21211}, {20001,21143}, {21198,28155}, {21201,23757}

X(32212) = midpoint of X(8) and X(5592)
X(32212) = {X(8), X(6546)}-harmonic conjugate of X(5592)


X(32213) = X(5)-OF-INNER-YFF TANGENTS TRIANGLE

Barycentrics    a^4*(b^2+8*b*c+c^2)*(a-b-c)-2*(b^4+c^4+2*(b^2-4*b*c+c^2)*b*c)*a^3+2*(b^2-c^2)*(b-c)*(b^2+5*b*c+c^2)*a^2+(b^2-c^2)^2*(b^2-4*b*c+c^2)*a-(b^2-c^2)^3*(b-c) : :
X(32213) = X(119)-3*X(10956) = 4*X(5719)-3*X(10283) = 2*X(5901)-3*X(17718) = 3*X(10056)-X(22758) = X(10679)-3*X(11239) = 3*X(11239)+X(12115) = X(13109)+3*X(22731)

X(32213) lies on these lines: {1,5}, {3,10528}, {4,12000}, {10,13373}, {26,10834}, {30,10679}, {56,15867}, {140,956}, {145,6842}, {381,10596}, {442,12645}, {518,5690}, {546,10531}, {549,10269}, {550,11248}, {632,26364}, {912,31397}, {1056,6911}, {1329,15178}, {1385,12607}, {1532,10247}, {1656,10586}, {2077,8703}, {3421,6883}, {3564,12430}, {3621,6937}, {3623,6941}, {3627,6256}, {3845,26333}, {3871,13199}, {5554,8728}, {5840,25439}, {5844,6907}, {5874,10930}, {5875,10929}, {5885,8256}, {6735,10202}, {6756,11400}, {6767,6929}, {6831,18526}, {6834,12001}, {6863,10530}, {6882,7967}, {6959,7373}, {7491,20060}, {7680,28204}, {7715,26378}, {8666,31659}, {8727,28224}, {10056,22758}, {10246,17757}, {10386,26358}, {10532,18518}, {10599,18544}, {10680,10786}, {10803,32134}, {10965,15171}, {11112,12331}, {11509,18990}, {11881,32146}, {11882,32147}, {11914,32162}, {11929,12116}, {11955,32177}, {11956,32178}, {12189,13112}, {12513,26487}, {12608,22791}, {12703,28174}, {12905,13121}, {13104,22931}, {13109,22731}, {13906,13925}, {13964,13993}, {18242,24680}, {19047,19116}, {19048,19117}, {21075,31838}, {22768,32153}, {24927,27385}

X(32213) = midpoint of X(i) and X(j) for these lines: {i,j}: {10679, 12115}, {12905, 13217}
X(32213) = reflection of X(i) in X(j) for these (i,j): (5, 495), (956, 140)
X(32213) = X(10942)-of-inner-Yff triangle
X(32213) = X(10943)-of-1st Johnson-Yff triangle
X(32213) = outer-Yff-to-inner-Yff similarity image of X(5)
X(32213) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 10942, 5), (1, 10958, 496), (5, 1483, 32214)


X(32214) = X(5)-OF-OUTER-YFF TANGENTS TRIANGLE

Barycentrics    a^4*(b^2-8*b*c+c^2)*(a-b-c)-2*(b^4+c^4-4*(b-c)^2*b*c)*a^3+2*(b^2-c^2)*(b-c)*(b^2-3*b*c+c^2)*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c) : :
X(32214) = 3*X(5886)-X(17857) = 3*X(10072)-X(11499) = X(10680)-3*X(11240) = 3*X(10959)-X(26470) = 3*X(11240)+X(12116) = X(13110)+3*X(22732)

X(32214) lies on these lines: {1,5}, {3,10529}, {4,12001}, {26,10835}, {30,10680}, {55,15868}, {140,5687}, {145,6882}, {381,10597}, {546,10532}, {549,4421}, {550,11249}, {632,26363}, {912,12053}, {946,3892}, {1058,3560}, {1385,3813}, {1532,18526}, {1656,10587}, {1898,30384}, {2886,15178}, {3434,16203}, {3564,12431}, {3621,6963}, {3622,6881}, {3623,6830}, {3655,15908}, {3845,26332}, {3880,5690}, {3913,26492}, {4187,12645}, {4847,31838}, {5770,9785}, {5844,6922}, {5874,10932}, {5875,10931}, {5884,21630}, {6001,22791}, {6713,8715}, {6756,11401}, {6767,6862}, {6831,10247}, {6833,12000}, {6841,10595}, {6842,7967}, {6911,14986}, {6914,15172}, {6917,7373}, {6958,10530}, {6968,18545}, {7681,28204}, {7715,26377}, {8703,11012}, {10072,11499}, {10085,12699}, {10246,24390}, {10386,26357}, {10531,18519}, {10598,18542}, {10679,10785}, {10804,32134}, {10879,32151}, {10902,15712}, {10966,15171}, {11510,15325}, {11883,32146}, {11884,32147}, {11915,32162}, {11928,12115}, {11957,32177}, {11958,32178}, {12190,13113}, {12331,13747}, {12558,13464}, {12704,28174}, {12906,13122}, {13106,22932}, {13107,22887}, {13110,22732}, {13607,24387}, {13907,13925}, {13965,13993}, {16216,21625}, {18967,18990}, {19049,19116}, {19050,19117}, {20418,26285}

X(32214) = midpoint of X(i) and X(j) for these lines: {i,j}: {10073, 12737}, {10085, 12699}, {10680, 12116}, {12906, 13218}
X(32214) = reflection of X(i) in X(j) for these (i,j): (5, 496), (5687, 140)
X(32214) = X(10942)-of-2nd Johnson-Yff triangle
X(32214) = X(10943)-of-outer-Yff triangle
X(32214) = inner-Yff-to-outer-Yff similarity image of X(5)
X(32214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 1483, 32213), (11, 10942, 5), (1483, 1484, 5)


X(32215) = X(5)-OF-YIU TRIANGLE

Barycentrics    (R^2*(21*R^2-2*SA-12*SW)-2*SB*SC+2*SW^2)*(S^2+SB*SC) : :
X(32215) = X(8154)-3*X(32084) = X(31991)+3*X(32084)

X(32215) lies on these lines: {5,15869}, {30,30685}, {6750,20424}, {8154,31991}

X(32215) = midpoint of X(8154) and X(31991)
X(32215) = {X(31991), X(32084)}-harmonic conjugate of X(8154)


X(32216) = COMPLEMENT OF X(26255)

Barycentrics    a^6-4 a^4 b^2-a^2 b^4+4 b^6-4 a^4 c^2+18 a^2 b^2 c^2-4 b^4 c^2-a^2 c^4-4 b^2 c^4+4 c^6 : :
Barycentrics    (36 R^2-5 SW)S^2 -3 SB SC SW : :

As a point on the Euler line, X(32216) has Shinagawa coefficients [4 E - 5 F, -3 E -3 F].

See Kadir Altintas and Ercole Suppa, Hyacinthos 28993.

X(32216) lies on these lines: {2,3}, {6,13857}, {115,21448}, {125,599}, {126,3014}, {524,26869}, {542,6090}, {2393,5650}, {2549,24855}, {2790,23234}, {5024,9745}, {5642,14982}, {6054,9717}, {7998,14984}, {9140,15066}, {9155,9759}, {11064,11179}, {15059,21766}, {15080,20772}, {15131,19153}, {16187,25561}, {19136,22112}

X(32216) = complement of X(26255)
X(32216) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {2,376,468}, {2,381,11284}, {2,858,381}, {2,10989,1995}, {2,16063,7426}, {381,3534,18325}, {427,468,6623}, {549,5159,2}, {1368,5159,18531}, {1995,10989,3830}, {7426,16063,3534}, {11284,21312,25}

leftri

Points associated with the Walsmith triangle: X(32217)-X(32229)

rightri

This preamble and centers X(32217)-X(32229) were contributed by Peter Moses, April 27, 2019.

For a definition of the Walsmith triangle, see K1091 (Walsmith Focal Cubic). See also the preamble just before X(32110).

The appearance of {i,j} in the following list means that X(j) = X(i)-of-Walsmith-triangle: {2,7426}, {4,32113}, {30,524}, {370,7426}, {523,1499}, {1144,7426}, {3413,542}, {3414,690}

The circumcircle of the Walsmith triangle passes through X(i) for i = 6, 23, 1316, 32221, 32222, 32224. This circle meets the Walsmith hyperbola and the Brocard circle in X(6). See X(32443).


X(32217) = X(3)-OF-WALSMITH-TRIANGLE

Barycentrics    a^2*(2*a^6 - 2*a^2*b^4 + 4*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4) : :
X(32217) = 2 X[23] + X[15826],X[110] - 3 X[18374],3 X[186] - X[1350],X[576] + 2 X[12105],X[691] - 3 X[1691],X[1351] + 3 X[2070],3 X[1495] + X[32127],5 X[3618] - X[5189],3 X[5085] - X[7464],3 X[7426] - X[32113],X[7574] - 3 X[14561],X[8550] + 2 X[16619],2 X[14810] - 3 X[15646]

X(32217) is the common radical trace of the harmonic circles of pairs of the Ehrmann circles. (Randy Hutson, June 7, 2019)

X(32217) lies on these lines: {6, 23}, {30, 182}, {110, 524}, {141, 468}, {184, 8584}, {186, 1350}, {206, 3629}, {237, 5467}, {265, 1177}, {511, 1511}, {523, 5027}, {576, 12105}, {691, 729}, {858, 3589}, {895, 12367}, {1112, 9019}, {1176, 6329}, {1316, 6322}, {1351, 2070}, {1428, 7286}, {1495, 2854}, {1513, 24975}, {1576, 2080}, {1976, 6094}, {2030, 28662}, {2330, 5160}, {2393, 11800}, {2781, 32110}, {3098, 18571}, {3564, 25338}, {3580, 27085}, {3581, 9970}, {3618, 5189}, {5085, 7464}, {5097, 11649}, {5159, 19126}, {5201, 9407}, {7574, 14561}, {8550, 16619}, {9306, 22165}, {9544, 15534}, {9973, 11443}, {10113, 11645}, {10295, 15472}, {10297, 19131}, {10510, 15107}, {11216, 20850}, {11692, 15516}, {12039, 16776}, {12112, 16010}, {14810, 15646}, {15118, 29012}, {16316, 19558}, {18323, 19129}, {18572, 19130}, {19118, 21284}, {23327, 31726}

X(32217) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 23}, {895, 12367}, {3581, 9970}, {10510, 15107}, {12112, 16010}
X(32217) = reflection of X(i) in X(j) for these lines: {i,j}: {141, 468}, {858, 3589}, {3098, 18571}, {15826, 6}, {18572, 19130}
X(32217) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 6800, 8546}, {19127, 19136, 597}
X(32217) = isogonal of the isotomic of X(26276)
X(32217) = crossdifference of every pair of points on line {3094, 3906}
X(32217) = barycentric product X(6)*X(26276)
X(32217) = barycentric quotient X(26276) / X(76)


X(32218) = X(5)-OF-WALSMITH-TRIANGLE

Barycentrics    2*a^8 + 3*a^6*b^2 - 3*a^4*b^4 - 3*a^2*b^6 + b^8 + 3*a^6*c^2 + 2*a^2*b^4*c^2 - 3*a^4*c^4 + 2*a^2*b^2*c^4 - 2*b^4*c^4 - 3*a^2*c^6 + c^8 : :
X(32218) = X[1352] + 3 X[2070],X[3448] + 3 X[19596],7 X[3619] + X[20063],5 X[3763] - X[5189],3 X[7426] + X[32113],X[7464] - 3 X[21167],3 X[10096] - X[18583],3 X[18374] - X[25329]

X(32218) lies on these lines: {23, 141}, {30, 14810}, {110, 524}, {373, 468}, {511, 10272}, {523, 5113}, {755, 1287}, {858, 5888}, {1352, 2070}, {1495, 8262}, {1503, 7575}, {3448, 19596}, {3619, 20063}, {3631, 13562}, {3763, 5189}, {5092, 22249}, {5972, 9019}, {6329, 15826}, {6698, 29012}, {7464, 21167}, {10096, 11649}, {11594, 16321}, {11799, 29181}, {12367, 25328}, {15067, 16619}

X(32218) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 141}, {1495, 8262}, {12367, 25328}
X(32218) = reflection of X(i) in X(j) for these lines: {i,j}: {3589, 468}, {5092, 22249}, {15826, 6329}


X(32219) = X(6)-OF-WALSMITH-TRIANGLE

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

X(32219) lies on these lines: {1495, 5663}, {8588, 19156}


X(32220) = X(20)-OF-WALSMITH-TRIANGLE

Barycentrics    4*a^8 - 3*a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 - 3*a^6*c^2 + 12*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 + 2*b^4*c^4 + 3*a^2*c^6 - c^8 : :
X(32220) = X[323] - 3 X[25321],3 X[403] - 2 X[1352],3 X[2072] - 4 X[18583],5 X[3618] - 4 X[5159],3 X[5032] - X[10989],3 X[5050] - 2 X[15122],3 X[5093] - X[7574],3 X[7426] - 2 X[32113],X[7464] - 3 X[14912],2 X[10297] - 3 X[14853]

X(32220) lies on these lines: {6, 858}, {23, 159}, {30, 1351}, {69, 468}, {110, 524}, {323, 25321}, {399, 3564}, {403, 1352}, {511, 1986}, {542, 32111}, {576, 12022}, {895, 1503}, {1513, 2407}, {2072, 18583}, {2366, 10423}, {3618, 5159}, {3629, 8705}, {5032, 10989}, {5050, 15122}, {5093, 7574}, {5486, 6800}, {7391, 11216}, {7464, 14912}, {8550, 15072}, {8681, 24981}, {9035, 32120}, {10169, 31074}, {10297, 14853}, {11064, 15471}, {18323, 21850}, {19504, 22151}

X(32220) = midpoint of X(23) and X(193)
X(32220) = reflection of X(i) in X(j) for these lines: {i,j}: {69, 468}, {858, 6}, {11064, 15471}, {18323, 21850}
X(32220) = crossdifference of every pair of points on line {5028, 7652}


X(32221) = X(99)-OF-WALSMITH-TRIANGLE

Barycentrics    2*a^14 - 4*a^12*b^2 + 5*a^10*b^4 - 10*a^8*b^6 + 11*a^6*b^8 - 4*a^4*b^10 - 4*a^12*c^2 + 10*a^8*b^4*c^2 - 6*a^6*b^6*c^2 - 3*a^4*b^8*c^2 + 7*a^2*b^10*c^2 - 2*b^12*c^2 + 5*a^10*c^4 + 10*a^8*b^2*c^4 - 20*a^6*b^4*c^4 + 11*a^4*b^6*c^4 - 23*a^2*b^8*c^4 + 7*b^10*c^4 - 10*a^8*c^6 - 6*a^6*b^2*c^6 + 11*a^4*b^4*c^6 + 30*a^2*b^6*c^6 - 5*b^8*c^6 + 11*a^6*c^8 - 3*a^4*b^2*c^8 - 23*a^2*b^4*c^8 - 5*b^6*c^8 - 4*a^4*c^10 + 7*a^2*b^2*c^10 + 7*b^4*c^10 - 2*b^2*c^12 : :

X(32221) lies on these lines: {6, 598}, {110, 1316}, {542, 2682}, {543, 14999}, {9144, 14559}


X(32222) = X(110)-OF-WALSMITH-TRIANGLE

Barycentrics    a^2*(2*a^16 - 8*a^14*b^2 - a^12*b^4 + 21*a^10*b^6 - 6*a^8*b^8 - 18*a^6*b^10 + 7*a^4*b^12 + 5*a^2*b^14 - 2*b^16 - 8*a^14*c^2 + 44*a^12*b^2*c^2 - 41*a^10*b^4*c^2 - 58*a^8*b^6*c^2 + 93*a^6*b^8*c^2 + a^4*b^10*c^2 - 44*a^2*b^12*c^2 + 13*b^14*c^2 - a^12*c^4 - 41*a^10*b^2*c^4 + 118*a^8*b^4*c^4 - 51*a^6*b^6*c^4 - 140*a^4*b^8*c^4 + 130*a^2*b^10*c^4 - 23*b^12*c^4 + 21*a^10*c^6 - 58*a^8*b^2*c^6 - 51*a^6*b^4*c^6 + 230*a^4*b^6*c^6 - 87*a^2*b^8*c^6 - 13*b^10*c^6 - 6*a^8*c^8 + 93*a^6*b^2*c^8 - 140*a^4*b^4*c^8 - 87*a^2*b^6*c^8 + 50*b^8*c^8 - 18*a^6*c^10 + a^4*b^2*c^10 + 130*a^2*b^4*c^10 - 13*b^6*c^10 + 7*a^4*c^12 - 44*a^2*b^2*c^12 - 23*b^4*c^12 + 5*a^2*c^14 + 13*b^2*c^14 - 2*c^16) : :

X(32222) lies on these lines: {6, 110}, {23, 2780}, {543, 7471}, {14688, 16165}, {15329, 15566}


X(32223) = MIDPOINT OF X(23) AND X(125)

Barycentrics    2*a^6 - 3*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 - b^4*c^2 - 3*a^2*c^4 - b^2*c^4 + c^6 : :
X(32223) = 3 X[2] + X[15107],3 X[186] - X[16163],X[265] + 3 X[2070],X[323] - 3 X[5642],X[323] + 3 X[15360],3 X[403] - X[1531],3 X[468] - X[11064],X[1495] - 3 X[7426],X[1539] - 3 X[11563],X[3580] + 3 X[7426],X[5189] - 5 X[15059],3 X[5972] - 2 X[11064],X[7574] - 3 X[23515],3 X[10096] - X[10272],X[12317] + 3 X[14157],2 X[16619] + X[20417]

X(32223) lies on these lines: {2, 3098}, {6, 21970}, {23, 125}, {25, 3818}, {30, 6699}, {51, 14389}, {69, 1974}, {74, 1533}, {110, 5965}, {113, 3581}, {140, 13598}, {143, 12242}, {182, 7493}, {184, 11225}, {186, 16163}, {265, 2070}, {316, 419}, {323, 5642}, {373, 7495}, {381, 31860}, {382, 25563}, {389, 13383}, {403, 1531}, {436, 32002}, {468, 511}, {476, 14595}, {541, 15361}, {542, 1495}, {575, 13394}, {826, 4142}, {858, 6723}, {1154, 10096}, {1209, 13621}, {1352, 4232}, {1539, 11563}, {1648, 8627}, {1658, 13403}, {1691, 6388}, {1853, 20850}, {1995, 24206}, {2777, 11799}, {2917, 22550}, {3147, 13346}, {3167, 6144}, {3231, 10418}, {3564, 15448}, {3589, 5943}, {3627, 20191}, {3629, 10192}, {3763, 5020}, {3819, 6677}, {4240, 14918}, {4846, 11438}, {5012, 32068}, {5112, 23698}, {5159, 29181}, {5189, 15059}, {5446, 10020}, {5449, 13419}, {5640, 25555}, {5663, 25338}, {5892, 25337}, {5907, 21841}, {6053, 13754}, {6292, 21513}, {6688, 7499}, {6689, 10095}, {6719, 22103}, {6759, 18917}, {7517, 20299}, {7542, 10110}, {7574, 23515}, {7575, 17702}, {7691, 21451}, {7820, 11328}, {8705, 15118}, {9714, 18381}, {9909, 26958}, {10112, 10282}, {10114, 20773}, {10154, 13567}, {10182, 13352}, {10201, 18388}, {11178, 26255}, {12317, 14157}, {12897, 15331}, {13163, 13565}, {13391, 14156}, {14070, 18390}, {14810, 30739}, {14915, 16619}, {15644, 16238}, {16111, 18325}, {16618, 16836}, {18534, 23329}, {21230, 30551}, {21849, 23292}

X(32223) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 125}, {74, 1533}, {113, 3581}, {1495, 3580}, {5642, 15360}, {11799, 32110}, {16111, 18325}
X(32223) = reflection of X(i) in X(j) for these lines: {i,j}: {858, 6723}, {5972, 468}
X(32223) = reflection of X(22104) in the orthic axis
X(32223) = X(i)-complementary conjugate of X(j) for these (i,j): {74, 21249}, {82, 113}, {2159, 6292}, {2349, 21248}
X(32223) = crosspoint of X(476) and X(18020)
X(32223) = crosssum of X(526) and X(20975)
X(32223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 20193, 18874}, {3580, 7426, 1495}


X(32224) = X(6)X(30)∩X(23)X(385)

Barycentrics    a^8 + a^6*b^2 - 2*a^4*b^4 + a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6 : :
X(32224) = 3 X[7426] - 2 X[16321]

X(32223) lies on these lines: {6, 30}, {23, 385}, {183, 7426}, {186, 8266}, {468, 15271}, {858, 11174}, {1316, 6322}, {2452, 8705}, {3329, 10989}, {5467, 11676}, {8177, 9462}, {8667, 16312}, {19221, 20897}

X(32224) = reflection of X(858) and X(16324)
X(32224) = crossdifference of every pair of points on line {39, 8675}


X(32225) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH AND 4th BROCARD

Barycentrics    (2*a^2 - b^2 - c^2)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 4*b^2*c^2 - 2*c^4) : :
X(32224) = X[381] - 3 X[15362],4 X[468] - X[3292],X[1495] + 2 X[3580],X[1531] + 2 X[3581],X[1531] - 6 X[15362],X[3581] + 3 X[15362],X[13857] + 2 X[15360],4 X[15448] - X[24981],X[16003] + 2 X[16619],2 X[19510] - 3 X[21358],2 X[32113] + X[32127]

X(32225) lies on these lines: {2, 51}, {5, 20192}, {6, 30516}, {23, 9140}, {30, 125}, {187, 1648}, {230, 6791}, {376, 18390}, {381, 1531}, {389, 7552}, {468, 524}, {541, 11799}, {542, 1495}, {543, 5112}, {549, 10564}, {597, 16789}, {599, 5651}, {858, 19924}, {1209, 23410}, {1316, 3849}, {1352, 26255}, {1995, 11178}, {2030, 6792}, {3066, 5055}, {3906, 9208}, {4232, 11180}, {5054, 22112}, {5449, 7540}, {5648, 9027}, {5655, 13754}, {6090, 15533}, {7493, 11179}, {7495, 10168}, {7505, 14531}, {9019, 12099}, {9169, 9181}, {10201, 14831}, {10418, 15993}, {10989, 15107}, {11284, 19510}, {11317, 13378}, {12824, 25566}, {13567, 22352}, {14002, 18553}, {14915, 20126}, {15004, 18449}, {15331, 18555}, {15448, 24981}, {15682, 18376}, {16003, 16619}, {26958, 31152}, {31174, 31953}, {32113, 32127}

X(32225) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 15360}, {23, 9140}, {381, 3581}, {3580, 7426}, {10989, 15107}
X(32225) = reflection of X(i) in X(j) for these lines: {i,j}: {1495, 7426}, {1531, 381}, {3292, 5642}, {5642, 468}, {10564, 549}, {13857, 2}, {32110, 15361}
X(32225) = {X(3581),X(15362)}-harmonic conjugate of X(381),X(897)-isoconjugate of X(3431)
X(32225) = crossdifference of every pair of points on line {353, 3288}
X(32225) = X(2)-of-pedal-triangle-of-X(23)
X(32225) = barycentric product X(381) and X(524)
X(32225) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {187, 3431}, {381, 671}, {5158, 895}, {18487, 9214}


X(32226) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH AND REFLECTION TRIANGLE

Barycentrics    a^2*(2*a^10 - 5*a^8*b^2 + 2*a^6*b^4 + 4*a^4*b^6 - 4*a^2*b^8 + b^10 - 5*a^8*c^2 + 10*a^6*b^2*c^2 - 7*a^4*b^4*c^2 + 3*a^2*b^6*c^2 - b^8*c^2 + 2*a^6*c^4 - 7*a^4*b^2*c^4 + 2*a^2*b^4*c^4 + 4*a^4*c^6 + 3*a^2*b^2*c^6 - 4*a^2*c^8 - b^2*c^8 + c^10) : :
X(32226) = 5 X[54] - X[74],X[74] + 5 X[2914],5 X[1493] + X[5609],X[5609] - 5 X[11702],5 X[12307] - 13 X[15042],X[12308] + 5 X[15089],7 X[15020] + 5 X[15801]

X(32226) lies on these lines: {49, 11557}, {51, 110}, {54, 74}, {113, 137}, {125, 11245}, {184, 10117}, {195, 568}, {323, 27866}, {373, 9977}, {389, 3043}, {399, 11424}, {539, 32123}, {575, 15059}, {578, 21650}, {826, 32120}, {1112, 1495}, {1154, 14708}, {1594, 10114}, {1614, 11807}, {1986, 13367}, {2904, 9707}, {3292, 3580}, {3448, 7703}, {3569, 14397}, {5095, 21637}, {5562, 12228}, {5663, 15739}, {6467, 13248}, {6593, 32114}, {7699, 18390}, {10264, 32136}, {10610, 25487}, {11003, 13201}, {11381, 15472}, {11402, 17847}, {11472, 12308}, {11806, 15087}, {12161, 21649}, {12174, 17824}, {12254, 22802}, {12307, 15042}, {12893, 14831}, {13171, 17809}, {13472, 18912}, {14531, 22109}, {15020, 15801}, {18400, 32111}

X(32226) = midpoint of X(i) and X(j) for these lines: {i,j}: {54, 2914}, {195, 11597}, {1493, 11702}, {3574, 14049}
X(32226) = crossdifference of every pair of points on line {3448, 13527}
X(32226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 1994, 11800}, {184, 19504, 13417}, {389, 3043, 17701}, {12227, 15463, 185}


X(32227) = X(2)X(265)∩X(6)X(5642)

Barycentrics    3*a^12 - 5*a^10*b^2 - 3*a^8*b^4 + 8*a^6*b^6 - a^4*b^8 - 3*a^2*b^10 + b^12 - 5*a^10*c^2 + 9*a^8*b^2*c^2 - 2*a^6*b^4*c^2 - 11*a^4*b^6*c^2 + 11*a^2*b^8*c^2 - 2*b^10*c^2 - 3*a^8*c^4 - 2*a^6*b^2*c^4 + 16*a^4*b^4*c^4 - 8*a^2*b^6*c^4 - b^8*c^4 + 8*a^6*c^6 - 11*a^4*b^2*c^6 - 8*a^2*b^4*c^6 + 4*b^6*c^6 - a^4*c^8 + 11*a^2*b^2*c^8 - b^4*c^8 - 3*a^2*c^10 - 2*b^2*c^10 + c^12 : :

X(32227) lies on these lines: {2, 265}, {6, 5642}, {22, 20127}, {23, 7728}, {25, 113}, {110, 468}, {125, 5085}, {427, 10733}, {542, 26864}, {858, 12121}, {1495, 14982}, {1986, 6353}, {1995, 14643}, {3581, 5655}, {3618, 12099}, {5094, 17702}, {5181, 6090}, {5523, 15144}, {5663, 7493}, {5972, 11284}, {6676, 10264}, {6677, 12228}, {7484, 19457}, {7495, 15061}, {11579, 13394}, {12022, 15034}, {12827, 18440}, {12828, 19118}, {12893, 21284}, {14852, 30714}, {15035, 30739}, {16042, 25714}, {16163, 31152}


X(32228) = X(30)X(511)∩X(74)X(6325)

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

X(32228) lies on these lines: {30,511}, {74,6325}, {110,6236}, {1649,9126}, {3569,6032}, {9184,11568}, {9191,16235}, {9829,19902}, {10097,11564}, {10163,24284}, {10294,11215}, {13241,20404}

X(32228) = isogonal conjugate of X(32229)
X(32228) = crossdifference of every pair of points on line {6, 16510}


X(32229) = ISOGONAL CONJUGATE OF X(32228)

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

X(32229) lies on the circumcircle and these lines: {30,6325}, {74,8705}, {111,7575}, {381,2770}, {523,6236}, {2373,10296}, {7464,14388}, {10102,14002}

X(32229) = reflection of X(6236) in the Euler line
X(32229) = isogonal conjugate of X(32228)
X(32229) = trilinear pole of line {6, 16510}


X(32230) = X(30)X(250)∩X(107)X(523)

Barycentrics    (a - b)^2*(a + b)^2*(a - c)^2*(a + c)^2*(a^2 + b^2 - c^2)^3*(a^2 - b^2 + c^2)^3 : :
Barycentrics    (tan^3 A)/(b^2 - c^2)^2 : :
X(32230) = 2X[107]+X[15459]

Line X(107)X(112) (the trilinear polar of X(32230)) is the locus of the trilinear pole of the tangent at P to hyperbola {{A,B,C,X(4),P}}, as P moves on the van Aubel line. Line X(107)X(112) is also the tangent to conic {{A,B,C,X(107),X(648)}} (the circumconic centered at X(1249)) at X(107). (Randy Hutson, June 7, 2019)

X(32230) lies on K1097 and these lines:{30,250}, {107,523}, {450,3260}, {648,8057}, {685,15352}, {1093,14254}, {1503,1559}, {1971,1990}, {2404,2409}, {2489,20031}, {6524,9214}, {16813,23286}, {23692,24000}

X(32230) = isogonal conjugate of X(2972)
X(32230) = polar conjugate of X(15526)
X(32230) = isotomic of the polar conjugate of X(23590)
X(32230) = polar conjugate of the isotomic of X(23582)
X(32230) = polar conjugate of the isogonal of X(23964)
X(32230) = X(92)-isoconjugate of X(35071)
X(32230) = complement of anticomplementary conjugate of X(35360)
X(32230) = X(i)-cross conjugate of X(j) for these (i,j): {{4, 107}, {6, 16813}, {133, 4240}, {184, 112}, {393, 15352}, {1249, 648}, {1614, 933}, {1990, 15459}, {6524, 6529}, {6759, 110}, {8779, 2966}, {9833, 925}, {11206, 99}, {14157, 1304}, {15262, 687}, {18400, 476}, {18685, 6335}, {23964, 23582}, {26883, 1301}, {31383, 1289}}
X(32230) = X(i)-isoconjugate of X(j) for these (i,j): {{1, 2972}, {3, 2632}, {25, 24020}, {48, 15526}, {63, 3269}, {115, 6507}, {122, 19614}, {125, 255}, {163, 23616}, {184, 17879}, {201, 1364}, {212, 1367}, {228, 17216}, {244, 4158}, {273, 7065}, {318, 1363}, {326, 20975}, {338, 4100}, {394, 3708}, {520, 656}, {525, 822}, {577, 20902}, {603, 7068}, {647, 24018}, {756, 7215}, {798, 4143}, {810, 3265}, {1092, 1109}, {1102, 3124}, {1425, 24031}, {1826, 16730}, {1973, 23974}, {2638, 6356}, {2643, 3964}, {2968, 7138}, {3682, 18210}, {3990, 4466}, {4064, 23224}, {4575, 5489}, {7004, 7066}, {18604, 21046}, {23606, 23994}}
X(32230) = cevapoint of X(i) and X(j) for these (i,j): {{4, 107}, {20, 110}, {112, 184}, {648, 17907}, {6524, 6529}}
X(32230) = trilinear pole of line {107, 112}
X(32230) = barycentric product X(i)*X(j) for these lines: {i,j}: {{4, 23582}, {19, 23999}, {63, 24021}, {69, 23590}, {92, 24000}, {99, 6529}, {107, 648}, {110, 15352}, {112, 6528}, {162, 823}, {249, 1093}, {250, 2052}, {264, 23964}, {304, 24022}, {305, 23975}, {393, 18020}, {811, 24019}, {877, 20031}, {1101, 6521}, {2326, 24032}, {4240, 15459}, {4590, 6524}, {6520, 24041}, {15384, 15466}}
X(32230) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {{4, 15526}, {6, 2972}, {19, 2632}, {25, 3269}, {27, 17216}, {63, 24020}, {69, 23974}, {92, 17879}, {99, 4143}, {107, 525}, {112, 520}, {158, 20902}, {162, 24018}, {249, 3964}, {250, 394}, {278, 1367}, {281, 7068}, {393, 125}, {523, 23616}, {593, 7215}, {648, 3265}, {823, 14208}, {850, 23107}, {1093, 338}, {1096, 3708}, {1101, 6507}, {1249, 122}, {1252, 4158}, {1437, 16730}, {1990, 1650}, {2052, 339}, {2189, 1364}, {2207, 20975}, {2326, 24031}, {2501, 5489}, {4590, 4176}, {5317, 18210}, {5379, 3998}, {6520, 1109}, {6521, 23994}, {6524, 115}, {6525, 1562}, {6528, 3267}, {6529, 523}, {7115, 7066}, {8747, 4466}, {10002, 12037}, {15352, 850}, {15384, 1073}, {18020, 3926}, {18831, 15414}, {20031, 879}, {23347, 1636}, {23357, 1092}, {23582, 69}, {23590, 4}, {23963, 23606}, {23964, 3}, {23975, 25}, {23984, 6356}, {23985, 1425}, {23995, 4100}, {23999, 304}, {24000, 63}, {24019, 656}, {24021, 92}, {24022, 19}, {24041, 1102}}


X(32231) = MIDPOINT OF X(3) AND X(17414)

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

X(32231) lies on these lines: {3, 17414}, {182, 9044}, {187, 30491}, {351, 1499}, {512, 5926}, {523, 549}, {647, 2780}, {3288, 21733}, {8552, 8675}, {8704, 11621}, {11615, 30230}, {16235, 23878}

X(32231) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 17414}, {3288, 21733}
X(32231) = reflection of X(5926) in X(9126)


X(32232) = X(523)X(5054)∩X(549)X(17414)

Barycentrics    (b^2 - c^2)*(5*a^8 - 13*a^6*b^2 + 11*a^4*b^4 - 3*a^2*b^6 - 13*a^6*c^2 + 18*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + b^6*c^2 + 11*a^4*c^4 - 2*a^2*b^2*c^4 - 2*b^4*c^4 - 3*a^2*c^6 + b^2*c^6) : :
X(32232) = 2 X[549] + X[17414],X[5996] + 2 X[9126]

X(32232) lies on these lines: {523, 5054}, {549, 17414}, {5215, 8704}, {5996, 9126}


X(32233) = MIDPOINT OF X(20) AND X(11061)

Barycentrics    3*a^12 - 5*a^10*b^2 - a^8*b^4 + 4*a^6*b^6 - a^4*b^8 + a^2*b^10 - b^12 - 5*a^10*c^2 + 5*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 + 2*b^10*c^2 - 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 + b^8*c^4 + 4*a^6*c^6 - a^4*b^2*c^6 + 2*a^2*b^4*c^6 - 4*b^6*c^6 - a^4*c^8 - 3*a^2*b^2*c^8 + b^4*c^8 + a^2*c^10 + 2*b^2*c^10 - c^12 : :
X(32233) = 2 X[5] - 3 X[15462],2 X[125] - 3 X[5085],2 X[141] - 3 X[15035],3 X[182] - 2 X[20301],3 X[186] - 2 X[8262],3 X[265] - 4 X[20301],5 X[631] - 4 X[6698],X[3448] - 3 X[25406],4 X[3589] - 3 X[14644],2 X[3818] - 3 X[14643],3 X[5050] - X[12902],4 X[5092] - 3 X[15061],3 X[5621] - 2 X[16003],3 X[5621] - X[25335],3 X[5622] - 2 X[25328],3 X[5648] - 4 X[12584],4 X[5972] - 3 X[10516],2 X[9969] - 3 X[16223],2 X[10113] - 3 X[14561],X[10296] - 3 X[22151],2 X[11799] - 3 X[18374],5 X[15027] - 8 X[20190],7 X[15036] - 6 X[21167],2 X[16111] + X[25336]

See Q152, the Walsmith circular quartic.

X(32233) lies on these lines: {3, 67}, {4, 6593}, {5, 15133}, {6, 7706}, {20, 2781}, {30, 9970}, {110, 858}, {125, 5085}, {141, 15035}, {146, 14927}, {182, 265}, {186, 8262}, {382, 15140}, {511, 11562}, {524, 10295}, {611, 18968}, {613, 12896}, {631, 6698}, {895, 8550}, {974, 2854}, {1071, 2836}, {1350, 16163}, {1352, 1511}, {1428, 12904}, {1498, 15063}, {1853, 15142}, {2330, 12903}, {2777, 11820}, {3313, 10628}, {3448, 25406}, {3589, 14644}, {3818, 7579}, {4549, 5663}, {5026, 11005}, {5050, 12902}, {5092, 15061}, {5094, 5642}, {5095, 11477}, {5480, 10733}, {5609, 14791}, {5622, 6146}, {5655, 7574}, {5972, 10516}, {6102, 12118}, {7493, 16165}, {7495, 9140}, {7519, 12824}, {7728, 19140}, {9143, 16063}, {9969, 16223}, {10113, 14561}, {10249, 12827}, {10296, 22151}, {10575, 18442}, {10752, 25329}, {11744, 19149}, {11799, 18374}, {15027, 20190}, {15036, 21167}, {15106, 24981}, {16111, 25336}, {19374, 19510}

X(32233) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 11061}, {146, 14927}, {6776, 12383}
X(32233) = reflection of X(i) in X(j) for these lines: {i,j}: {4, 6593}, {67, 3}, {265, 182}, {895, 8550}, {1350, 16163}, {1352, 1511}, {2930, 30714}, {7728, 19140}, {10733, 5480}, {10752, 25329}, {11005, 5026}, {11477, 5095}, {11744, 19149}, {14982, 110}, {15069, 5181}, {25335, 16003}
X(32233) = {X(5621),X(25335)}-harmonic conjugate of X(16003)


X(32234) = MIDPOINT OF X(7731) AND X(12283)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(5*a^8 - 12*a^6*b^2 + 11*a^4*b^4 - 6*a^2*b^6 + 2*b^8 - 12*a^6*c^2 + 11*a^4*b^2*c^2 - a^2*b^4*c^2 + 11*a^4*c^4 - a^2*b^2*c^4 - 4*b^4*c^4 - 6*a^2*c^6 + 2*c^8) : :
X(32234) = 4 X[6] - 3 X[14644],2 X[67] - 3 X[5622],2 X[69] - 3 X[15035],2 X[113] - 3 X[25321],2 X[125] - 3 X[14912],3 X[403] - 4 X[15471],8 X[468] - 9 X[19128],6 X[5050] - 5 X[15059],3 X[5093] - 2 X[10113],4 X[5181] - 5 X[15034],3 X[5622] - 4 X[8550],X[5921] - 3 X[25321],2 X[7574] - 3 X[11416],4 X[9970] - 3 X[10706],6 X[10519] - 7 X[15036],10 X[11482] - 7 X[15044],2 X[14913] - 3 X[16223],3 X[18449] - 2 X[18572]

See Q152, the Walsmith circular quartic.

X(32234) lies on these lines: {4, 542}, {6, 7699}, {24, 2930}, {54, 67}, {68, 16534}, {69, 15035}, {74, 5486}, {110, 468}, {113, 5921}, {125, 14912}, {182, 3043}, {186, 12584}, {193, 17702}, {265, 1353}, {378, 16010}, {403, 15471}, {511, 7722}, {524, 10295}, {1177, 1614}, {1351, 10733}, {1503, 10721}, {1511, 11898}, {1594, 25328}, {1986, 2854}, {2501, 14932}, {2781, 5925}, {2892, 11457}, {2914, 9976}, {4232, 9143}, {4235, 8593}, {5050, 15059}, {5093, 10113}, {5094, 9140}, {5181, 15034}, {5477, 6103}, {5663, 15531}, {5889, 13148}, {6193, 30714}, {6467, 10628}, {6593, 15069}, {7574, 11416}, {7577, 20301}, {7731, 12283}, {8548, 11441}, {9744, 9769}, {9967, 12219}, {10519, 15036}, {10990, 19467}, {11179, 13169}, {11180, 15303}, {11443, 18440}, {11482, 15044}, {11579, 15463}, {12292, 25336}, {14357, 14649}, {14913, 16223}, {14982, 25329}, {15116, 23294}, {15118, 18912}, {18449, 18572}, {18909, 20417}, {18947, 24981}

X(32234) = midpoint of X(7731) and X(12283)
X(32234) = reflection of X(i) in X(j) for these lines: {i,j}: {4, 5095}, {67, 8550}, {74, 6776}, {265, 1353}, {5921, 113}, {6403, 1986}, {10721, 10752}, {10733, 1351}, {11005, 5477}, {11180, 15303}, {11898, 1511}, {12219, 9967}, {13169, 11179}, {14094, 11061}, {14982, 25329}, {15069, 6593}
X(32234) = anticomplement of X(32275)
X(32234) = polar-circle-inverse of X(9880)
X(32234) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {67, 8550, 5622}, {5921, 25321, 113}, {17983, 20774, 4}


X(32235) = X(2)X(98)∩X(6)X(16510)

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

See Q152, the Walsmith circular quartic.

X(32235) lies on these lines: {2, 98}, {6, 16510}, {265, 7579}, {373, 6593}, {1350, 15106}, {1495, 5663}, {1511, 5650}, {1995, 19140}, {2088, 2502}, {2854, 3292}, {2930, 6090}, {5609, 9730}, {5640, 25556}, {5655, 7706}, {7574, 15136}, {10113, 15432}, {10264, 13394}, {10620, 12893}, {11438, 14094}, {11562, 20772}, {11801, 13413}, {12041, 14855}, {12584, 15066}, {13339, 20397}, {13352, 15132}, {14389, 20301}, {16010, 26864}

X(32235) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 5651, 5642}, {110, 9140, 11003}, {110, 11579, 184}
X(32235) = crossdifference of every pair of points on line {3569, 6032}


X(32236) = (name pending)

Barycentrics    4 a^12-21 a^10 b^2-87 a^8 b^4-94 a^6 b^6-30 a^4 b^8+3 a^2 b^10+b^12-21 a^10 c^2+324 a^8 b^2 c^2-9 a^6 b^4 c^2+546 a^4 b^6 c^2-72 a^2 b^8 c^2-87 a^8 c^4-9 a^6 b^2 c^4-954 a^4 b^4 c^4+93 a^2 b^6 c^4-9 b^8 c^4-94 a^6 c^6+546 a^4 b^2 c^6+93 a^2 b^4 c^6-16 b^6 c^6-30 a^4 c^8-72 a^2 b^2 c^8-9 b^4 c^8+3 a^2 c^10+c^12 : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 28997.

X(32236) lies on this line: {2,6}

leftri

More centers related to Walsmith triangle: X(32237)-X(32317)

rightri

This preamble and centers X(32237)-X(32317) were contributed by César Eliud Lozada, May 1, 2019.

This section continues the lists of centers related to Walsmith triangle given in X(32217)-X(32229).

The appearance of (T,n) in the following list means that triangles Walsmith and T are perspective with perspector X(n):

(ABC, 6), (anti-Conway, 6), (2nd anti-Conway, 6), (anti-inner-Grebe, 6), (anti-outer-Grebe, 6), (anti-Honsberger, 6), (2nd Brocard, 6), (circumsymmedial, 6), (Ehrmann-mid, 7703), (2nd Ehrmann, 6), (9th Fermat-Dao, 6), (10th Fermat-Dao, 6), (13th Fermat-Dao, 6), (14th Fermat-Dao, 6), (inner-Grebe, 6), (outer-Grebe, 6), (1st Kenmotu diagonals, 6), (2nd Kenmotu diagonals, 6), (2nd orthosymmedial, 6), (symmedial, 6), (tangential, 6), (inner tri-equilateral, 6), (outer tri-equilateral, 6)

The appearance of (T,i,j) in the following list means that triangles Walsmith and T are orthologic with orthologic centers X(i) and X(j):

(ABC, 125, 67), (ABC-X3 reflections, 125, 32233), (anti-Aquila, 125, 32238), (anti-Ara, 125, 32239), (anti-Ascella, 110, 32240), (anti-Atik, 110, 32241), (5th anti-Brocard, 125, 32242), (2nd anti-circumperp-tangential, 125, 32243), (1st anti-circumperp, 110, 32244), (anti-Conway, 110, 32245), (2nd anti-Conway, 110, 32246), (anti-Euler, 125, 32247), (3rd anti-Euler, 110, 32248), (4th anti-Euler, 110, 32249), (anti-excenters-reflections, 110, 32250), (2nd anti-extouch, 110, 32251), (anti-inner-Grebe, 125, 32252), (anti-outer-Grebe, 125, 32253), (anti-Honsberger, 110, 110), (anti-Hutson intouch, 110, 16010), (anti-incircle-circles, 110, 32254), (anti-inverse-in-incircle, 110, 32255), (anti-Mandart-incircle, 125, 32256), (6th anti-mixtilinear, 110, 32257), (anti-orthocentroidal, 1495, 6), (1st anti-Sharygin, 110, 32258), (anti-tangential-midarc, 110, 32259), (anti-Ursa minor, 110, 25328), (anti-Wasat, 110, 32260), (antiAOA, 3580, 67), (anticomplementary, 125, 11061), (AOA, 3580, 15118), (Aquila, 125, 32261), (Ara, 125, 32262), (Aries, 32263, 32264), (1st Auriga, 125, 32265), (2nd Auriga, 125, 32266), (4th Brocard, 32225, 6), (5th Brocard, 125, 32268), (circummedial, 1316, 110), (circumorthic, 110, 32234), (2nd circumperp tangential, 125, 32270), (Ehrmann-mid, 125, 32271), (Ehrmann-side, 110, 32272), (Ehrmann-vertex, 110, 32273), (1st Ehrmann, 6, 16510), (2nd Ehrmann, 110, 895), (Euler, 125, 32274), (2nd Euler, 110, 32275), (5th Euler, 1316, 125), (1st excosine, 110, 32276), (extangents, 110, 32277), (outer-Garcia, 125, 32278), (Gossard, 125, 32279), (inner-Grebe, 125, 32280), (outer-Grebe, 125, 32281), (Hatzipolakis-Moses, 32316, 32317), (3rd Hatzipolakis, 32282, 32283), (1st Hyacinth, 3580, 32284), (2nd Hyacinth, 32263, 32285), (intangents, 110, 32286), (Johnson, 125, 9970), (inner-Johnson, 125, 32287), (outer-Johnson, 125, 32288), (1st Johnson-Yff, 125, 32289), (2nd Johnson-Yff, 125, 32290), (1st Kenmotu diagonals, 110, 32291), (2nd Kenmotu diagonals, 110, 32292), (Kosnita, 110, 12584), (Lucas antipodal tangents, 110, 32293), (Lucas homothetic, 125, 32295), (Lucas(-1) antipodal tangents, 110, 32294), (Lucas(-1) homothetic, 125, 32296), (Mandart-incircle, 125, 32297), (medial, 125, 6593), (midheight, 10117, 15118), (5th mixtilinear, 125, 32298), (orthic, 110, 5095), (orthocentroidal, 1495, 6), (reflection, 32226, 16176), (submedial, 110, 32300), (tangential, 110, 2930), (inner tri-equilateral, 110, 32301), (outer tri-equilateral, 110, 32302), (3rd tri-squares-central, 125, 32303), (4th tri-squares-central, 125, 32304), (Trinh, 110, 32305), (X3-ABC reflections, 125, 32306), (inner-Yff, 125, 32307), (outer-Yff, 125, 32308), (inner-Yff tangents, 125, 32309), (outer-Yff tangents, 125, 32310)

The appearance of (T,i,j) in the following list means that triangles Walsmith and T are parallelogic with parallelogic centers X(i) and X(j):

(circummedial, 32224, 74), (1st Ehrmann, 23, 32305), (5th Euler, 32224, 113), (1st Parry, 125, 32312), (2nd Parry, 125, 32313)

The Walsmith triangle is directly similar to the 2nd Brocard and the 2nd orthosymmedial triangles. In both cases, the center of direct similitude is X(1316).

The Walsmith triangle is inversely similar to the circummedial and the 1st Ehrmann triangles with centers of inverse similitude X(32314) and X(32315), respectively. It is also inversely similar to the 5th Euler triangle, with a non interesting center on inverse similitude.


X(32237) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: WALSMITH TO ABC-X3 REFLECTIONS

Barycentrics    a^2*(4*a^4-(b^2+c^2)*a^2-3*b^4+4*b^2*c^2-3*c^4) : :
X(32237) = 3*X(23)+X(110) = 7*X(23)+X(323) = 5*X(23)+X(3292) = 5*X(23)-X(15107) = 11*X(23)+X(23061) = 7*X(110)-3*X(323) = X(110)-3*X(1495) = 5*X(110)-3*X(3292) = 5*X(110)+3*X(15107) = 11*X(110)-3*X(23061) = X(323)-7*X(1495) = 5*X(323)-7*X(3292) = 5*X(323)+7*X(15107) = 11*X(323)-7*X(23061) = 5*X(1495)-X(3292) = 5*X(1495)+X(15107) = 11*X(1495)-X(23061) = 11*X(3292)-5*X(23061) = X(5972)-3*X(32267) = 2*X(15448)-3*X(32267)

See preamble just before X(31353).

X(32237) lies on these lines: {3,5646}, {22,3819}, {23,110}, {25,182}, {26,5907}, {30,5972}, {51,11003}, {125,7426}, {154,1351}, {184,5097}, {187,20998}, {373,14002}, {468,6723}, {542,32269}, {567,10110}, {575,6800}, {576,26864}, {858,29323}, {1112,11649}, {1350,9306}, {1503,32223}, {1533,10295}, {1614,16625}, {1658,13474}, {1995,5092}, {2030,3124}, {2070,6000}, {2080,14673}, {2393,11800}, {2937,11793}, {3129,13350}, {3130,13349}, {3291,8627}, {3448,32225}, {3518,9729}, {3581,12308}, {3818,7493}, {5050,31860}, {5085,5544}, {5640,5645}, {5650,7492}, {5663,12105}, {6030,10219}, {6353,14927}, {6644,8717}, {6660,18860}, {6688,13595}, {6759,9714}, {7464,15036}, {7517,10282}, {7530,11430}, {7555,10170}, {7556,15030}, {7575,12041}, {8547,19136}, {8589,21292}, {8681,12310}, {9544,21969}, {10154,21243}, {10244,17814}, {10254,15432}, {10298,32062}, {10301,13394}, {10330,26276}, {10564,15040}, {11002,11663}, {11064,29317}, {11202,18534}, {11284,17508}, {11381,11454}, {11472,14070}, {11695,13339}, {11799,12295}, {11801,25338}, {11807,20773}, {12039,19127}, {12045,16042}, {12088,13348}, {12106,16836}, {13335,20897}, {13383,13419}, {14169,21402}, {14170,21401}, {14683,15360}, {14913,20987}, {15606,18350}, {15644,17714}, {16619,17702}

X(32237) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 1495}, {1533, 10295}, {3292, 15107}
X(32237) = reflection of X(5972) in X(15448)
X(32237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (22, 5651, 14810), (5651, 14810, 3819)


X(32238) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-AQUILA TO WALSMITH

Barycentrics
(b+c)*a^8-(b^2+c^2)*a^7-(b+c)*(b^2+c^2)*a^6+2*(b^4+c^4)*a^5+(b+c)*b^2*c^2*a^4+(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*a^2-2*(b^4-c^4)^2*a-(b^4-c^4)^2*(b+c) : :
X(32238) = 3*X(1)+X(32261) = 3*X(1)-X(32298) = 3*X(67)-X(32261) = 3*X(67)+X(32298) = 5*X(3616)-X(11061) = 3*X(5603)+X(32247) = 3*X(5886)-X(9970) = 3*X(10246)+X(32306) = 3*X(10516)-X(12368) = 3*X(11831)-X(32279)

The reciprocal orthologic center of these triangles is X(125).

X(32238) lies on these lines: {1,67}, {2,32278}, {10,6698}, {125,518}, {511,12261}, {515,32274}, {542,1385}, {942,15116}, {946,2781}, {960,2836}, {999,32270}, {1125,6593}, {1319,32243}, {1386,11735}, {1503,11709}, {2646,32297}, {2854,13605}, {3242,13211}, {3295,32256}, {3416,7984}, {3616,11061}, {4663,15118}, {5603,32247}, {5886,9970}, {9955,32271}, {10246,32306}, {10516,12368}, {10693,24476}, {11363,32239}, {11364,32242}, {11365,32262}, {11366,32265}, {11367,32266}, {11368,32268}, {11370,32280}, {11371,32281}, {11373,32287}, {11374,32288}, {11375,32289}, {11376,32290}, {11377,32295}, {11378,32296}, {11831,32279}, {12259,14984}, {13883,32303}, {13936,32304}, {18991,32252}, {18992,32253}

X(32238) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 67}, {3242, 13211}, {3416, 7984}, {10693, 24476}, {32261, 32298}
X(32238) = reflection of X(i) in X(j) for these (i,j): (10, 6698), (1386, 11735), (4663, 15118), (6593, 1125), (32271, 9955)
X(32238) = complement of X(32278)
X(32238) = X(67)-of-anti-Aquila-triangle
X(32238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32261, 32298), (67, 32298, 32261)


X(32239) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ARA TO WALSMITH

Barycentrics    SC*SB*(R^2*(13*SW^2-6*SA*SW+9*SA^2)-SW*(3*SW^2-2*SA*SW+3*SA^2)) : :

The reciprocal orthologic center of these triangles is X(125).

X(32239) lies on these lines: {4,542}, {23,32257}, {25,67}, {33,32297}, {34,32243}, {66,125}, {235,32274}, {427,6593}, {468,6698}, {511,12140}, {1205,11381}, {1503,12133}, {1593,32233}, {1598,32306}, {1843,13417}, {1853,15128}, {2781,3575}, {3541,15462}, {3867,25329}, {5090,32278}, {5169,32300}, {5410,32253}, {5411,32252}, {5596,13198}, {5622,14216}, {7487,32247}, {7519,32244}, {7530,32275}, {7713,32261}, {11363,32238}, {11380,32242}, {11383,32256}, {11384,32265}, {11385,32266}, {11386,32268}, {11388,32280}, {11389,32281}, {11390,32287}, {11391,32288}, {11392,32289}, {11393,32290}, {11394,32295}, {11395,32296}, {11396,32298}, {11398,32307}, {11399,32308}, {11400,32309}, {11401,32310}, {11746,26926}, {11832,32279}, {12134,14984}, {12294,17702}, {13884,32303}, {13937,32304}, {22479,32270}, {32246,32285}, {32251,32264}

X(32239) = reflection of X(i) in X(j) for these (i,j): (26926, 11746), (32285, 32246)
X(32239) = X(67)-of-anti-Ara-triangle


X(32240) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ASCELLA TO WALSMITH

Barycentrics    a^2*(a^8-(2*b^4+15*b^2*c^2+2*c^4)*a^4+17*(b^2+c^2)*b^2*c^2*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :
X(32240) = 3*X(11402)-4*X(32245) = 3*X(11402)-2*X(32251)

The reciprocal orthologic center of these triangles is X(110)

X(32240) lies on these lines: {3,32244}, {4,32254}, {6,32260}, {24,9925}, {25,2930}, {110,19118}, {184,32276}, {193,12310}, {195,8537}, {427,32255}, {511,12165}, {524,21284}, {542,1593}, {895,11405}, {1177,26864}, {1398,32259}, {1598,5609}, {1993,32248}, {2781,12174}, {2836,11396}, {2854,12167}, {3043,5050}, {3515,12584}, {3516,16010}, {3564,12168}, {5094,25328}, {5410,32291}, {5411,32292}, {6467,17847}, {7071,32286}, {7395,32275}, {7484,32257}, {7592,32249}, {9777,32246}, {9818,32272}, {9924,13417}, {10602,15141}, {11160,21844}, {11216,15140}, {11245,32241}, {11284,32300}, {11402,32245}, {11403,32250}, {11406,32277}, {11408,32301}, {11409,32302}, {11410,32305}, {12160,14984}, {13171,19459}, {16030,32258}, {16176,32262}, {18386,32273}, {19404,32293}, {19405,32294}

X(32240) = reflection of X(i) in X(j) for these (i,j): (12167, 19504), (13171, 19459), (32251, 32245)
X(32240) = X(1156)-of-anti-Ascella-triangle if ABC is acute
X(32240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2930, 5095, 25), (32245, 32251, 11402)


X(32241) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ATIK TO WALSMITH

Barycentrics    SA*((3*R^2*(12*R^2-7*SW)+2*SW^2)*S^2+(3*SA+SW)*(SB+SC)*R^2*SW) : :

The reciprocal orthologic center of these triangles is X(110).

X(32241) lies on these lines: {2,32251}, {4,67}, {69,125}, {110,19119}, {511,18933}, {542,18909}, {631,5181}, {1177,6353}, {1843,13203}, {1899,32255}, {2854,18935}, {2930,6776}, {3043,14912}, {3548,23296}, {3564,18932}, {5095,11433}, {6515,32244}, {6643,14984}, {8263,22467}, {8889,15116}, {10519,19457}, {11061,32285}, {11245,32240}, {11411,32275}, {12324,32250}, {12584,18925}, {13567,32276}, {14683,26926}, {16010,18913}, {18911,32248}, {18912,32249}, {18914,32254}, {18915,32259}, {18916,32234}, {18917,32272}, {18918,32273}, {18921,32277}, {18922,32286}, {18923,32291}, {18924,32292}, {18926,32293}, {18927,32294}, {18928,32300}, {18929,32301}, {18930,32302}, {18931,32305}, {19166,32258}, {23291,25328}

X(32241) = X(1156)-of-anti-Atik-triangle if ABC is acute
X(32241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (67, 32246, 2892), (2892, 32246, 4)


X(32242) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th ANTI-BROCARD TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32242) lies on these lines: {32,67}, {83,6593}, {98,32274}, {125,1691}, {182,265}, {511,12201}, {542,3398}, {1078,6698}, {1503,12192}, {2781,12110}, {5038,15118}, {7787,11061}, {9970,10796}, {10788,32247}, {10789,32261}, {10790,32262}, {10791,32278}, {10792,32280}, {10793,32281}, {10795,32288}, {10797,32289}, {10798,32290}, {10800,32298}, {10801,32307}, {10802,32308}, {10803,32309}, {10804,32310}, {11364,32238}, {11380,32239}, {11490,32256}, {11837,32265}, {11838,32266}, {11839,32279}, {11840,32295}, {11841,32296}, {11842,32306}, {12193,14984}, {12835,32243}, {13885,32303}, {13938,32304}, {18502,32271}, {18993,32252}, {18994,32253}, {22520,32270}

X(32242) = X(67)-of-5th-anti-Brocard-triangle


X(32243) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32243) lies on these lines: {1,542}, {3,32307}, {4,32290}, {6,12903}, {11,32274}, {12,6593}, {34,32239}, {55,32233}, {56,67}, {57,32261}, {110,12588}, {125,1428}, {265,613}, {388,11061}, {498,15462}, {511,18968}, {999,32306}, {1319,32238}, {1352,10091}, {1503,3024}, {2099,32298}, {2781,7354}, {3056,17702}, {3585,32271}, {4293,32247}, {5095,19369}, {5252,32278}, {5433,6698}, {5621,9672}, {11509,32256}, {12835,32242}, {14984,18970}, {18954,32262}, {18955,32265}, {18956,32266}, {18957,32268}, {18958,32279}, {18959,32280}, {18960,32281}, {18961,32287}, {18962,32288}, {18963,32295}, {18964,32296}, {18965,32303}, {18966,32304}, {18967,32310}, {18995,32252}, {18996,32253}

X(32243) = reflection of X(32297) in X(1)
X(32243) = X(67)-of-2nd-anti-circumperp-tangential-triangle
X(32243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 11061, 32289), (999, 32306, 32308)


X(32244) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-CIRCUMPERP TO WALSMITH

Barycentrics    3*a^8-4*(b^2+c^2)*a^6-(b^4-9*b^2*c^2+c^4)*a^4+(b^2+c^2)*(2*b^2+b*c-2*c^2)*(2*b^2-b*c-2*c^2)*a^2-2*(b^4-c^4)^2 : :
X(32244) = 3*X(2)-4*X(32257) = 9*X(2)-8*X(32300) = 3*X(6)-4*X(6698) = 4*X(6)-5*X(15059) = 4*X(67)-3*X(9140) = 2*X(67)-3*X(13169) = 3*X(67)-2*X(25328) = 3*X(69)-2*X(5181) = 3*X(69)-X(11061) = 3*X(110)-4*X(5181) = 3*X(110)-2*X(11061) = 4*X(858)-3*X(11416) = 2*X(895)-3*X(9140) = X(895)-3*X(13169) = 3*X(895)-4*X(25328) = X(2930)-3*X(15533) = 3*X(5095)-4*X(32300) = 16*X(6698)-15*X(15059) = 9*X(9140)-8*X(25328) = 9*X(13169)-4*X(25328) = 3*X(32257)-2*X(32300)

The reciprocal orthologic center of these triangles is X(110).

X(32244) lies on these lines: {2,5095}, {3,32240}, {4,32275}, {6,6698}, {20,542}, {22,2930}, {30,32272}, {67,524}, {69,110}, {74,3564}, {97,32258}, {125,193}, {325,9769}, {394,32276}, {511,10296}, {576,15025}, {599,6593}, {690,16093}, {1205,8681}, {1297,20404}, {1351,14644}, {1352,10752}, {1353,15061}, {1370,32255}, {1494,4226}, {1992,15118}, {1993,32251}, {2071,32305}, {2407,30789}, {2777,5921}, {2781,5895}, {2836,3962}, {2854,12220}, {2892,11442}, {2979,32248}, {3043,19131}, {3060,32246}, {3100,32286}, {3101,32277}, {3146,32250}, {3153,32273}, {3448,20080}, {3620,5972}, {3631,25329}, {4296,32259}, {5012,32245}, {5093,20304}, {5505,18125}, {5622,15057}, {5663,11898}, {5847,7984}, {5965,11579}, {6515,32241}, {6699,14912}, {6776,15055}, {7488,12584}, {7519,32239}, {7691,32233}, {8541,31857}, {10519,15051}, {10721,18440}, {11008,25320}, {11411,16003}, {11412,12429}, {11413,16010}, {11414,32254}, {11417,32291}, {11418,32292}, {11420,32301}, {11421,32302}, {11477,15044}, {12272,13201}, {13171,19588}, {13417,14913}, {14683,32114}, {15116,23293}, {15303,21356}, {15534,30744}, {16266,20379}, {19406,32293}, {19407,32294}, {19510,22151}

X(32244) = midpoint of X(i) and X(j) for these lines: {i,j}: {3448, 20080}, {11412, 32249}, {12272, 13201}
X(32244) = reflection of X(i) in X(j) for these (i,j): (4, 32275), (110, 69), (193, 125), (895, 67), (3146, 32250), (5095, 32257), (9140, 13169), (10721, 18440), (10752, 1352), (11061, 5181), (11477, 32274), (13417, 14913), (14683, 32114), (15054, 32247), (16176, 6593), (25329, 3631), (32234, 3)
X(32244) = anticomplement of X(5095)
X(32244) = X(1156)-of-1st-anti-circumperp-triangle if ABC is acute
X(32244) = anticomplementary conjugate of the anticomplement of X(15398)
X(32244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (67, 895, 9140), (895, 13169, 67), (5095, 32257, 2)


X(32245) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-CONWAY TO WALSMITH

Barycentrics    (SB+SC)*((6*R^2-SW)^2*S^2-(4*R^2-SW)*(3*SA-2*SW)*SA*SW) : :
X(32245) = 3*X(11402)+X(32240) = 3*X(11402)-X(32251)

The reciprocal orthologic center of these triangles is X(110).

X(32245) lies on these lines: {6,110}, {54,67}, {159,1112}, {182,32257}, {184,1177}, {389,12584}, {511,12227}, {542,578}, {567,32272}, {569,32275}, {1147,5181}, {1181,2781}, {1353,19138}, {1503,15472}, {1614,2904}, {1899,15116}, {2892,6776}, {3043,14912}, {3047,25321}, {3564,12228}, {5012,32244}, {6467,13248}, {8537,9971}, {9306,32300}, {11402,32240}, {11423,32249}, {11424,32250}, {11425,16010}, {11426,32254}, {11427,32255}, {11428,32277}, {11429,32286}, {11430,32305}, {11536,32284}, {12161,14984}, {13366,32260}, {15471,18374}, {17809,32276}, {18388,32273}, {19128,32113}, {19365,32259}, {19408,32293}, {19409,32294}, {19459,19504}, {23292,25328}

X(32245) = midpoint of X(i) and X(j) for these lines: {i,j}: {19459, 19504}, {32240, 32251}
X(32245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 2930, 32246), (54, 32234, 5622)
X(32245) = X(1156)-of-anti-Conway-triangle if ABC is acute


X(32246) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CONWAY TO WALSMITH

Barycentrics    (SB+SC)*((6*R^2*(6*R^2-5*SW)+5*SW^2)*S^2-(4*R^2-SW)*(3*SA-2*SW)*SA*SW) : :
X(32246) = 3*X(51)-X(5095) = 3*X(51)+X(32260) = X(67)+3*X(9971) = 3*X(125)-X(1205) = 3*X(568)+X(32272) = X(895)+3*X(11188) = X(1205)+3*X(1843) = 3*X(3060)+X(32244) = 5*X(3567)-X(32234) = X(5181)-3*X(29959) = 9*X(5640)-X(32248) = 3*X(5943)-2*X(32300) = X(6403)+3*X(14644) = X(6593)-3*X(16776) = 7*X(9781)+X(32249) = X(9967)-3*X(23515) = X(11061)-3*X(12824) = 3*X(12099)-2*X(15118) = X(12220)-5*X(15059)

The reciprocal orthologic center of these triangles is X(110).

X(32246) lies on these lines: {4,67}, {5,5181}, {6,110}, {24,5622}, {25,1177}, {51,5095}, {52,32275}, {125,1205}, {159,13198}, {185,32250}, {389,542}, {427,15116}, {468,2393}, {511,7687}, {568,32272}, {578,12584}, {599,11444}, {858,6698}, {974,1503}, {1112,9969}, {1192,5621}, {3060,32244}, {3313,13416}, {3564,12236}, {3567,32234}, {3575,31978}, {3867,23315}, {5663,19161}, {5943,14763}, {5972,9822}, {6217,32281}, {6218,32280}, {6403,14644}, {6642,15462}, {6723,11574}, {7716,10117}, {9777,32240}, {9781,32249}, {9786,16010}, {9792,32258}, {9967,23515}, {10821,12367}, {11061,12824}, {11433,32255}, {11435,32277}, {11436,32286}, {11438,32305}, {11579,12412}, {11585,16789}, {11800,14913}, {12061,20303}, {12167,13248}, {12220,15059}, {13567,25328}, {15128,23327}, {15647,20987}, {17810,32276}, {18390,32273}, {19039,32252}, {19040,32253}, {19366,32259}, {19410,32293}, {19411,32294}, {22968,23047}, {23292,25488}, {32239,32285}

X(32246) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 32275}, {125, 1843}, {185, 32250}, {5095, 32260}, {11800, 14913}, {32239, 32285}
X(32246) = reflection of X(i) in X(j) for these (i,j): (6, 11746), (1112, 9969), (3313, 13416), (5972, 9822), (11574, 6723), (15738, 32274)
X(32246) = polar-circle-inverse of X(34163)
X(32246) = X(1156)-of-2nd-anti-Conway-triangle if ABC is acute
X(32246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32241, 2892), (2892, 32241, 67)


X(32247) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EULER TO WALSMITH

Barycentrics    3*S^4-3*(R^2*(3*SA+SW)-SA^2+SB*SC)*S^2+(9*R^2-SW)*SB*SC*SW : :
X(32247) = 3*X(4)-4*X(32274) = 3*X(67)-2*X(32274) = 3*X(74)-X(32234) = 2*X(110)-3*X(10519) = 4*X(125)-3*X(14853) = 4*X(182)-3*X(25321) = 3*X(376)-2*X(32233) = 5*X(631)-4*X(6593) = 2*X(1351)-3*X(25320) = 7*X(3090)-8*X(6698) = 5*X(3091)-4*X(32271) = 2*X(5095)-3*X(5622) = 3*X(5621)-2*X(8550) = 3*X(5621)-X(16176) = 3*X(5622)-4*X(20417) = 3*X(6776)-2*X(32234) = 4*X(10264)-3*X(25320) = 2*X(10752)-3*X(14853) = 3*X(11180)-4*X(32275) = 3*X(13169)-2*X(32275)

The reciprocal orthologic center of these triangles is X(125).

X(32247) lies on these lines: {2,9970}, {3,11061}, {4,67}, {20,542}, {24,32262}, {30,32306}, {66,11564}, {69,5663}, {74,5486}, {104,32270}, {110,10519}, {125,10752}, {146,1352}, {182,25321}, {193,11579}, {376,32233}, {388,32307}, {468,15106}, {497,32308}, {511,3448}, {515,32261}, {524,7464}, {541,11180}, {578,5095}, {631,6593}, {842,13574}, {895,16003}, {1205,15073}, {1350,12383}, {1351,10264}, {1503,12244}, {1992,20126}, {2393,32249}, {2777,32250}, {2854,12317}, {3085,32289}, {3086,32290}, {3090,6698}, {3091,32271}, {3520,5621}, {3523,15462}, {3541,11431}, {3547,16534}, {3564,10620}, {3618,15061}, {3619,14643}, {4293,32243}, {4294,32297}, {5085,25329}, {5181,14094}, {5480,15081}, {5603,32238}, {5655,21356}, {5657,32278}, {5900,22336}, {6103,10766}, {7487,32239}, {7492,9143}, {7581,32253}, {7582,32252}, {7731,19161}, {7967,32298}, {9140,31099}, {9862,32268}, {10753,15357}, {10783,32280}, {10784,32281}, {10785,32287}, {10786,32288}, {10788,32242}, {10805,32309}, {10806,32310}, {11411,14984}, {11477,25328}, {11491,32256}, {11843,32265}, {11844,32266}, {11845,32279}, {11846,32295}, {11847,32296}, {12041,25406}, {12112,32113}, {12164,23296}, {13886,32303}, {13939,32304}, {14927,20127}, {15063,32257}, {15122,22151}, {20301,20423}, {25336,31884}

X(32247) = midpoint of X(15054) and X(32244)
X(32247) = reflection of X(i) in X(j) for these (i,j): (4, 67), (146, 1352), (193, 11579), (895, 16003), (1351, 10264), (1992, 20126), (5095, 20417), (6776, 74), (7731, 19161), (10752, 125), (10753, 15357), (11061, 3), (11180, 13169), (11477, 25328), (12112, 32113), (12164, 23296), (12383, 1350), (14094, 5181), (14927, 20127), (15063, 32257), (15073, 1205), (16176, 8550)
X(32247) = anticomplement of X(9970)
X(32247) = X(67)-of-anti-Euler-triangle
X(32247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (125, 10752, 14853), (5095, 20417, 5622)


X(32248) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-EULER TO WALSMITH

Barycentrics    (SB+SC)*((3*R^2*(48*R^2-25*SW)+10*SW^2)*S^2-(7*R^2-2*SW)*(3*SA-2*SW)*SA*SW) : :
X(32248) = 2*X(895)-3*X(15531) = 2*X(1843)-3*X(25321) = 3*X(2979)-2*X(32244) = 3*X(3060)-4*X(5095) = 9*X(5640)-8*X(32246) = 4*X(6593)-3*X(11188) = 9*X(7998)-8*X(32257) = 5*X(11439)-4*X(32250) = 5*X(11444)-4*X(32275) = 15*X(11451)-16*X(32300) = 3*X(11459)-2*X(32272)

The reciprocal orthologic center of these triangles is X(110).

X(32248) lies on these lines: {2,32260}, {3,32249}, {6,110}, {22,32276}, {511,12270}, {542,12111}, {1177,26881}, {1843,25321}, {1993,32240}, {2393,11061}, {2781,12279}, {2979,32244}, {3060,5095}, {3448,6467}, {3564,12273}, {5012,32251}, {5486,11442}, {5663,12283}, {5889,13148}, {7998,32257}, {9019,16176}, {9973,25329}, {11416,15141}, {11439,32250}, {11440,16010}, {11441,32254}, {11444,32275}, {11445,32277}, {11446,32286}, {11449,12584}, {11451,32300}, {11454,32305}, {11459,32272}, {12220,13201}, {12281,18438}, {15074,32306}, {18392,32273}, {18911,32241}, {19167,32258}, {19367,32259}, {19412,32293}, {19413,32294}, {23293,25328}

X(32248) = reflection of X(i) in X(j) for these (i,j): (3448, 6467), (5889, 32234), (9973, 25329), (12272, 110), (12281, 18438), (13201, 12220), (32249, 3), (32306, 15074)
X(32248) = anticomplement of X(32260)
X(32248) = X(1156)-of-3rd-anti-Euler-triangle if ABC is acute
X(32248) = {X(12272), X(15531)}-harmonic conjugate of X(11443)


X(32249) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-EULER TO WALSMITH

Barycentrics    (SB+SC)*((3*R^2*(48*R^2-25*SW)+2*(3*SA+5*SW)*SW)*S^2-(R^2*(36*R^2+21*SA-22*SW)-6*SA^2+6*SB*SC+4*SW^2)*SA*SW) : :
X(32249) = 5*X(3567)-4*X(5095) = 3*X(5890)-2*X(32234) = 7*X(7999)-8*X(32257) = 7*X(9781)-8*X(32246) = 2*X(9970)-3*X(11188) = 3*X(11455)-4*X(32250) = 3*X(11459)-4*X(32275) = 17*X(11465)-16*X(32300)

The reciprocal orthologic center of these triangles is X(110).

X(32249) lies on these lines: {3,32248}, {4,32260}, {24,32276}, {54,32251}, {67,15073}, {74,1296}, {110,19123}, {511,12281}, {542,6241}, {895,11458}, {1177,26882}, {1205,11457}, {1614,2930}, {2393,32247}, {2781,12290}, {3564,12284}, {3567,5095}, {5663,12272}, {5890,32234}, {6403,7731}, {7592,32240}, {7999,32257}, {8537,15141}, {9781,32246}, {9970,11188}, {11412,12429}, {11423,32245}, {11455,32250}, {11456,32254}, {11459,32275}, {11460,32277}, {11461,32286}, {11462,32291}, {11463,32292}, {11464,12584}, {11465,32300}, {11466,32301}, {11467,32302}, {11468,32305}, {11898,12273}, {12111,32272}, {15106,23061}, {18394,32273}, {18912,32241}, {19168,32258}, {19368,32259}, {19414,32293}, {19415,32294}, {23294,25328}

X(32249) = reflection of X(i) in X(j) for these (i,j): (4, 32260), (7731, 6403), (11412, 32244), (12111, 32272), (12273, 11898), (12283, 74), (15073, 67), (32248, 3)
X(32249) = X(1156)-of-4th-anti-Euler-triangle if ABC is acute


X(32250) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EXCENTERS-REFLECTIONS TO WALSMITH

Barycentrics    (8*a^8-12*(b^2+c^2)*a^6+(5*b^4+14*b^2*c^2+5*c^4)*a^4-2*(b^2+c^2)*(3*b^4-4*b^2*c^2+3*c^4)*a^2+5*(b^4-c^4)^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
X(32250) = 3*X(4)-X(32234) = 3*X(125)-4*X(32274) = 5*X(3091)-4*X(32300) = 3*X(5095)-2*X(32234) = 3*X(5642)-2*X(32233) = 4*X(6723)-3*X(25406) = 3*X(10151)-2*X(15471) = 5*X(11439)-X(32248) = 3*X(11455)+X(32249) = 4*X(18440)-X(32114)

The reciprocal orthologic center of these triangles is X(110).

X(32250) lies on these lines: {4,542}, {20,32257}, {24,32305}, {25,16010}, {30,32275}, {33,32259}, {34,32286}, {64,67}, {110,15431}, {113,15432}, {125,468}, {185,32246}, {235,25328}, {378,12584}, {382,32272}, {403,20301}, {511,12292}, {541,32306}, {1177,26883}, {1205,15738}, {1352,16163}, {1498,32251}, {1593,2930}, {1597,32254}, {1843,5663}, {1902,2836}, {1974,11579}, {2777,32247}, {2781,11381}, {2854,12133}, {3091,32300}, {3146,32244}, {3515,5621}, {3564,12295}, {4232,9140}, {5094,5642}, {5622,6759}, {5921,10733}, {6103,11646}, {6723,25406}, {6776,7687}, {10151,15471}, {10295,11645}, {10301,12828}, {11403,32240}, {11424,32245}, {11439,32248}, {11455,32249}, {11471,32277}, {11472,17702}, {11473,32291}, {11474,32292}, {11475,32301}, {11476,32302}, {12134,18488}, {12162,14984}, {12324,32241}, {14216,20417}, {14982,24981}, {15118,19153}, {15133,16534}, {15811,32276}, {19169,32258}, {19416,32293}, {19417,32294}

X(32250) = midpoint of X(i) and X(j) for these lines: {i,j}: {382, 32272}, {3146, 32244}, {5921, 10733}, {11381, 32260}
X(32250) = reflection of X(i) in X(j) for these (i,j): (20, 32257), (185, 32246), (1205, 15738), (5095, 4), (6776, 7687), (10990, 67), (12294, 12133), (16163, 1352), (24981, 14982)
X(32250) = X(1156)-of-anti-excenters-reflections-triangle if ABC is acute


X(32251) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-EXTOUCH TO WALSMITH

Barycentrics
a^2*(-a^2+b^2+c^2)*(a^10-(b^2+c^2)*a^8-(2*b^2-c^2)*(b^2-2*c^2)*a^6+2*(b^4-c^4)*(b^2-c^2)*a^4+(b^4-b^2*c^2+c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4)) : :
X(32251) = 3*X(5050)-2*X(12228) = 3*X(11402)-X(32240) = 3*X(11402)-2*X(32245)

The reciprocal orthologic center of these triangles is X(110).

X(32251) lies on these lines: {2,32241}, {3,895}, {5,9512}, {6,67}, {25,1177}, {54,32249}, {69,23296}, {110,19125}, {155,32275}, {184,2930}, {185,16010}, {371,19385}, {372,19384}, {394,32257}, {427,2892}, {511,19457}, {542,1181}, {974,11579}, {1204,1205}, {1498,32250}, {1593,2781}, {1843,10117}, {1899,25328}, {1992,18281}, {1993,32244}, {2393,21284}, {2854,13198}, {2931,19131}, {2935,19124}, {3448,26926}, {3564,19456}, {3594,19399}, {5012,32248}, {5050,12228}, {5159,22151}, {6593,11284}, {6776,32255}, {7592,32234}, {9970,15738}, {10510,21639}, {10601,32300}, {10605,32305}, {11402,32240}, {12167,13171}, {12584,19357}, {14683,19119}, {14853,18933}, {15059,26206}, {15122,19348}, {16063,18919}, {18396,32273}, {18445,32272}, {19170,32258}, {19347,32254}, {19349,32259}, {19350,32277}, {19354,32286}, {19355,32291}, {19356,32292}, {19358,32293}, {19359,32294}, {19363,32301}, {19364,32302}, {32239,32264}

X(32251) = midpoint of X(12167) and X(13171)
X(32251) = reflection of X(i) in X(j) for these (i,j): (19459, 13198), (19504, 6), (32240, 32245)
X(32251) = X(1156)-of-2nd-anti-extouch-triangle if ABC is acute
X(32251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 67, 15141), (6, 32276, 5095), (125, 15118, 15128)


X(32252) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GREBE TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32252) lies on these lines: {2,32304}, {6,67}, {141,19111}, {372,32233}, {511,19051}, {542,3312}, {1503,19059}, {1587,32274}, {1588,2781}, {3068,6698}, {3069,6593}, {3299,32307}, {3301,32308}, {3763,8998}, {5085,13969}, {5411,32239}, {5648,32291}, {6418,32306}, {7582,32247}, {7584,9970}, {7585,32303}, {7586,11061}, {7968,32298}, {9971,19043}, {12367,19001}, {13785,32271}, {13910,15059}, {13936,32278}, {13966,15462}, {13979,14561}, {14984,19061}, {18991,32238}, {18993,32242}, {18995,32243}, {18999,32256}, {19003,32261}, {19005,32262}, {19007,32265}, {19009,32266}, {19011,32268}, {19013,32270}, {19017,32279}, {19023,32287}, {19025,32288}, {19027,32289}, {19029,32290}, {19031,32295}, {19033,32296}, {19037,32297}, {19039,32246}, {19047,32309}, {19049,32310}

X(32252) = X(67)-of-anti-inner-Grebe-triangle
X(32252) = {X(6), X(67)}-harmonic conjugate of X(32253)


X(32253) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-GREBE TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32253) lies on these lines: {2,32303}, {6,67}, {141,19110}, {371,32233}, {511,19052}, {542,3311}, {1503,19060}, {1587,2781}, {1588,32274}, {3068,6593}, {3069,6698}, {3299,32308}, {3301,32307}, {3763,13990}, {5085,8994}, {5410,32239}, {5648,32292}, {6417,32306}, {7581,32247}, {7583,9970}, {7585,11061}, {7586,32304}, {7969,32298}, {8981,15462}, {9971,19044}, {12367,19002}, {13665,32271}, {13883,32278}, {13915,14561}, {13972,15059}, {14984,19062}, {18992,32238}, {18994,32242}, {18996,32243}, {19000,32256}, {19004,32261}, {19006,32262}, {19008,32265}, {19010,32266}, {19012,32268}, {19014,32270}, {19018,32279}, {19024,32287}, {19026,32288}, {19028,32289}, {19030,32290}, {19032,32295}, {19034,32296}, {19038,32297}, {19040,32246}, {19048,32309}, {19050,32310}

X(32253) = X(67)-of-anti-outer-Grebe-triangle
X(32253) = {X(6), X(67)}-harmonic conjugate of X(32252)


X(32254) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INCIRCLE-CIRCLES TO WALSMITH

Barycentrics    (SB+SC)*((18*R^2-6*SW)*S^2+(9*R^2-6*SA+2*SW)*SA*SW) : :
X(32254) = 7*X(3)-6*X(5621) = 3*X(3)-4*X(12584) = 3*X(3)-2*X(16010) = 5*X(3)-4*X(32305) = 4*X(110)-3*X(5050) = 3*X(399)-2*X(9970) = 4*X(895)-5*X(11482) = 4*X(1177)-5*X(14530) = 3*X(1351)-4*X(9970) = 7*X(2930)-3*X(5621) = 3*X(2930)-2*X(12584) = 3*X(2930)-X(16010) = 5*X(2930)-2*X(32305) = 8*X(5609)-5*X(11482) = 9*X(5621)-14*X(12584) = 9*X(5621)-7*X(16010) = 15*X(5621)-14*X(32305) = 5*X(12584)-3*X(32305) = 5*X(16010)-6*X(32305) = 4*X(32275)-3*X(32306)

The reciprocal orthologic center of these triangles is X(110).

X(32254) lies on these lines: {3,67}, {4,32240}, {5,32255}, {23,3564}, {25,32234}, {110,5050}, {399,1351}, {511,12308}, {575,18350}, {895,3527}, {999,32259}, {1177,14530}, {1181,32260}, {1352,8546}, {1482,2836}, {1597,32250}, {1598,5095}, {1656,25328}, {1995,9143}, {2781,12315}, {3295,32286}, {3311,32291}, {3312,32292}, {3843,32273}, {5055,20301}, {5093,19140}, {5655,16510}, {5663,11820}, {5921,12168}, {5965,25336}, {6403,12165}, {6759,32276}, {7530,11061}, {9920,15581}, {9924,10628}, {10272,25320}, {10306,32277}, {10510,19377}, {11414,32244}, {11426,32245}, {11432,32246}, {11441,32248}, {11456,32249}, {11477,12316}, {11484,32300}, {11485,32301}, {11486,32302}, {11579,12017}, {12106,18951}, {12164,12271}, {12902,14982}, {15039,15462}, {17702,19588}, {18440,31861}, {18583,20125}, {18914,32241}, {19173,32258}, {19347,32251}, {19418,32293}, {19419,32294}, {24206,25330}

X(32254) = reflection of X(i) in X(j) for these (i,j): (3, 2930), (895, 5609), (1351, 399), (12902, 14982), (16010, 12584), (32255, 5), (32262, 15581), (32276, 6759)
X(32254) = inverse of X(8724) in the Stammler circle
X(32254) = X(1156)-of-anti-incircle-circles-triangle if ABC is acute
X(32254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2930, 16010, 12584), (12584, 16010, 3)


X(32255) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INVERSE-IN-INCIRCLE TO WALSMITH

Barycentrics    a^8+2*(b^2+c^2)*a^6-11*b^2*c^2*a^4-(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4)*a^2-(b^4-c^4)^2 : :
X(32255) = 3*X(2)-4*X(25328) = 3*X(4)-4*X(32273) = 4*X(67)-3*X(69) = 2*X(67)-3*X(3448) = 4*X(110)-5*X(3618) = 3*X(110)-4*X(15118) = 2*X(110)-3*X(25320) = 8*X(125)-7*X(3619) = 2*X(141)-3*X(25330) = 3*X(193)-2*X(16176) = 3*X(376)-4*X(32305) = 2*X(399)-3*X(14853) = 4*X(895)-3*X(1992) = 3*X(895)-2*X(5095) = 9*X(1992)-8*X(5095) = 3*X(1992)-2*X(11061) = 15*X(3618)-16*X(15118) = 5*X(3618)-6*X(25320) = 4*X(5095)-3*X(11061) = 8*X(15118)-9*X(25320)

The reciprocal orthologic center of these triangles is X(110).

X(32255) lies on these lines: {2,2930}, {4,542}, {5,32254}, {6,7533}, {8,2836}, {20,16010}, {67,69}, {110,3618}, {125,3619}, {141,25330}, {193,16176}, {265,18489}, {376,32305}, {388,32259}, {399,14853}, {427,32240}, {497,32286}, {511,12317}, {524,5189}, {631,12584}, {1177,11206}, {1205,11457}, {1370,32244}, {1503,17812}, {1843,18947}, {1899,32241}, {2407,5984}, {2550,32277}, {2781,12324}, {2892,32064}, {3068,32291}, {3069,32292}, {3090,20301}, {3522,5621}, {3564,7574}, {3629,25336}, {4558,10991}, {5181,9140}, {5486,11442}, {5622,13336}, {5648,6698}, {5987,7735}, {6593,9143}, {6643,32275}, {6776,32251}, {7386,32257}, {7392,32300}, {8550,14516}, {9976,14912}, {10264,10519}, {11008,13203}, {11411,14984}, {11427,32245}, {11433,32246}, {11488,32301}, {11489,32302}, {11579,12383}, {12308,21850}, {14561,20125}, {14791,32306}, {14927,17702}, {15583,17847}, {18531,32272}, {19174,32258}, {19420,32293}, {19421,32294}

X(32255) = reflection of X(i) in X(j) for these (i,j): (20, 16010), (69, 3448), (2930, 25328), (11061, 895), (12308, 21850), (12383, 11579), (14683, 6), (17847, 15583), (25336, 3629), (32254, 5)
X(32255) = anticomplementary conjugate of the anticomplement of X(13574)
X(32255) = anticomplement of X(2930)
X(32255) = inverse of X(671) in the anticomplementary circle
X(32255) = X(1156)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(32255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (895, 11061, 1992), (2930, 25328, 2)


X(32256) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32256) lies on these lines: {3,32270}, {35,32261}, {55,67}, {56,32298}, {100,11061}, {197,32262}, {511,12334}, {542,11248}, {1001,6698}, {1376,6593}, {1503,12327}, {2781,11500}, {2836,3811}, {2930,4062}, {3295,32238}, {5687,32278}, {5846,22586}, {9970,11499}, {10310,32233}, {11383,32239}, {11490,32242}, {11491,32247}, {11492,32265}, {11493,32266}, {11494,32268}, {11496,32274}, {11497,32280}, {11498,32281}, {11501,32289}, {11502,32290}, {11503,32295}, {11504,32296}, {11507,32307}, {11508,32308}, {11509,32243}, {11510,32310}, {11848,32279}, {11849,32306}, {12328,14984}, {13887,32303}, {13940,32304}, {15622,16010}, {18491,32271}, {18999,32252}, {19000,32253}

X(32256) = reflection of X(i) in X(j) for these (i,j): (32270, 3), (32287, 6593)
X(32256) = X(67)-of-anti-Mandart-incircle-triangle


X(32257) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR TO WALSMITH

Barycentrics    (-a^2+b^2+c^2)*(2*a^6-2*(b^2+c^2)*a^4-(b^4-4*b^2*c^2+c^4)*a^2+3*(b^4-c^4)*(b^2-c^2)) : :
X(32257) = 3*X(2)+X(32244) = 3*X(3)+X(32272) = X(67)+3*X(599) = 3*X(67)+X(2930) = 5*X(67)+3*X(5648) = 5*X(67)-X(25335) = 3*X(69)+X(895) = 5*X(69)+3*X(25320) = 3*X(125)-X(895) = 5*X(125)-3*X(25320) = 9*X(599)-X(2930) = 3*X(599)-X(5181) = 5*X(599)-X(5648) = 15*X(599)+X(25335) = 5*X(895)-9*X(25320) = X(2930)-3*X(5181) = 5*X(2930)-9*X(5648) = 5*X(2930)+3*X(25335) = 5*X(5181)-3*X(5648) = 5*X(5181)+X(25335) = 3*X(5648)+X(25335) = 3*X(20417)-2*X(32305) = X(32244)+2*X(32300) = X(32272)-3*X(32275)

The reciprocal orthologic center of these triangles is X(110).

X(32257) lies on these lines: {2,5095}, {3,67}, {6,6723}, {20,32250}, {23,32239}, {69,125}, {95,32258}, {110,3620}, {141,5972}, {182,32245}, {193,15059}, {394,32251}, {511,7687}, {524,5159}, {631,32234}, {1038,32259}, {1040,32286}, {1092,5622}, {1112,9822}, {1177,9306}, {1216,14984}, {1270,13774}, {1271,13654}, {1351,23515}, {1352,2777}, {1368,22165}, {2781,5893}, {2854,3631}, {3284,15993}, {3292,32285}, {3448,15812}, {3564,6699}, {3917,32260}, {5642,11061}, {5847,11735}, {5894,8263}, {5921,15055}, {7386,32255}, {7484,32240}, {7998,32248}, {7999,32249}, {8542,15116}, {9970,11487}, {9972,14076}, {10319,32277}, {10510,19378}, {10519,16163}, {11178,32271}, {11284,12828}, {11513,32291}, {11514,32292}, {11515,32301}, {11516,32302}, {11585,20301}, {11850,15027}, {11898,15061}, {12359,15115}, {12363,15605}, {14645,15359}, {15063,32247}, {15303,16176}, {15533,30771}, {16111,18440}, {17811,32276}, {18323,19924}, {18531,32273}, {19422,32293}, {19423,32294}, {29012,32113}

X(32257) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32275}, {20, 32250}, {67, 5181}, {69, 125}, {3448, 32114}, {5095, 32244}, {5642, 13169}, {15063, 32247}, {16111, 18440}, {30714, 32306}
X(32257) = reflection of X(i) in X(j) for these (i,j): (6, 6723), (1112, 9822), (5095, 32300), (5972, 141), (11574, 13416), (15118, 6698)
X(32257) = anticomplement of X(32300)
X(32257) = complement of X(5095)
X(32257) = inverse of X(9876) in the circumcircle
X(32257) = X(1156)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(32257) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5095, 32300), (2, 32244, 5095)


X(32258) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-SHARYGIN TO WALSMITH

Barycentrics    SB*SC*(S^2+SA*SB)*(S^2+SA*SC)*(3*S^4-(12*(3*SA+SW)*R^2-12*SA^2+3*SB*SC-3*SW^2)*S^2+SB*SC*SW^2) : :

The reciprocal orthologic center of these triangles is X(110).

X(32258) lies on these lines: {54,67}, {95,32257}, {97,32244}, {110,19171}, {275,5095}, {511,19195}, {542,8884}, {895,8795}, {1177,26887}, {2781,19206}, {2854,19197}, {2930,19189}, {3564,19193}, {9792,32246}, {12584,19185}, {14984,19194}, {16010,19172}, {16030,32240}, {19166,32241}, {19167,32248}, {19168,32249}, {19169,32250}, {19170,32251}, {19173,32254}, {19174,32255}, {19175,32259}, {19176,32272}, {19177,32273}, {19179,32275}, {19180,32276}, {19181,32277}, {19182,32286}, {19183,32291}, {19184,32292}, {19186,32293}, {19187,32294}, {19188,32300}, {19190,32301}, {19191,32302}, {19192,32305}, {21638,32260}, {23295,25328}

X(32258) = X(1156)-of-1st-anti-Sharygin-triangle if ABC is acute


X(32259) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(110).

X(32259) lies on these lines: {1,542}, {12,25328}, {33,32250}, {34,5095}, {35,32305}, {36,12584}, {55,16010}, {56,2930}, {65,651}, {67,73}, {110,1428}, {221,32276}, {388,32255}, {399,613}, {511,19470}, {524,7286}, {999,32254}, {1038,32257}, {1060,32275}, {1177,26888}, {1398,32240}, {1425,32260}, {1431,2842}, {1442,12739}, {1469,2854}, {1503,5160}, {1870,32234}, {2067,32291}, {2330,10088}, {2781,7355}, {3056,5663}, {3448,12588}, {3564,19469}, {3585,32273}, {4296,32244}, {4551,5018}, {5217,5621}, {5297,9140}, {6126,9976}, {6502,32292}, {7051,32301}, {7352,14984}, {7951,20301}, {8540,9970}, {12904,14982}, {14094,32290}, {18447,32272}, {18915,32241}, {19175,32258}, {19349,32251}, {19365,32245}, {19366,32246}, {19367,32248}, {19368,32249}, {19370,32293}, {19371,32294}, {19372,32300}, {19373,32302}

X(32259) = reflection of X(i) in X(j) for these (i,j): (1469, 3028), (32286, 1)
X(32259) = X(1156)-of-anti-tangential-midarc-triangle if ABC is acute
X(32259) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (895, 32289, 19369), (10088, 11579, 2330)


X(32260) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-WASAT TO WALSMITH

Barycentrics    a^2*(-a^2+b^2+c^2)*((b^2+c^2)*a^8-4*b^2*c^2*a^6-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^4+3*(b^2-c^2)^2*b^2*c^2*a^2+(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4)) : :
X(32260) = 3*X(51)-2*X(5095) = 3*X(51)-4*X(32246) = 9*X(373)-8*X(32300) = 3*X(3917)-4*X(32257) = 2*X(6593)-3*X(29959) = 3*X(9971)-X(16176) = X(11061)-3*X(11188)

The reciprocal orthologic center of these triangles is X(110).

X(32260) lies on these lines: {2,32248}, {4,32249}, {6,32240}, {25,32276}, {51,5095}, {67,1205}, {69,18125}, {110,14913}, {125,126}, {182,17701}, {184,2930}, {185,542}, {193,11800}, {373,32300}, {389,32234}, {511,10296}, {895,3292}, {1147,19361}, {1177,1495}, {1181,32254}, {1204,16010}, {1216,15133}, {1425,32259}, {1843,13417}, {1899,32241}, {2781,11381}, {2888,11444}, {2892,11550}, {3270,32286}, {3448,12272}, {3564,21649}, {3611,32277}, {3917,32257}, {5562,14984}, {5622,12584}, {6403,10628}, {6593,29959}, {7722,21851}, {8541,15141}, {9924,13171}, {9971,16176}, {11061,11188}, {12167,17847}, {13366,32245}, {13754,32272}, {13851,32273}, {16270,30714}, {21638,32258}, {21640,32291}, {21641,32292}, {21642,32293}, {21643,32294}, {21647,32301}, {21648,32302}, {21663,32305}

X(32260) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32249}, {3448, 12272}
X(32260) = reflection of X(i) in X(j) for these (i,j): (110, 14913), (193, 11800), (1205, 67), (5095, 32246), (5562, 32275), (6467, 125), (7722, 21851), (11381, 32250), (13417, 1843), (32234, 389)
X(32260) = complement of X(32248)
X(32260) = X(1156)-of-anti-Wasat-triangle if ABC is acute
X(32260) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2930, 32251, 184), (5095, 32246, 51)


X(32261) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AQUILA TO WALSMITH

Barycentrics
3*a^9+2*(b+c)*a^8-2*(b^2+c^2)*a^7-2*(b+c)*(b^2+c^2)*a^6-(2*b^4-3*b^2*c^2+2*c^4)*a^5+2*(b+c)*b^2*c^2*a^4+(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^3+2*(b^4-c^4)*(b^2-c^2)*(b+c)*a^2-(b^4-c^4)^2*a-2*(b^4-c^4)^2*(b+c) : :
X(32261) = 3*X(1)-4*X(32238) = 3*X(1)-2*X(32298) = 3*X(67)-2*X(32238) = 3*X(67)-X(32298) = 4*X(125)-3*X(16475) = 3*X(165)-2*X(32233) = 5*X(1698)-4*X(6593) = 3*X(1699)-4*X(32274) = 7*X(3624)-8*X(6698) = 3*X(3679)-2*X(32278) = 3*X(5587)-2*X(9970) = 3*X(11852)-2*X(32279) = 6*X(15462)-7*X(31423) = 5*X(18492)-4*X(32271)

The reciprocal orthologic center of these triangles is X(125).

X(32261) lies on these lines: {1,67}, {10,11061}, {35,32256}, {36,32270}, {40,542}, {57,32243}, {125,16475}, {165,32233}, {511,12407}, {515,32247}, {517,32306}, {1503,9904}, {1697,32297}, {1698,6593}, {1699,32274}, {2781,5691}, {2836,5904}, {2948,3416}, {3099,32268}, {3448,5847}, {3624,6698}, {3679,32278}, {3751,13211}, {4663,16176}, {5587,9970}, {5588,32281}, {5589,32280}, {7713,32239}, {8185,32262}, {8186,32265}, {8187,32266}, {8188,32295}, {8189,32296}, {9578,32289}, {9581,32290}, {9896,14984}, {10789,32242}, {10826,32287}, {10827,32288}, {11852,32279}, {13888,32303}, {13942,32304}, {15462,31423}, {18492,32271}, {19003,32252}, {19004,32253}

X(32261) = reflection of X(i) in X(j) for these (i,j): (1, 67), (2948, 3416), (3751, 13211), (11061, 10), (16176, 4663), (32298, 32238)
X(32261) = X(67)-of-Aquila-triangle
X(32261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (67, 32298, 32238), (32238, 32298, 1)


X(32262) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARA TO WALSMITH

Barycentrics    (SB+SC)*(3*(6*R^2-SW)*R^2*S^2+(2*SW^2+(3*SA-11*SW)*R^2)*SA*SW) : :
X(32262) = 3*X(159)-2*X(2930) = 3*X(1177)-2*X(6593) = 4*X(1177)-3*X(19153) = X(2930)-3*X(10117) = 4*X(6593)-3*X(15141) = 8*X(6593)-9*X(19153) = 2*X(15141)-3*X(19153)

The reciprocal orthologic center of these triangles is X(125).

X(32262) lies on these lines: {3,1177}, {6,1205}, {22,11061}, {24,32247}, {25,67}, {159,2930}, {197,32256}, {206,17847}, {382,25328}, {511,12412}, {542,7387}, {597,14130}, {1204,19136}, {1503,9919}, {1593,5621}, {1598,32274}, {1995,2892}, {2393,32276}, {2777,23049}, {2916,25331}, {2937,15582}, {3556,5904}, {5020,6698}, {5594,32281}, {5595,32280}, {6293,9968}, {7517,32306}, {8185,32261}, {8190,32265}, {8191,32266}, {8192,32298}, {8193,32278}, {8194,32295}, {8195,32296}, {9818,32271}, {9908,14984}, {9914,16010}, {9920,15581}, {10037,32307}, {10046,32308}, {10628,19149}, {10790,32242}, {10828,32268}, {10829,32287}, {10830,32288}, {10831,32289}, {10832,32290}, {10833,32297}, {10834,32309}, {10835,32310}, {11284,15116}, {11365,32238}, {11414,32233}, {11853,32279}, {13201,20806}, {13203,23300}, {13889,32303}, {13943,32304}, {15579,20427}, {16176,32240}, {18954,32243}, {19005,32252}, {19006,32253}, {22654,32270}

X(32262) = reflection of X(i) in X(j) for these (i,j): (159, 10117), (13203, 23300), (15141, 1177), (17847, 206), (32254, 15581)
X(32262) = X(67)-of-Ara-triangle
X(32262) = {X(1177), X(15141)}-harmonic conjugate of X(19153)


X(32263) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH TO ARIES

Barycentrics    SA*((28*R^2-SA-3*SW)*S^2-(SB+SC)*(2*(6*SA-SW)*R^2-SA^2+SB*SC+SW^2)) : :
X(32263) = 5*X(113)-4*X(22660) = X(12295)+2*X(15085)

The reciprocal orthologic center of these triangles is X(32264).

X(32263) lies on these lines: {6,5181}, {20,68}, {52,113}, {110,6353}, {125,343}, {161,542}, {511,32125}, {569,5504}, {1209,10170}, {1495,3564}, {1511,13292}, {2777,17834}, {2931,3515}, {3569,14391}, {5448,11002}, {5449,7999}, {5642,32226}, {6053,12164}, {6146,16163}, {8057,32112}, {8673,32120}, {8681,32113}, {9517,32121}, {11472,12295}, {12893,15078}, {13198,19131}, {13399,20725}, {13754,32111}

X(32263) = reflection of X(i) in X(j) for these (i,j): (12164, 6053), (30714, 2931)


X(32264) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARIES TO WALSMITH

Barycentrics    (24*(3*SA-2*SW)*R^4-(39*SA-29*SW)*R^2*SW+(5*SA-4*SW)*SW^2)*S^2-(14*R^2-3*SW)*SB*SC*SW^2 : :
X(32264) = 3*X(154)-2*X(5181) = 3*X(1853)-4*X(15118) = 2*X(2892)-3*X(15131) = 3*X(5622)-2*X(6247) = 4*X(5972)-5*X(19132) = 4*X(6593)-3*X(15131) = 2*X(11598)-3*X(25406) = X(13203)-3*X(25321) = 2*X(15116)-3*X(19153) = X(20079)-3*X(25320)

The reciprocal orthologic center of these triangles is X(32263).

X(32264) lies on these lines: {20,2781}, {25,32285}, {67,468}, {69,15647}, {125,19118}, {154,5181}, {159,2930}, {382,17813}, {542,1498}, {895,1503}, {1853,15118}, {2854,5596}, {2892,6593}, {3564,9934}, {5095,5895}, {5622,6247}, {5648,31166}, {5972,19132}, {9833,14984}, {11598,25406}, {13203,25321}, {14982,19149}, {15116,19153}, {15126,15128}, {15141,31152}, {15462,16196}, {20079,25320}, {32239,32251}

X(32264) = reflection of X(i) in X(j) for these (i,j): (67, 1177), (69, 15647), (2892, 6593), (5648, 31166), (14982, 19149)
X(32264) = {X(2892), X(6593)}-harmonic conjugate of X(15131)


X(32265) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st AURIGA TO WALSMITH

Barycentrics
(2*a^9+(b+c)*a^8-(b^2+c^2)*a^7-(b+c)*(b^2+c^2)*a^6-2*(b^4-b^2*c^2+c^4)*a^5+(b+c)*b^2*c^2*a^4+(b^6+c^6)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*a^2-(b^4-c^4)^2*(b+c))*D+a^2*(a+b+c)*(a-b-c)*(a^2+b^2+c^2)*(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)) : : , where D = 4*S*sqrt(R*(4*R+r))

The reciprocal orthologic center of these triangles is X(125).

X(32265) lies on these lines: {55,32266}, {67,5597}, {542,11252}, {2781,9834}, {5598,32298}, {5599,6593}, {5601,11061}, {5846,13209}, {8186,32261}, {8190,32262}, {8196,32274}, {8197,32278}, {8198,32280}, {8199,32281}, {8200,9970}, {11366,32238}, {11384,32239}, {11492,32256}, {11493,32270}, {11822,32233}, {11837,32242}, {11843,32247}, {11861,32268}, {11865,32287}, {11867,32288}, {11869,32289}, {11871,32290}, {11873,32297}, {11875,32306}, {11877,32307}, {11879,32308}, {11881,32309}, {11883,32310}, {13890,32303}, {13944,32304}, {18495,32271}, {18955,32243}, {19007,32252}, {19008,32253}

X(32265) = reflection of X(32266) in X(55)
X(32265) = X(67)-of-1st-Auriga-triangle


X(32266) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd AURIGA TO WALSMITH

Barycentrics
-(2*a^9+(b+c)*a^8-(b^2+c^2)*a^7-(b+c)*(b^2+c^2)*a^6-2*(b^4-b^2*c^2+c^4)*a^5+(b+c)*b^2*c^2*a^4+(b^6+c^6)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*a^2-(b^4-c^4)^2*(b+c))*D+a^2*(a+b+c)*(a-b-c)*(a^2+b^2+c^2)*(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)) : : , where D = 4*S*sqrt(R*(4*R+r))

The reciprocal orthologic center of these triangles is X(125).

X(32266) lies on these lines: {55,32265}, {67,5598}, {542,11253}, {2781,9835}, {5597,32298}, {5600,6593}, {5602,11061}, {5846,13208}, {8187,32261}, {8191,32262}, {8203,32274}, {8204,32278}, {8205,32280}, {8206,32281}, {8207,9970}, {11367,32238}, {11385,32239}, {11492,32270}, {11493,32256}, {11823,32233}, {11838,32242}, {11844,32247}, {11862,32268}, {11866,32287}, {11868,32288}, {11870,32289}, {11872,32290}, {11874,32297}, {11876,32306}, {11878,32307}, {11880,32308}, {11882,32309}, {11884,32310}, {13891,32303}, {13945,32304}, {18497,32271}, {18956,32243}, {19009,32252}, {19010,32253}

X(32266) = reflection of X(32265) in X(55)
X(32266) = X(67)-of-2nd-Auriga-triangle


X(32267) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: WALSMITH TO 4th BROCARD

Barycentrics    10*a^6-4*(b^2+c^2)*a^4-(7*b^4-12*b^2*c^2+7*c^4)*a^2+(b^4-c^4)*(b^2-c^2) : :
X(32267) = 5*X(1495)+X(3580) = 2*X(1495)+X(32223) = 3*X(1495)+X(32225) = 3*X(2070)+X(5655) = X(3580)-5*X(7426) = 2*X(3580)-5*X(32223) = 3*X(3580)-5*X(32225) = X(5972)-4*X(15448) = X(5972)+2*X(32237) = 3*X(7426)-X(32225) = 2*X(12105)+X(16534) = X(15303)-3*X(18374) = 2*X(15448)+X(32237) = 3*X(32223)-2*X(32225)

See preamble just before X(31353).

X(32267) lies on these lines: {2,6030}, {23,5642}, {25,5476}, {30,5972}, {154,11225}, {182,26255}, {376,1533}, {468,11645}, {541,7575}, {542,1495}, {575,20192}, {1995,10168}, {2070,5655}, {3524,16187}, {4232,11179}, {5646,15706}, {5965,15360}, {7493,11178}, {12100,15082}, {12105,16534}, {13857,29317}, {14002,25555}, {14848,31860}, {14915,18579}, {15303,18374}

X(32267) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 5642}, {376, 1533}, {1495, 7426}
X(32267) = reflection of X(32223) in X(7426)
X(32267) = {X(15448), X(32237)}-harmonic conjugate of X(5972)


X(32268) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th BROCARD TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32268) lies on these lines: {32,67}, {511,12501}, {542,7826}, {1503,9984}, {2781,9873}, {2896,11061}, {3096,6593}, {3098,32233}, {3099,32261}, {6698,7846}, {9301,32306}, {9857,32278}, {9862,32247}, {9923,14984}, {9970,9996}, {9993,32274}, {9994,32280}, {9995,32281}, {9997,32298}, {10038,32307}, {10047,32308}, {10828,32262}, {10871,32287}, {10872,32288}, {10873,32289}, {10874,32290}, {10875,32295}, {10876,32296}, {10877,32297}, {10878,32309}, {10879,32310}, {11368,32238}, {11386,32239}, {11494,32256}, {11861,32265}, {11862,32266}, {11885,32279}, {13892,32303}, {13946,32304}, {18500,32271}, {18957,32243}, {19011,32252}, {19012,32253}, {22744,32270}

X(32268) = X(67)-of-5th-Brocard-triangle


X(32269) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: WALSMITH TO CIRCUMORTHIC

Barycentrics    2*a^6+(b^2+c^2)*a^4-4*(b^4-b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2) : :
X(32269) = 3*X(23)+X(3448) = X(110)-3*X(7426) = X(110)+3*X(15360) = X(125)-3*X(32225) = 3*X(468)-2*X(5972) = 3*X(858)-5*X(15059) = 3*X(1495)-X(24981) = X(1514)+2*X(3581) = 3*X(1514)-2*X(7728) = X(3448)-3*X(3580) = 3*X(3581)+X(7728) = 4*X(5972)-3*X(11064) = X(5972)-3*X(32223) = 3*X(7426)-2*X(15448) = X(7728)-3*X(11799) = X(11064)-4*X(32223) = X(12041)-3*X(15361) = 5*X(15059)+3*X(15107) = 3*X(15360)+2*X(15448) = 4*X(16111)-3*X(20725) = X(16111)-3*X(32110) = X(20725)-4*X(32110) = X(25329)-3*X(32217)

See preamble just before X(31353).

X(32269) lies on these lines: {2,1350}, {3,16657}, {6,7493}, {22,13567}, {23,1503}, {25,343}, {26,6146}, {30,125}, {51,6676}, {52,13383}, {68,9714}, {69,4232}, {107,297}, {110,524}, {140,373}, {141,1995}, {154,6515}, {184,1353}, {187,6388}, {193,15585}, {230,3124}, {237,23181}, {381,4549}, {394,6353}, {428,21243}, {460,13449}, {462,20429}, {463,20428}, {468,511}, {542,32237}, {549,22112}, {599,26255}, {858,15059}, {1211,4228}, {1213,7474}, {1330,4248}, {1370,26958}, {1495,3564}, {1514,3581}, {1620,30552}, {1624,5201}, {1648,4226}, {1853,7500}, {1899,9909}, {1993,10192}, {2070,12310}, {3060,23292}, {3098,30739}, {3146,6696}, {3542,17834}, {3589,5640}, {3631,10546}, {3658,15447}, {3796,10565}, {3818,10301}, {3917,6677}, {4239,26543}, {5054,5544}, {5094,31670}, {5104,24855}, {5446,7542}, {5449,7553}, {5562,21841}, {5663,16619}, {5889,16252}, {5943,7499}, {5946,25337}, {6243,9820}, {6329,15019}, {6723,19924}, {6800,8550}, {7391,23332}, {7465,25964}, {7488,12241}, {7494,10601}, {7503,15873}, {7517,12359}, {7530,16654}, {7556,12022}, {7568,10095}, {7570,7693}, {7706,15760}, {9019,11746}, {9730,16618}, {9970,32227}, {10020,10263}, {10516,31860}, {10625,16238}, {11002,14389}, {11003,12007}, {11594,32311}, {11649,11800}, {11745,13160}, {12088,26879}, {12107,12370}, {12828,16165}, {13142,13367}, {14449,18282}, {14693,15366}, {15993,20998}, {16195,19467}, {16789,19136}, {17522,26579}, {20850,31383}

X(32269) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 3580}, {858, 15107}, {3581, 11799}, {7426, 15360}
X(32269) = reflection of X(i) in X(j) for these (i,j): (110, 15448), (468, 32223), (1514, 11799), (11064, 468)
X(32269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 7493, 13394), (5640, 7495, 3589)


X(32270) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd CIRCUMPERP TANGENTIAL TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32270) lies on these lines: {1,15141}, {3,32256}, {36,32261}, {55,32298}, {56,67}, {104,32247}, {511,19478}, {542,11249}, {956,32278}, {958,6593}, {999,32238}, {1503,22583}, {2781,12114}, {2930,23361}, {2975,11061}, {3428,32233}, {5846,13204}, {6698,25524}, {9970,22758}, {10966,32297}, {11492,32266}, {11493,32265}, {14984,22659}, {18761,32271}, {19013,32252}, {19014,32253}, {22479,32239}, {22520,32242}, {22654,32262}, {22744,32268}, {22753,32274}, {22755,32279}, {22756,32280}, {22757,32281}, {22759,32289}, {22760,32290}, {22761,32295}, {22762,32296}, {22763,32303}, {22764,32304}, {22765,32306}, {22766,32307}, {22767,32308}, {22768,32309}

X(32270) = reflection of X(i) in X(j) for these (i,j): (32256, 3), (32288, 6593)
X(32270) = X(67)-of-2nd-circumperp-tangential-triangle


X(32271) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-MID TO WALSMITH

Barycentrics
4*(b^2+c^2)*a^10-(7*b^4-2*b^2*c^2+7*c^4)*a^8-2*(b^4-c^4)*(b^2-c^2)*a^6+2*(4*b^8+4*c^8-(5*b^4-4*b^2*c^2+5*c^4)*b^2*c^2)*a^4-2*(b^6-c^6)*(b^4-c^4)*a^2-(b^4-c^4)^2*(b^2-c^2)^2 : :
X(32271) = 3*X(4)+X(11061) = 3*X(5)-2*X(6698) = X(20)-3*X(15462) = X(67)-3*X(381) = X(74)-3*X(14561) = 3*X(113)-X(5181) = X(146)+3*X(14853) = 3*X(182)-4*X(32300) = 3*X(265)-X(25335) = X(895)+3*X(10706) = X(895)-3*X(20423) = X(1350)-3*X(14643) = 3*X(1352)-X(32244) = X(2930)-3*X(5655) = 5*X(3091)-X(32247) = 3*X(5476)-2*X(15118) = 3*X(5476)-X(32305) = 3*X(9970)-X(11061) = 3*X(10752)+X(32244) = X(11579)-3*X(14853)

The reciprocal orthologic center of these triangles is X(125).

X(32271) lies on these lines: {4,542}, {5,2781}, {6,7728}, {20,15462}, {23,5642}, {30,6593}, {67,381}, {74,14561}, {110,7519}, {113,511}, {125,5169}, {146,11579}, {182,1177}, {265,25335}, {382,15140}, {389,16003}, {541,5476}, {546,32274}, {611,12374}, {613,12373}, {858,12824}, {1350,14643}, {1351,14982}, {1352,10752}, {1478,32290}, {1479,32289}, {1503,1539}, {1511,29181}, {2854,21850}, {2930,5655}, {3091,32247}, {3098,5972}, {3583,32297}, {3585,32243}, {3589,12041}, {3618,12244}, {3843,32306}, {5085,20127}, {5092,16111}, {5480,5663}, {7527,10990}, {7530,12584}, {7540,30714}, {9818,32262}, {9955,32238}, {10296,13202}, {10510,18325}, {10605,15128}, {10895,32307}, {10896,32308}, {11178,32257}, {11444,18504}, {11645,15303}, {12061,14984}, {12699,32278}, {13665,32253}, {13785,32252}, {14483,18125}, {16163,29317}, {16176,32272}, {17702,19139}, {18491,32256}, {18492,32261}, {18495,32265}, {18497,32266}, {18500,32268}, {18502,32242}, {18507,32279}, {18509,32280}, {18511,32281}, {18516,32287}, {18517,32288}, {18520,32295}, {18522,32296}, {18525,32298}, {18538,32303}, {18542,32309}, {18544,32310}, {18553,32275}, {18761,32270}, {18762,32304}

X(32271) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 9970}, {6, 7728}, {110, 31670}, {146, 11579}, {382, 32233}, {1351, 14982}, {1352, 10752}, {10510, 18325}, {10706, 20423}, {12699, 32278}, {16176, 32272}, {18507, 32279}, {18525, 32298}
X(32271) = reflection of X(i) in X(j) for these (i,j): (125, 19130), (3098, 5972), (5642, 25566), (12041, 3589), (12584, 16534), (16003, 20301), (16111, 5092), (32238, 9955), (32274, 546), (32275, 18553), (32305, 15118)
X(32271) = X(67)-of-Ehrmann-mid-triangle
X(32271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (146, 14853, 11579), (5476, 32305, 15118)


X(32272) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-SIDE TO WALSMITH

Barycentrics    SA*(12*(3*R^2-SW)*S^2-(SB+SC)*(27*R^2-3*SA-7*SW)*SW) : :
X(32272) = 3*X(3)-4*X(32257) = 4*X(67)-3*X(20126) = 3*X(67)-2*X(32305) = 3*X(265)-2*X(895) = 3*X(381)-2*X(5095) = 3*X(568)-4*X(32246) = 3*X(1352)-2*X(6593) = 4*X(1352)-3*X(14643) = 2*X(1353)-3*X(14644) = X(2930)-3*X(15069) = 4*X(2930)-3*X(23236) = 9*X(5055)-8*X(32300) = 3*X(5093)-4*X(7687) = 3*X(5655)-2*X(11061) = 8*X(6593)-9*X(14643) = 4*X(10297)-3*X(18449) = X(11061)-3*X(11180) = 4*X(15069)-X(23236) = 9*X(20126)-8*X(32305) = 2*X(32257)-3*X(32275)

The reciprocal orthologic center of these triangles is X(110).

X(32272) lies on these lines: {3,67}, {5,32234}, {30,32244}, {49,5622}, {69,12121}, {110,19129}, {193,10113}, {265,895}, {381,5095}, {382,32250}, {511,22584}, {524,18323}, {567,32245}, {568,32246}, {1177,10540}, {1352,6593}, {1353,14644}, {1503,20127}, {2072,25328}, {2781,18439}, {2854,7723}, {3448,16051}, {3545,10294}, {5055,32300}, {5093,7687}, {5159,9140}, {5655,11061}, {5663,5921}, {6288,9970}, {6698,11179}, {6776,15061}, {7728,18440}, {9818,32240}, {10255,20301}, {10510,18441}, {11459,32248}, {11562,14913}, {11898,17702}, {12111,32249}, {12272,12281}, {13754,32260}, {14516,15054}, {14912,20304}, {14984,18436}, {15027,15128}, {16176,32271}, {18403,32273}, {18445,32251}, {18447,32259}, {18451,32276}, {18453,32277}, {18455,32286}, {18457,32291}, {18459,32292}, {18462,32293}, {18463,32294}, {18468,32301}, {18470,32302}, {18531,32255}, {18917,32241}, {19176,32258}, {20397,26944}

X(32272) = midpoint of X(i) and X(j) for these lines: {i,j}: {12111, 32249}, {12272, 12281}
X(32272) = reflection of X(i) in X(j) for these (i,j): (3, 32275), (193, 10113), (382, 32250), (5655, 11180), (7728, 18440), (11562, 14913), (12121, 69), (16176, 32271), (18438, 7723), (32234, 5)
X(32272) = X(1156)-of-Ehrmann-side-triangle if ABC is acute
X(32272) = Stammler-circle-inverse of X(9876)


X(32273) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-VERTEX TO WALSMITH

Barycentrics    3*(3*SA-2*SW)*R^2*S^2-(27*R^2-8*SW)*SB*SC*SW : :
X(32273) = 3*X(4)+X(32255) = X(67)-3*X(265) = 3*X(182)-4*X(15118) = 3*X(381)-X(2930) = 3*X(576)-2*X(5095) = 3*X(1351)-X(16176) = X(1657)-3*X(5621) = 5*X(3843)-X(32254) = 2*X(5181)-3*X(11178) = 3*X(5476)-2*X(6593) = X(10620)-3*X(25330) = X(11061)-3*X(20423) = X(12383)-3*X(14561) = 3*X(14644)-2*X(24206) = 2*X(14810)-3*X(15061) = 3*X(14853)-2*X(25556) = 2*X(15116)-3*X(23325) = X(15141)-3*X(23049) = 3*X(15462)-4*X(25555) = 2*X(16163)-3*X(17508)

The reciprocal orthologic center of these triangles is X(110).

X(32273) lies on these lines: {3,20301}, {4,542}, {5,12584}, {6,12902}, {30,25328}, {67,265}, {74,29317}, {110,7533}, {125,3098}, {141,11801}, {182,15118}, {381,2930}, {382,16010}, {524,18572}, {575,32233}, {578,30714}, {1177,18400}, {1351,16176}, {1352,18387}, {1503,9976}, {1657,5621}, {2781,10263}, {2836,18480}, {2854,3818}, {3153,32244}, {3448,16981}, {3564,19479}, {3583,32286}, {3585,32259}, {3843,32254}, {3845,16510}, {5092,12121}, {5181,11178}, {5189,9140}, {5476,6593}, {5480,19140}, {5622,21659}, {5648,25561}, {5987,9993}, {6288,18553}, {6564,32291}, {6565,32292}, {9143,25566}, {9927,11591}, {10264,29181}, {10620,25330}, {10733,11579}, {11477,32306}, {11564,18125}, {11645,18325}, {12370,18428}, {12383,14561}, {13293,23300}, {13434,15462}, {13851,32260}, {14644,24206}, {14810,15061}, {14853,25556}, {15116,23325}, {15141,23049}, {16163,17508}, {16808,32301}, {16809,32302}, {18382,19506}, {18386,32240}, {18388,32245}, {18390,32246}, {18392,32248}, {18394,32249}, {18396,32251}, {18403,32272}, {18404,32275}, {18405,32276}, {18406,32277}, {18414,32293}, {18415,32294}, {18420,32300}, {18531,32257}, {18918,32241}, {19177,32258}

X(32273) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 12902}, {382, 16010}, {3448, 31670}, {10733, 11579}, {11477, 32306}
X(32273) = reflection of X(i) in X(j) for these (i,j): (3, 20301), (110, 19130), (141, 11801), (3098, 125), (3818, 10113), (5648, 25561), (9143, 25566), (12121, 5092), (12584, 5), (13293, 23300), (19140, 5480), (19506, 18382), (32233, 575), (32305, 25328)
X(32273) = X(1156)-of-Ehrmann-vertex-triangle if ABC is acute


X(32274) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EULER TO WALSMITH

Barycentrics    3*S^4-3*(R^2*(SW+3*SA)-SA^2+SB*SC)*S^2-(18*R^2-5*SW)*SB*SC*SW : :
X(32274) = 3*X(4)+X(32247) = X(6)-3*X(14644) = 3*X(6)-X(32234) = 3*X(67)-X(32247) = X(110)-3*X(10516) = 3*X(125)+X(32250) = 3*X(381)-X(9970) = 3*X(381)+X(32306) = 5*X(1656)-3*X(15462) = 3*X(1699)+X(32261) = 5*X(3091)-X(11061) = 2*X(3589)-3*X(23515) = 5*X(3763)-3*X(15035) = 3*X(5085)-5*X(15059) = 3*X(5587)-X(32278) = 3*X(5603)-X(32298) = X(5921)+3*X(25320) = X(6776)-5*X(15081) = 3*X(9140)-X(16010) = 9*X(14644)-X(32234)

The reciprocal orthologic center of these triangles is X(125).

X(32274) lies on these lines: {2,32233}, {3,6698}, {4,67}, {5,542}, {6,7699}, {11,32243}, {12,32297}, {24,5621}, {30,8262}, {66,10293}, {98,32242}, {110,10516}, {113,25488}, {125,468}, {141,17702}, {182,20304}, {235,32239}, {265,1352}, {371,32303}, {372,32304}, {381,9970}, {511,10113}, {515,32238}, {524,10297}, {546,32271}, {895,15069}, {1350,10733}, {1478,32308}, {1479,32307}, {1511,24206}, {1587,32252}, {1588,32253}, {1598,32262}, {1614,5622}, {1656,15462}, {1699,32261}, {1986,32191}, {1995,9140}, {2493,11005}, {2836,5777}, {3091,11061}, {3448,14982}, {3564,11801}, {3574,5095}, {3575,10990}, {3589,23515}, {3763,15035}, {3818,5663}, {5085,15059}, {5480,7687}, {5587,32278}, {5603,32298}, {5921,25320}, {6103,28343}, {6201,32281}, {6202,32280}, {6247,13419}, {6776,15081}, {7495,16165}, {7533,12824}, {7547,16176}, {7574,9019}, {7575,11645}, {8196,32265}, {8203,32266}, {8212,32295}, {8213,32296}, {9517,18312}, {9815,25711}, {9927,11591}, {9969,10628}, {9993,32268}, {10531,32309}, {10532,32310}, {10893,32287}, {10894,32288}, {10895,32289}, {10896,32290}, {11178,12584}, {11477,15044}, {11496,32256}, {11579,18440}, {11897,32279}, {12041,29012}, {12061,18383}, {12106,20379}, {12295,29181}, {12588,12904}, {12589,12903}, {14094,25335}, {14787,23236}, {15577,19457}, {19161,21650}, {22753,32270}

X(32274) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 67}, {265, 1352}, {895, 15069}, {1350, 10733}, {3448, 14982}, {9970, 32306}, {11005, 11646}, {11477, 32244}, {11579, 18440}, {14094, 25335}, {15738, 32246}, {19161, 21650}
X(32274) = reflection of X(i) in X(j) for these (i,j): (3, 6698), (182, 20304), (1511, 24206), (1986, 32191), (5480, 7687), (6593, 5), (8550, 15118), (32271, 546), (32305, 20379)
X(32274) = complement of X(32233)
X(32274) = X(67)-of-Euler-triangle
X(32274) = {X(381), X(32306)}-harmonic conjugate of X(9970)


X(32275) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd EULER TO WALSMITH

Barycentrics    SA*(12*(3*R^2-SW)*S^2-(SB+SC)*(18*R^2-3*SA-5*SW)*SW) : :
X(32275) = 2*X(6)-3*X(23515) = 3*X(67)-X(16010) = 3*X(113)-2*X(9970) = X(193)-3*X(14644) = 3*X(599)-X(32233) = 3*X(1352)-X(9970) = 5*X(1656)-4*X(32300) = 5*X(3620)-3*X(15035) = 3*X(5050)-4*X(6723) = 3*X(5181)-2*X(12584) = 3*X(5622)-4*X(20397) = 4*X(9822)-3*X(16222) = 3*X(11180)+X(32247) = 4*X(12584)-3*X(30714) = 3*X(13169)-X(32247) = 2*X(15069)+X(16003) = 3*X(15069)+X(16010) = 3*X(16003)-2*X(16010) = X(32254)+3*X(32306) = 2*X(32257)+X(32272)

The reciprocal orthologic center of these triangles is X(110).

X(32275) lies on these lines: {2,32234}, {3,67}, {4,32244}, {5,5095}, {6,23515}, {30,32250}, {52,32246}, {68,895}, {69,4549}, {74,5921}, {110,19131}, {113,1352}, {125,3292}, {155,32251}, {193,14644}, {265,11898}, {511,7723}, {524,10297}, {541,11180}, {569,32245}, {575,24572}, {1060,32259}, {1062,32286}, {1147,5622}, {1177,10539}, {1209,6593}, {1351,7687}, {1353,20304}, {1503,16111}, {1656,32300}, {1995,12828}, {2072,20301}, {2777,18440}, {2781,12162}, {2854,9967}, {3620,15035}, {5050,6723}, {5562,14984}, {5609,31831}, {5965,18449}, {6334,9003}, {6403,12219}, {6643,32255}, {6698,8550}, {6699,6776}, {7395,32240}, {7530,32239}, {8251,32277}, {9140,16051}, {9822,16222}, {10510,19380}, {10628,14913}, {10634,32301}, {10635,32302}, {10897,32291}, {10898,32292}, {11061,16534}, {11178,15303}, {11411,32241}, {11444,32248}, {11459,32249}, {11585,25328}, {14912,15059}, {17814,32276}, {18404,32273}, {18553,32271}, {19179,32258}, {19428,32293}, {19429,32294}

X(32275) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32272}, {4, 32244}, {67, 15069}, {74, 5921}, {265, 11898}, {5562, 32260}, {6403, 12219}, {11180, 13169}
X(32275) = reflection of X(i) in X(j) for these (i,j): (3, 32257), (52, 32246), (113, 1352), (1351, 7687), (1353, 20304), (5095, 5), (6776, 6699), (8550, 6698), (9967, 12358), (11061, 16534), (15303, 11178), (16003, 67), (30714, 5181), (32271, 18553)
X(32275) = complement of X(32234)
X(32275) = X(1156)-of-2nd-Euler-triangle if ABC is acute


X(32276) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st EXCOSINE TO WALSMITH

Barycentrics    (SB+SC)*((3*R^2*(24*R^2-11*SW)+2*(SA+2*SW)*SW)*S^2-2*((3*SA+SW)*R^2-SA^2+SB*SC)*SA*SW) : :
X(32276) = 3*X(6)-2*X(15141) = 2*X(66)-3*X(25330) = 4*X(110)-5*X(19132) = 3*X(154)-4*X(1177) = 3*X(154)-2*X(2930) = 4*X(895)-3*X(17813) = 3*X(1853)-2*X(2892) = 3*X(1853)-4*X(25328) = 6*X(5621)-5*X(8567) = 3*X(10606)-4*X(32305) = 4*X(12584)-5*X(17821) = 4*X(15118)-3*X(15131) = 4*X(15141)-3*X(17847) = 3*X(18405)-4*X(32273) = 2*X(23315)-3*X(25320)

The reciprocal orthologic center of these triangles is X(110).

X(32276) lies on these lines: {6,67}, {22,32248}, {24,32249}, {25,32260}, {64,895}, {66,25330}, {110,19132}, {154,1177}, {184,32240}, {221,32259}, {394,32244}, {511,15138}, {542,1498}, {1181,32234}, {1205,10602}, {1351,10628}, {1503,17812}, {1853,2892}, {1992,17823}, {2192,32286}, {2393,32262}, {2854,9924}, {2888,11061}, {2935,11579}, {3197,32277}, {3564,17838}, {5505,31860}, {5621,8567}, {5622,11425}, {6467,13171}, {6759,32254}, {10606,32305}, {10982,15738}, {12167,13417}, {12584,17821}, {13203,15583}, {13567,32241}, {14984,17834}, {15811,32250}, {16003,17822}, {17809,32245}, {17810,32246}, {17811,32257}, {17814,32275}, {17819,32291}, {17820,32292}, {17825,32300}, {17826,32301}, {17827,32302}, {18405,32273}, {18451,32272}, {19180,32258}, {19430,32293}, {19431,32294}, {23315,25320}

X(32276) = reflection of X(i) in X(j) for these (i,j): (64, 16010), (2892, 25328), (2930, 1177), (2935, 11579), (9924, 10117), (13203, 15583), (17847, 6), (32254, 6759)
X(32276) = X(1156)-of-1st-excosine-triangle if ABC is acute
X(32276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1177, 2930, 154), (5095, 32251, 6)


X(32277) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EXTANGENTS TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(110).

X(32277) lies on these lines: {19,5095}, {40,542}, {55,2930}, {65,651}, {67,71}, {110,1963}, {511,7724}, {1177,10536}, {2550,32255}, {2781,6254}, {2854,3779}, {3101,32244}, {3197,32276}, {3564,12661}, {3611,32260}, {3925,25328}, {5415,32291}, {5416,32292}, {5584,16010}, {6197,32234}, {6237,14984}, {7067,16563}, {7688,32305}, {8251,32275}, {9816,32300}, {10306,32254}, {10319,32257}, {10636,32301}, {10637,32302}, {10902,12584}, {11406,32240}, {11428,32245}, {11435,32246}, {11445,32248}, {11460,32249}, {11471,32250}, {18406,32273}, {18453,32272}, {18921,32241}, {19181,32258}, {19350,32251}, {19432,32293}, {19433,32294}

X(32277) = reflection of X(32286) in X(2930)
X(32277) = X(1156)-of-extangents-triangle if ABC is acute


X(32278) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GARCIA TO WALSMITH

Barycentrics    a*(a^8+2*(b+c)*a^7-(b^2+c^2)*a^6-(b+c)*(b^2+c^2)*a^5+b^2*c^2*a^4-2*(b+c)*(b^4-b^2*c^2+c^4)*a^3+(b^4-c^4)*(b^2-c^2)*a^2+(b^6+c^6)*(b+c)*a-(b^4-c^4)^2) : :
X(32278) = 2*X(1385)-3*X(15462) = 5*X(1698)-4*X(6698) = 3*X(3679)-X(32261) = 3*X(5085)-2*X(11709) = 3*X(5587)-2*X(32274) = 3*X(5657)-X(32247) = 3*X(5790)-X(32306) = 2*X(12261)-3*X(14561)

The reciprocal orthologic center of these triangles is X(125).

X(32278) lies on these lines: {1,6593}, {2,32238}, {8,11061}, {10,67}, {40,2781}, {65,651}, {72,692}, {110,518}, {355,542}, {511,12778}, {515,32233}, {517,9970}, {519,32298}, {956,32270}, {1385,15462}, {1386,7984}, {1503,12368}, {1698,6698}, {1737,32308}, {1837,32297}, {2771,11579}, {2854,2948}, {3057,32290}, {3242,11720}, {3679,32261}, {3827,13248}, {5085,11709}, {5090,32239}, {5252,32243}, {5587,32274}, {5657,32247}, {5687,32256}, {5688,32281}, {5689,32280}, {5790,32306}, {5846,25329}, {8193,32262}, {8197,32265}, {8204,32266}, {8214,32295}, {8215,32296}, {9857,32268}, {9928,14984}, {10039,32307}, {10791,32242}, {10914,32287}, {10915,32309}, {10916,32310}, {11900,32279}, {12261,14561}, {12699,32271}, {13883,32253}, {13893,32303}, {13936,32252}, {13947,32304}

X(32278) = midpoint of X(i) and X(j) for these lines: {i,j}: {8, 11061}, {2948, 3751}
X(32278) = reflection of X(i) in X(j) for these (i,j): (1, 6593), (67, 10), (895, 4663), (3242, 11720), (7984, 1386), (12699, 32271)
X(32278) = anticomplement of X(32238)
X(32278) = X(67)-of-outer-Garcia-triangle


X(32279) = ORTHOLOGIC CENTER OF THESE TRIANGLES: GOSSARD TO WALSMITH

Barycentrics    (S^2-3*SB*SC)*(3*S^4+(9*R^2*(12*R^2-SA-5*SW)+3*SA^2-3*SB*SC+4*SW^2)*S^2-54*R^4*(2*SW^2+3*SB*SC)+R^2*SW*(47*SW^2+12*SA^2+69*SB*SC)-SW^2*(3*SA^2+7*SB*SC+5*SW^2)) : :
X(32279) = 4*X(6698)-5*X(15183) = 3*X(11831)-2*X(32238) = 3*X(11845)-X(32247) = 3*X(11852)-X(32261) = 3*X(11897)-2*X(32274) = 3*X(11911)-X(32306)

The reciprocal orthologic center of these triangles is X(125).

X(32279) lies on these lines: {30,9970}, {67,402}, {511,12790}, {542,11251}, {1503,12369}, {1650,6593}, {2781,12113}, {4240,11061}, {6698,15183}, {11831,32238}, {11832,32239}, {11839,32242}, {11845,32247}, {11848,32256}, {11852,32261}, {11853,32262}, {11885,32268}, {11897,32274}, {11900,32278}, {11901,32280}, {11902,32281}, {11903,32287}, {11904,32288}, {11905,32289}, {11906,32290}, {11907,32295}, {11908,32296}, {11909,32297}, {11910,32298}, {11911,32306}, {11912,32307}, {11913,32308}, {11914,32309}, {11915,32310}, {12418,14984}, {13894,32303}, {13948,32304}, {18507,32271}, {18958,32243}, {19017,32252}, {19018,32253}, {22755,32270}

X(32279) = midpoint of X(4240) and X(11061)
X(32279) = reflection of X(i) in X(j) for these (i,j): (67, 402), (1650, 6593), (18507, 32271)
X(32279) = X(67)-of-Gossard-triangle


X(32280) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-GREBE TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32280) lies on these lines: {6,67}, {511,12803}, {542,1161}, {1271,11061}, {1503,7725}, {2781,5871}, {2930,8903}, {5589,32261}, {5591,6593}, {5595,32262}, {5605,32298}, {5689,32278}, {6202,32274}, {6215,9970}, {6218,32246}, {7720,9971}, {8198,32265}, {8205,32266}, {8216,32295}, {8217,32296}, {8974,32303}, {9929,14984}, {9994,32268}, {10040,32307}, {10048,32308}, {10783,32247}, {10792,32242}, {10814,12367}, {10919,32287}, {10921,32288}, {10923,32289}, {10925,32290}, {10927,32297}, {10929,32309}, {10931,32310}, {11370,32238}, {11388,32239}, {11497,32256}, {11824,32233}, {11901,32279}, {11916,32306}, {13949,32304}, {18509,32271}, {18959,32243}, {22756,32270}

X(32280) = reflection of X(32281) in X(67)
X(32280) = X(67)-of-inner-Grebe-triangle


X(32281) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GREBE TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32281) lies on these lines: {6,67}, {511,12804}, {542,1160}, {1270,11061}, {1503,7726}, {2781,5870}, {2930,8904}, {5588,32261}, {5590,6593}, {5594,32262}, {5604,32298}, {5688,32278}, {6201,32274}, {6214,9970}, {6217,32246}, {7721,9971}, {8199,32265}, {8206,32266}, {8218,32295}, {8219,32296}, {8975,32303}, {9930,14984}, {9995,32268}, {10041,32307}, {10049,32308}, {10784,32247}, {10793,32242}, {10815,12367}, {10920,32287}, {10922,32288}, {10924,32289}, {10926,32290}, {10928,32297}, {10930,32309}, {10932,32310}, {11371,32238}, {11389,32239}, {11498,32256}, {11825,32233}, {11902,32279}, {11917,32306}, {13950,32304}, {18511,32271}, {18960,32243}, {22757,32270}

X(32281) = reflection of X(32280) in X(67)
X(32281) = X(67)-of-outer-Grebe-triangle


X(32282) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH TO 3rd HATZIPOLAKIS

Barycentrics    (336*R^6-R^4*(49*SA+183*SW)+R^2*SW*(33*SW+20*SA)-2*SW^2*(SW+SA))*S^2-(4*R^2-SW)*R^2*SB*SC*SW : :

The reciprocal orthologic center of these triangles is X(32283).

X(32282) lies on these lines: {74,5894}, {110,13567}, {113,389}, {370,18604}, {1112,32125}, {1899,10117}, {2929,2931}, {11444,23308}, {11472,11801}, {15059,22830}, {15739,22530}


X(32283) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd HATZIPOLAKIS TO WALSMITH

Barycentrics    (6*(21*SA+SW)*R^4-3*(25*SA-6*SW)*R^2*SW+2*(5*SA-2*SW)*SW^2)*S^2-(11*R^2-2*SW)*SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(32282).

X(32283) lies on these lines: {6,67}, {542,13630}, {5012,5181}

X(32283) = midpoint of X(15118) and X(32285)


X(32284) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HYACINTH TO WALSMITH

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b^4+5*b^2*c^2+c^4)*a^6+16*(b^2+c^2)*b^2*c^2*a^4+2*(b^4+c^4+(b-c)^2*b*c)*(b^4+c^4-(b+c)^2*b*c)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(32284) = X(4)+3*X(15531) = 3*X(6)-2*X(5462) = 3*X(51)-5*X(11482) = X(52)-3*X(1992) = 3*X(193)+X(11412) = 4*X(575)-3*X(5892) = 3*X(1353)-X(6102) = X(1843)-3*X(5093) = 3*X(1992)+X(15073) = 5*X(3567)-9*X(5032) = 3*X(6776)-X(10575) = 7*X(7999)-3*X(11160) = 3*X(9967)-X(11412) = 5*X(10574)-9*X(14912) = 2*X(10627)-3*X(11574) = 3*X(12294)-X(18439)

The reciprocal orthologic center of these triangles is X(3580).

X(32284) lies on these lines: {4,15531}, {5,8681}, {6,1147}, {51,8780}, {52,1992}, {67,15134}, {143,15471}, {182,22829}, {193,9967}, {195,18449}, {389,14984}, {511,550}, {524,1216}, {542,12370}, {567,32127}, {575,5892}, {576,2393}, {578,8548}, {1181,1351}, {1493,6153}, {1503,12897}, {1843,5093}, {1993,8538}, {1994,8537}, {2854,16534}, {2883,21850}, {3564,5907}, {3567,5032}, {5097,9969}, {5447,18951}, {5965,12899}, {6403,21852}, {6776,10575}, {7999,11160}, {9027,10170}, {9306,9925}, {10574,14912}, {10627,11574}, {11426,21651}, {11470,18445}, {11511,16266}, {11536,32245}, {12007,22952}, {12242,14913}, {12294,18439}, {15116,15129}, {15118,15120}

X(32284) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 15073}, {193, 9967}, {1351, 6467}
X(32284) = reflection of X(i) in X(j) for these (i,j): (182, 22829), (5446, 576), (6403, 21852), (9969, 5097), (12585, 13292), (14913, 18583)
X(32284) = {X(1992), X(15073)}-harmonic conjugate of X(52)


X(32285) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HYACINTH TO WALSMITH

Barycentrics    SA*((36*R^2*(2*R^2-SW)-(SA-5*SW)*SW)*S^2-(SB+SC)*((3*SA-5*SW)*R^2-SA^2+SB*SC+SW^2)*SW) : :

The reciprocal orthologic center of these triangles is X(32263).

X(32285) lies on these lines: {6,67}, {25,32264}, {69,13198}, {184,5181}, {185,542}, {858,21639}, {895,1899}, {974,3564}, {1885,2781}, {2854,26926}, {3091,9970}, {3292,32257}, {5622,15057}, {5972,21637}, {6146,14984}, {6699,15136}, {9825,25711}, {10938,17702}, {11061,32241}, {15063,32306}, {17818,32233}, {32239,32246}

X(32285) = reflection of X(i) in X(j) for these (i,j): (15118, 32283), (32239, 32246)
X(32285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 67, 15116), (67, 32251, 125)


X(32286) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INTANGENTS TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(110).

X(32286) lies on these lines: {1,542}, {11,25328}, {33,5095}, {34,32250}, {35,12584}, {36,32305}, {55,2930}, {56,16010}, {110,2330}, {399,611}, {497,32255}, {511,7727}, {524,5160}, {895,8540}, {1040,32257}, {1062,32275}, {1177,10535}, {1250,32302}, {1428,10091}, {1469,5663}, {1503,7286}, {2066,32291}, {2192,32276}, {2781,6285}, {2836,3057}, {2854,3024}, {3100,32244}, {3270,32260}, {3295,32254}, {3448,12589}, {3564,12888}, {3583,32273}, {5204,5621}, {5414,32292}, {6198,32234}, {6238,14984}, {7071,32240}, {7281,7312}, {7292,9140}, {7343,9976}, {7741,20301}, {9817,32300}, {9970,19369}, {10638,32301}, {11429,32245}, {11436,32246}, {11446,32248}, {11461,32249}, {11670,24471}, {12903,14982}, {14094,32289}, {18455,32272}, {18922,32241}, {19182,32258}, {19354,32251}, {19434,32293}, {19435,32294}

X(32286) = reflection of X(i) in X(j) for these (i,j): (11670, 24471), (32259, 1), (32277, 2930)
X(32286) = X(1156)-of-intangents-triangle if ABC is acute
X(32286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (895, 32290, 8540), (10091, 11579, 1428)


X(32287) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-JOHNSON TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32287) lies on these lines: {11,67}, {12,32309}, {355,9970}, {511,12889}, {542,10525}, {1376,6593}, {1503,12371}, {2781,12114}, {3434,11061}, {10523,32307}, {10785,32247}, {10794,32242}, {10826,32261}, {10829,32262}, {10871,32268}, {10893,32274}, {10914,32278}, {10919,32280}, {10920,32281}, {10944,32289}, {10945,32295}, {10946,32296}, {10947,32297}, {10948,32308}, {10949,32310}, {11373,32238}, {11390,32239}, {11826,32233}, {11865,32265}, {11866,32266}, {11903,32279}, {11928,32306}, {12422,14984}, {13895,32303}, {13952,32304}, {18516,32271}, {18961,32243}, {19023,32252}, {19024,32253}

X(32287) = reflection of X(i) in X(j) for these (i,j): (32256, 6593), (32288, 9970)
X(32287) = X(67)-of-inner-Johnson-triangle
X(32287) = X(32309)-of-outer-Johnson-triangle


X(32288) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-JOHNSON TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32288) lies on these lines: {11,32310}, {12,67}, {72,692}, {355,9970}, {511,12890}, {542,10526}, {895,15232}, {958,6593}, {1503,12372}, {2781,11500}, {3436,11061}, {10523,32308}, {10786,32247}, {10795,32242}, {10827,32261}, {10830,32262}, {10872,32268}, {10894,32274}, {10921,32280}, {10922,32281}, {10950,32290}, {10951,32295}, {10952,32296}, {10953,32297}, {10954,32307}, {10955,32309}, {11374,32238}, {11391,32239}, {11827,32233}, {11867,32265}, {11868,32266}, {11904,32279}, {11929,32306}, {12423,14984}, {13896,32303}, {13953,32304}, {18517,32271}, {18962,32243}, {19025,32252}, {19026,32253}

X(32288) = reflection of X(i) in X(j) for these (i,j): (32270, 6593), (32287, 9970)
X(32288) = X(67)-of-outer-Johnson-triangle
X(32288) = X(32310)-of-inner-Johnson-triangle


X(32289) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JOHNSON-YFF TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32289) lies on these lines: {1,9970}, {4,32297}, {5,32308}, {6,3028}, {12,67}, {36,15462}, {55,2781}, {56,6593}, {65,651}, {73,1177}, {74,2330}, {110,1469}, {113,12589}, {182,10081}, {388,11061}, {495,32307}, {511,10088}, {542,1478}, {1479,32271}, {1503,12373}, {1870,8540}, {3056,10752}, {3085,32247}, {3157,14984}, {5480,12904}, {7286,10510}, {7354,32233}, {9578,32261}, {9654,32306}, {10091,19140}, {10797,32242}, {10831,32262}, {10873,32268}, {10895,32274}, {10923,32280}, {10924,32281}, {10944,32287}, {10956,32309}, {10957,32310}, {11375,32238}, {11392,32239}, {11501,32256}, {11579,19470}, {11869,32265}, {11870,32266}, {11905,32279}, {11930,32295}, {11931,32296}, {12896,31670}, {13897,32303}, {13954,32304}, {14094,32286}, {15128,26955}, {19027,32252}, {19028,32253}, {22759,32270}

X(32289) = reflection of X(32307) in X(495)
X(32289) = X(67)-of-1st-Johnson-Yff-triangle
X(32289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 9970, 32290), (19369, 32259, 895)


X(32290) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd JOHNSON-YFF TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32290) lies on these lines: {1,9970}, {4,32243}, {5,32307}, {6,3024}, {11,67}, {35,15462}, {55,6593}, {56,2781}, {74,1428}, {110,3056}, {113,12588}, {182,10065}, {496,32308}, {497,11061}, {511,10091}, {542,1479}, {613,5663}, {895,8540}, {1069,14984}, {1469,10752}, {1478,32271}, {1503,12374}, {3057,32278}, {3086,32247}, {5160,10510}, {5480,12903}, {6198,19369}, {6284,32233}, {7727,11579}, {9581,32261}, {9669,32306}, {10088,19140}, {10798,32242}, {10832,32262}, {10874,32268}, {10896,32274}, {10925,32280}, {10926,32281}, {10950,32288}, {10958,32309}, {10959,32310}, {11376,32238}, {11393,32239}, {11502,32256}, {11871,32265}, {11872,32266}, {11906,32279}, {11932,32295}, {11933,32296}, {13898,32303}, {13955,32304}, {14094,32259}, {15128,26956}, {18968,31670}, {19029,32252}, {19030,32253}, {22760,32270}

X(32290) = reflection of X(32308) in X(496)
X(32290) = X(67)-of-2nd-Johnson-Yff-triangle
X(32290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 9970, 32289), (497, 11061, 32297)


X(32291) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU DIAGONALS TO WALSMITH

Barycentrics    (SB+SC)*((9*R^2-3*SW)*S^2-(9*R^2-2*SW)*SW*S-(3*SA-2*SW)*SA*SW) : :

The reciprocal orthologic center of these triangles is X(110).

X(32291) lies on these lines: {6,110}, {67,6413}, {159,13288}, {371,542}, {372,12584}, {511,12375}, {590,25328}, {1151,16010}, {1177,10533}, {2066,32286}, {2067,32259}, {2781,12964}, {2836,7969}, {3068,32255}, {3311,32254}, {3564,12891}, {5095,5412}, {5181,10960}, {5410,32240}, {5415,32277}, {5621,6409}, {5648,32252}, {6200,32305}, {6564,32273}, {8253,13774}, {10576,20301}, {10665,14984}, {10819,11579}, {10880,32234}, {10897,32275}, {10961,32300}, {11417,32244}, {11462,32249}, {11473,32250}, {11513,32257}, {17819,32276}, {18457,32272}, {18923,32241}, {19183,32258}, {19355,32251}, {19436,32293}, {19438,32294}, {21640,32260}

X(32291) = X(1156)-of-1st-Kenmotu-diagonals-triangle if ABC is acute
X(32291) = {X(6), X(2930)}-harmonic conjugate of X(32292)


X(32292) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU DIAGONALS TO WALSMITH

Barycentrics    (SB+SC)*((9*R^2-3*SW)*S^2+(9*R^2-2*SW)*SW*S-(3*SA-2*SW)*SA*SW) : :

The reciprocal orthologic center of these triangles is X(110).

X(32292) lies on these lines: {6,110}, {67,6414}, {159,13287}, {371,12584}, {372,542}, {511,12376}, {615,25328}, {1152,16010}, {1177,10534}, {2781,12970}, {2836,7968}, {3069,32255}, {3312,32254}, {3564,12892}, {5095,5413}, {5181,10962}, {5411,32240}, {5414,32286}, {5416,32277}, {5621,6410}, {5648,32253}, {6396,32305}, {6502,32259}, {6565,32273}, {8252,13654}, {10577,20301}, {10666,14984}, {10820,11579}, {10881,32234}, {10898,32275}, {10963,32300}, {11418,32244}, {11463,32249}, {11474,32250}, {11514,32257}, {17820,32276}, {18459,32272}, {18924,32241}, {19184,32258}, {19356,32251}, {19437,32294}, {19439,32293}, {21641,32260}

X(32292) = {X(6), X(2930)}-harmonic conjugate of X(32291)
X(32292) = X(1156)-of-2nd-Kenmotu-diagonals-triangle if ABC is acute


X(32293) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS ANTIPODAL TANGENTIAL TO WALSMITH

Barycentrics
(SB+SC)*(4*SW*S^4-2*(12*(3*R^2-SW)*R^2+(SA+SW)*SW)*S^3-((72*R^2+18*SA-29*SW)*R^2-4*SA^2+4*SB*SC+3*SW^2)*SW*S^2+2*SA*SW*(2*SW^2-SA^2+SB*SC+(-8*SW+3*SA)*R^2)*S+(4*R^2-SW)*(3*SA-2*SW)*SA*SW^2) : :

The reciprocal orthologic center of these triangles is X(110).

X(32293) lies on these lines: {110,19134}, {511,19484}, {542,18980}, {895,19426}, {2781,19500}, {2854,12590}, {2930,8939}, {3564,19482}, {5095,19446}, {9723,32294}, {12584,19440}, {13021,16010}, {14984,18939}, {18414,32273}, {18462,32272}, {18926,32241}, {19186,32258}, {19358,32251}, {19370,32259}, {19404,32240}, {19406,32244}, {19408,32245}, {19410,32246}, {19412,32248}, {19414,32249}, {19416,32250}, {19418,32254}, {19420,32255}, {19422,32257}, {19424,32234}, {19428,32275}, {19430,32276}, {19432,32277}, {19434,32286}, {19436,32291}, {19439,32292}, {19448,32300}, {19450,32301}, {19452,32302}, {19454,32305}, {21642,32260}, {23298,25328}

X(32293) = X(1156)-of-Lucas-antipodal-tangents-triangle if ABC is acute


X(32294) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) ANTIPODAL TANGENTIAL TO WALSMITH

Barycentrics
(SB+SC)*(4*SW*S^4+2*(12*(3*R^2-SW)*R^2+(SA+SW)*SW)*S^3-((72*R^2+18*SA-29*SW)*R^2-4*SA^2+4*SB*SC+3*SW^2)*SW*S^2-2*SA*SW*(2*SW^2-SA^2+SB*SC+(-8*SW+3*SA)*R^2)*S+(4*R^2-SW)*(3*SA-2*SW)*SA*SW^2) : :

The reciprocal orthologic center of these triangles is X(110).

X(32294) lies on these lines: {110,19135}, {511,19485}, {542,18981}, {895,19427}, {2781,19501}, {2854,12591}, {2930,8943}, {3564,19483}, {5095,19447}, {9723,32293}, {12584,19441}, {13022,16010}, {14984,18940}, {18415,32273}, {18463,32272}, {18927,32241}, {19187,32258}, {19359,32251}, {19371,32259}, {19405,32240}, {19407,32244}, {19409,32245}, {19411,32246}, {19413,32248}, {19415,32249}, {19417,32250}, {19419,32254}, {19421,32255}, {19423,32257}, {19425,32234}, {19429,32275}, {19431,32276}, {19433,32277}, {19435,32286}, {19437,32292}, {19438,32291}, {19449,32300}, {19451,32301}, {19453,32302}, {19455,32305}, {21643,32260}, {23299,25328}

X(32294) = X(1156)-of-Lucas(-1)-antipodal-tangents-triangle if ABC is acute


X(32295) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS HOMOTHETIC TO WALSMITH

Barycentrics    2*((12*(3*SA-2*SW)*R^4-(3*SA+SW)*SW*R^2+2*(SB+SC)*SW^2)*S^2-4*R^2*SB*SC*SW^2)*S+((3*(6*SA^2+3*SA*SW-5*SW^2)*R^2-(4*SA^2+3*SA*SW-4*SW^2)*SW)*S^2-SB*SC*SW^3)*SW : :

The reciprocal orthologic center of these triangles is X(125).

X(32295) lies on these lines: {67,493}, {511,12894}, {542,10669}, {1503,12377}, {2781,9838}, {6461,32296}, {6462,11061}, {6593,8222}, {8188,32261}, {8194,32262}, {8210,32298}, {8212,32274}, {8214,32278}, {8218,32281}, {8220,9970}, {8408,19398}, {10875,32268}, {10945,32287}, {10951,32288}, {11377,32238}, {11394,32239}, {11503,32256}, {11828,32233}, {11840,32242}, {11846,32247}, {11907,32279}, {11930,32289}, {11932,32290}, {11947,32297}, {11949,32306}, {11951,32307}, {11953,32308}, {11955,32309}, {11957,32310}, {12426,14984}, {13899,32303}, {13956,32304}, {18520,32271}, {18963,32243}, {19031,32252}, {19032,32253}, {22761,32270}

X(32295) = X(67)-of-Lucas-homothetic-triangle


X(32296) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) HOMOTHETIC TO WALSMITH

Barycentrics    -2*((12*(3*SA-2*SW)*R^4-(3*SA+SW)*SW*R^2+2*(SB+SC)*SW^2)*S^2-4*R^2*SB*SC*SW^2)*S+((3*(6*SA^2+3*SA*SW-5*SW^2)*R^2-(4*SA^2+3*SA*SW-4*SW^2)*SW)*S^2-SB*SC*SW^3)*SW : :

The reciprocal orthologic center of these triangles is X(125).

X(32296) lies on these lines: {67,494}, {511,12895}, {542,10673}, {1503,12378}, {2781,9839}, {6461,32295}, {6463,11061}, {6593,8223}, {8189,32261}, {8195,32262}, {8211,32298}, {8213,32274}, {8215,32278}, {8217,32280}, {8219,32281}, {8221,9970}, {8420,19399}, {10876,32268}, {10946,32287}, {10952,32288}, {11378,32238}, {11395,32239}, {11504,32256}, {11829,32233}, {11841,32242}, {11847,32247}, {11908,32279}, {11931,32289}, {11933,32290}, {11948,32297}, {11950,32306}, {11952,32307}, {11954,32308}, {11956,32309}, {11958,32310}, {12427,14984}, {13900,32303}, {13957,32304}, {18522,32271}, {18964,32243}, {19033,32252}, {19034,32253}, {22762,32270}

X(32296) = X(67)-of-Lucas(-1)-homothetic-triangle


X(32297) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MANDART-INCIRCLE TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32297) lies on these lines: {1,542}, {3,32308}, {4,32289}, {6,12904}, {11,6593}, {12,32274}, {33,32239}, {55,67}, {56,32233}, {110,12589}, {125,2330}, {265,611}, {497,11061}, {499,15462}, {511,12896}, {1352,10088}, {1479,9970}, {1503,3028}, {1697,32261}, {1837,32278}, {1858,2836}, {2098,32298}, {2646,32238}, {2781,6284}, {3295,32306}, {3583,32271}, {4294,32247}, {5095,8540}, {5432,6698}, {5621,9659}, {10833,32262}, {10877,32268}, {10927,32280}, {10928,32281}, {10947,32287}, {10953,32288}, {10965,32309}, {10966,32270}, {11873,32265}, {11874,32266}, {11909,32279}, {11947,32295}, {11948,32296}, {12428,14984}, {13901,32303}, {13958,32304}, {19037,32252}, {19038,32253}

X(32297) = reflection of X(32243) in X(1)
X(32297) = X(67)-of-Mandart-incircle-triangle
X(32297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 11061, 32290), (3295, 32306, 32307)


X(32298) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th MIXTILINEAR TO WALSMITH

Barycentrics
3*a^9+(b+c)*a^8-(b^2+c^2)*a^7-(b^2+c^2)*(b+c)*a^6-(4*b^4-3*b^2*c^2+4*c^4)*a^5+(b+c)*b^2*c^2*a^4+(b^4+c^4)*(b^2+c^2)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*a^2+(b^4-c^4)^2*a-(b^4-c^4)^2*(b+c) : :
X(32298) = 3*X(1)-2*X(32238) = 3*X(1)-X(32261) = 3*X(67)-4*X(32238) = 3*X(67)-2*X(32261) = 3*X(5603)-2*X(32274) = 3*X(10516)-4*X(11723)

The reciprocal orthologic center of these triangles is X(125).

X(32298) lies on these lines: {1,67}, {8,6593}, {55,32270}, {56,32256}, {110,5846}, {145,11061}, {511,12898}, {517,32233}, {519,32278}, {542,1482}, {944,2781}, {952,9970}, {1386,13211}, {1503,7978}, {2098,32297}, {2099,32243}, {2836,3555}, {3416,11720}, {5603,32274}, {5648,28538}, {8192,32262}, {8211,32296}, {9053,25329}, {9933,14984}, {10516,11723}, {10944,32287}, {11396,32239}, {11910,32279}, {13959,32304}, {18525,32271}

X(32298) = midpoint of X(145) and X(11061)
X(32298) = reflection of X(i) in X(j) for these (i,j): (8, 6593), (67, 1), (3416, 11720), (13211, 1386), (18525, 32271), (32261, 32238)
X(32298) = X(67)-of-5th-mixtilinear-triangle
X(32298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32261, 32238), (32238, 32261, 67), (32309, 32310, 67)


X(32299) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: REFLECTION TO WALSMITH

Barycentrics    (SB+SC)*((9*R^2*(10*R^2-7*SW)+10*SW^2)*S^2-(7*R^2-2*SW)*(3*SA-2*SW)*SA*SW) : :
X(32299) = 3*X(6)-X(32248) = X(2930)-3*X(11188) = 3*X(3060)-X(16176) = 2*X(6593)-3*X(16776) = 3*X(9971)-X(11061) = 3*X(16776)-4*X(32246)

See preamble just before X(31353).

X(32299) lies on these lines: {6,110}, {67,5189}, {125,17710}, {382,2781}, {524,32260}, {542,6102}, {1205,8705}, {2393,8262}, {3060,16176}, {3448,9973}, {3629,11800}, {9927,11591}, {9969,25329}, {9971,11061}, {10095,11536}, {11412,15738}, {11477,32249}, {15074,20301}, {19127,32251}

X(32299) = midpoint of X(i) and X(j) for these lines: {i,j}: {3448, 9973}, {11477, 32249}
X(32299) = reflection of X(i) in X(j) for these (i,j): (3629, 11800), (6593, 32246), (15074, 20301), (17710, 125), (25329, 9969)
X(32299) = {X(6593), X(32246)}-harmonic conjugate of X(16776)


X(32300) = ORTHOLOGIC CENTER OF THESE TRIANGLES: SUBMEDIAL TO WALSMITH

Barycentrics    6*a^8-4*(b^2+c^2)*a^6-(7*b^4-12*b^2*c^2+7*c^4)*a^4+2*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^2+(b^4-c^4)^2 : :
X(32300) = 3*X(2)+X(5095) = 9*X(2)-X(32244) = 3*X(6)+X(5181) = X(67)+3*X(15303) = X(113)+3*X(5050) = X(125)-5*X(3618) = 3*X(125)+X(11061) = 3*X(182)+X(32271) = 9*X(373)-X(32260) = 3*X(597)+X(6593) = 3*X(597)-X(15118) = 9*X(597)-X(25328) = X(89)+3*X(5642) = X(1205)+3*X(12824) = 15*X(3618)+X(11061) = 3*X(5095)+X(32244) = X(5181)-3*X(5972) = 3*X(6593)+X(25328) = 3*X(15118)-X(25328) = X(32244)-3*X(32257)

The reciprocal orthologic center of these triangles is X(110).

X(32300) lies on these lines: {2,5095}, {5,542}, {6,5181}, {67,15303}, {110,19137}, {113,5050}, {125,3618}, {182,1177}, {373,32260}, {511,9826}, {578,9815}, {895,5642}, {1112,11574}, {1205,12824}, {1656,32275}, {1974,7519}, {2781,9729}, {2854,6329}, {2930,5020}, {3090,32234}, {3091,32250}, {3564,12900}, {3589,6698}, {5055,32272}, {5159,15471}, {5169,32239}, {5182,16278}, {5462,14984}, {5622,15063}, {5943,14763}, {6053,11579}, {6642,12584}, {6721,24975}, {7392,32255}, {7493,11511}, {7687,14561}, {9306,32245}, {9816,32277}, {9817,32286}, {9818,32305}, {9967,16222}, {9970,20417}, {10168,18580}, {10601,32251}, {10643,32301}, {10644,32302}, {10961,32291}, {10963,32292}, {11284,32240}, {11451,32248}, {11465,32249}, {11479,16010}, {11484,32254}, {12017,16111}, {13202,25406}, {14853,16163}, {15059,25321}, {15119,19510}, {15141,15805}, {15473,19128}, {16238,22330}, {17702,18583}, {17825,32276}, {18420,32273}, {18928,32241}, {19188,32258}, {19372,32259}, {19448,32293}, {19449,32294}, {22973,32163}, {24981,25320}

X(32300) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 5972}, {1112, 11574}, {5095, 32257}, {5159, 15471}, {6053, 11579}, {6593, 15118}, {9970, 20417}
X(32300) = reflection of X(6723) in X(3589)
X(32300) = complement of X(32257)
X(32300) = X(1156)-of-submedial-triangle if ABC is acute
X(32300) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5095, 32257), (597, 6593, 15118)


X(32301) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER TRI-EQUILATERAL TO WALSMITH

Barycentrics    (SB+SC)*(9*(3*R^2-SW)*S^2-sqrt(3)*(9*R^2-2*SW)*SW*S-3*(3*SA-2*SW)*SA*SW) : :

The reciprocal orthologic center of these triangles is X(110).

X(32301) lies on these lines: {6,110}, {15,542}, {16,12584}, {159,10682}, {187,13859}, {511,10657}, {599,11130}, {1177,30402}, {2781,10675}, {3564,10663}, {5095,10641}, {5181,10639}, {5191,14173}, {5648,11081}, {7051,32259}, {9142,14179}, {10632,32234}, {10634,32275}, {10636,32277}, {10638,32286}, {10643,32300}, {10645,32305}, {10661,14984}, {11408,32240}, {11420,32244}, {11466,32249}, {11475,32250}, {11480,16010}, {11488,32255}, {11515,32257}, {16808,32273}, {16966,20301}, {17826,32276}, {18468,32272}, {18929,32241}, {19190,32258}, {19363,32251}, {19450,32293}, {19451,32294}, {21647,32260}, {23302,25328}

X(32301) = X(1156)-of-inner-tri-equilateral-triangle if ABC is acute
X(32301) = {X(6), X(2930)}-harmonic conjugate of X(32302)


X(32302) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER TRI-EQUILATERAL TO WALSMITH

Barycentrics    (SB+SC)*(9*(3*R^2-SW)*S^2+sqrt(3)*(9*R^2-2*SW)*SW*S-3*(3*SA-2*SW)*SA*SW) : :

The reciprocal orthologic center of these triangles is X(110).

X(32302) lies on these lines: {6,110}, {15,12584}, {16,542}, {159,10681}, {187,13858}, {511,10658}, {574,13859}, {599,11131}, {1177,30403}, {1250,32286}, {2781,10676}, {3564,10664}, {5095,10642}, {5181,10640}, {5191,14179}, {5648,11086}, {9142,14173}, {10633,32234}, {10635,32275}, {10637,32277}, {10644,32300}, {10646,32305}, {10662,14984}, {11409,32240}, {11421,32244}, {11467,32249}, {11476,32250}, {11481,16010}, {11486,32254}, {11489,32255}, {11516,32257}, {16809,32273}, {16967,20301}, {17827,32276}, {18470,32272}, {18930,32241}, {19191,32258}, {19364,32251}, {19373,32259}, {19452,32293}, {19453,32294}, {21648,32260}, {23303,25328}

X(32302) = X(1156)-of-outer-tri-equilateral-triangle if ABC is acute
X(32302) = {X(6), X(2930)}-harmonic conjugate of X(32301)


X(32303) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES-CENTRAL TO WALSMITH

Barycentrics    3*S^4-(3*R^2*(3*SA+7*SW)-3*SA^2+3*SB*SC-4*SW^2)*S^2-2*(9*R^2-2*SW)*(SB+SC)*SW*S+SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(125).

X(32303) lies on these lines: {2,32253}, {6,6698}, {67,3068}, {371,32274}, {485,2781}, {511,13915}, {542,8981}, {590,6593}, {1503,8994}, {3763,19110}, {6723,13972}, {7585,32252}, {8972,11061}, {8974,32280}, {8975,32281}, {8976,9970}, {9540,32233}, {10516,19060}, {13883,32238}, {13884,32239}, {13886,32247}, {13887,32256}, {13888,32261}, {13889,32262}, {13890,32265}, {13891,32266}, {13892,32268}, {13893,32278}, {13895,32287}, {13896,32288}, {13897,32289}, {13898,32290}, {13899,32295}, {13900,32296}, {13901,32297}, {13902,32298}, {13903,32306}, {13904,32307}, {13905,32308}, {13906,32309}, {13907,32310}, {13909,14984}, {18538,32271}, {18965,32243}, {22763,32270}

X(32303) = X(67)-of-3rd-tri-squares-central-triangle
X(32303) = {X(6), X(6698)}-harmonic conjugate of X(32304)


X(32304) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES-CENTRAL TO WALSMITH

Barycentrics    3*S^4-(3*R^2*(3*SA+7*SW)-3*SA^2+3*SB*SC-4*SW^2)*S^2+2*(9*R^2-2*SW)*(SB+SC)*SW*S+SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(125).

X(32304) lies on these lines: {2,32252}, {6,6698}, {67,3069}, {372,32274}, {486,2781}, {511,13979}, {542,13966}, {615,6593}, {1503,13969}, {3763,19111}, {6723,13910}, {7586,32253}, {9970,13951}, {10516,19059}, {11061,13941}, {13935,32233}, {13936,32238}, {13937,32239}, {13938,32242}, {13939,32247}, {13940,32256}, {13942,32261}, {13943,32262}, {13944,32265}, {13945,32266}, {13946,32268}, {13947,32278}, {13948,32279}, {13949,32280}, {13950,32281}, {13952,32287}, {13953,32288}, {13954,32289}, {13955,32290}, {13956,32295}, {13957,32296}, {13958,32297}, {13959,32298}, {13961,32306}, {13962,32307}, {13963,32308}, {13964,32309}, {13965,32310}, {13970,14984}, {18762,32271}, {18966,32243}, {22764,32270}

X(32304) = X(67)-of-4th-tri-squares-central-triangle
X(32304) = {X(6), X(6698)}-harmonic conjugate of X(32303)


X(32305) = ORTHOLOGIC CENTER OF THESE TRIANGLES: TRINH TO WALSMITH

Barycentrics    (SB+SC)*((9*R^2-3*SW)*S^2+(27*R^2-3*SA-4*SW)*SA*SW) : :
X(32305) = 3*X(3)-X(2930) = X(3)-3*X(5621) = 5*X(3)-X(32254) = X(67)-3*X(20126) = 3*X(67)-X(32272) = 3*X(74)+X(895) = 2*X(74)+X(9976) = 2*X(895)-3*X(9976) = X(895)-3*X(11579) = X(2930)-9*X(5621) = 2*X(2930)-3*X(12584) = X(2930)+3*X(16010) = 5*X(2930)-3*X(32254) = 6*X(5621)-X(12584) = 3*X(5621)+X(16010) = 15*X(5621)-X(32254) = X(12584)+2*X(16010) = 5*X(12584)-2*X(32254) = 5*X(16010)+X(32254) = 9*X(20126)-X(32272) = 3*X(20417)-X(32257)

The reciprocal orthologic center of these triangles is X(110).

X(32305) lies on these lines: {3,67}, {4,20301}, {6,10620}, {23,9140}, {24,32250}, {30,25328}, {35,32259}, {36,32286}, {74,511}, {98,20404}, {110,5092}, {125,1995}, {146,14561}, {182,4550}, {185,575}, {265,29012}, {376,32255}, {378,5095}, {399,5085}, {541,5476}, {576,2781}, {690,13233}, {1177,6000}, {1350,15041}, {1428,7727}, {1503,7575}, {1511,17508}, {1691,14901}, {1974,12292}, {1986,19124}, {2071,32244}, {2330,19470}, {2393,16219}, {2777,23049}, {2836,3579}, {2854,3098}, {3448,7492}, {3520,32234}, {3564,12901}, {5050,25556}, {5097,10752}, {5655,10168}, {5907,7550}, {6200,32291}, {6396,32292}, {6698,11178}, {6800,32315}, {7530,18381}, {7545,15027}, {7555,12359}, {7556,11457}, {7688,32277}, {7689,14984}, {7691,15021}, {7728,19130}, {8546,16510}, {9517,13247}, {9818,32300}, {10249,15141}, {10510,19402}, {10605,32251}, {10606,32276}, {10628,19150}, {10645,32301}, {10646,32302}, {10733,29323}, {11061,11179}, {11410,32240}, {11430,32245}, {11438,32246}, {11454,32248}, {11468,32249}, {11572,15044}, {11643,19905}, {12017,12308}, {12106,20379}, {12244,25320}, {12317,25406}, {12902,25330}, {14677,29181}, {14810,15055}, {14865,22330}, {14982,15061}, {15116,23329}, {16042,25561}, {18931,32241}, {19192,32258}, {19454,32293}, {19455,32294}, {19506,23300}, {20127,29317}, {21663,32260}

X(32305) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 16010}, {6, 10620}, {74, 11579}, {9970, 15054}, {12244, 31670}
X(32305) = reflection of X(i) in X(j) for these (i,j): (4, 20301), (110, 5092), (3098, 12041), (3818, 125), (5655, 10168), (7728, 19130), (9970, 575), (9976, 11579), (10752, 5097), (12584, 3), (14982, 24206), (16510, 8546), (19140, 182), (19506, 23300), (32271, 15118), (32273, 25328), (32274, 20379)
X(32305) = circumperp conjugate of X(8724)
X(32305) = circumtangential isogonal conjugate of X(23)
X(32305) = inverse of X(14830) in the circumcircle
X(32305) = X(1156)-of-Trinh-triangle if ABC is acute
X(32305) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5621, 16010, 3), (5622, 9970, 575), (5622, 15054, 9970)


X(32306) = ORTHOLOGIC CENTER OF THESE TRIANGLES: X3-ABC REFLECTIONS TO WALSMITH

Barycentrics    (3*(6*SA-SW)*R^2-2*(3*SA-SW)*SW)*S^2+(9*R^2-4*SW)*SB*SC*SW : :
X(32306) = 3*X(3)-2*X(32233) = 3*X(6)-4*X(20301) = 3*X(67)-X(32233) = 4*X(125)-3*X(5050) = 3*X(381)-2*X(9970) = 3*X(381)-4*X(32274) = 3*X(599)-2*X(12584) = 2*X(1353)-3*X(25320) = 5*X(1656)-4*X(6593) = 3*X(2070)-4*X(8262) = 7*X(3526)-8*X(6698) = 7*X(3526)-6*X(15462) = 5*X(3843)-4*X(32271) = 4*X(5095)-5*X(11482) = 3*X(5622)-4*X(20379) = 3*X(5790)-2*X(32278) = 4*X(6698)-3*X(15462) = 3*X(9140)-X(32234) = 2*X(9976)-3*X(25330) = X(32254)-4*X(32275)

The reciprocal orthologic center of these triangles is X(125).

X(32306) lies on these lines: {3,67}, {5,9512}, {6,7579}, {30,32247}, {125,5050}, {182,11597}, {195,15141}, {265,1351}, {323,858}, {381,9970}, {382,2781}, {399,1352}, {511,12902}, {517,32261}, {524,7574}, {541,32250}, {576,16176}, {895,11255}, {999,32243}, {1353,25320}, {1503,10620}, {1598,32239}, {1656,6593}, {2070,8262}, {2854,11898}, {3295,32297}, {3526,6698}, {3843,32271}, {5094,9140}, {5095,11482}, {5169,15135}, {5622,15132}, {5663,11188}, {5790,32278}, {5921,12317}, {6193,23296}, {6403,15100}, {6417,32253}, {6418,32252}, {6776,10264}, {7495,9143}, {7517,32262}, {9301,32268}, {9654,32289}, {9669,32290}, {9976,25330}, {10113,10752}, {10246,32238}, {10247,32298}, {10516,19140}, {11412,12429}, {11477,32273}, {11579,11935}, {11801,14853}, {11842,32242}, {11849,32256}, {11875,32265}, {11876,32266}, {11911,32279}, {11916,32280}, {11917,32281}, {11928,32287}, {11929,32288}, {11949,32295}, {11950,32296}, {12000,32309}, {12001,32310}, {12017,15061}, {12308,14982}, {13903,32303}, {13961,32304}, {14561,25329}, {14677,14927}, {14791,32255}, {15027,15118}, {15063,32285}, {15074,32248}, {15081,18583}, {19510,22115}, {22765,32270}, {25331,25556}

X(32306) = midpoint of X(i) and X(j) for these lines: {i,j}: {5921, 12317}, {6403, 15100}, {15069, 25335}
X(32306) = reflection of X(i) in X(j) for these (i,j): (3, 67), (399, 1352), (1351, 265), (6776, 10264), (9970, 32274), (10752, 10113), (11061, 5), (11477, 32273), (12308, 14982), (14927, 14677), (16176, 576), (23236, 5181), (25336, 19140), (30714, 32257), (32248, 15074)
X(32306) = X(67)-of-X3-ABC-reflections-triangle
X(32306) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9970, 32274, 381), (32243, 32308, 999)


X(32307) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TO WALSMITH

Barycentrics    (3*R^2*(3*SA+SW)-4*SA*SW)*S^2+(SB+SC)*(SA^2-SB*SC+(9*R^2-2*SW)*b*c)*SW : :

The reciprocal orthologic center of these triangles is X(125).

X(32307) lies on these lines: {1,67}, {3,32243}, {5,32290}, {12,9970}, {35,32233}, {55,542}, {125,613}, {141,10091}, {265,3056}, {388,32247}, {495,32289}, {498,6593}, {499,6698}, {511,12903}, {1350,18968}, {1352,3024}, {1428,15061}, {1478,2781}, {1479,32274}, {1503,10065}, {3085,11061}, {3295,32297}, {3299,32252}, {3301,32253}, {3818,12374}, {5432,15462}, {5622,26956}, {5663,12588}, {7727,14982}, {10037,32262}, {10038,32268}, {10039,32278}, {10041,32281}, {10055,14984}, {10387,12896}, {10523,32287}, {10801,32242}, {10895,32271}, {10954,32288}, {11398,32239}, {11507,32256}, {11877,32265}, {11878,32266}, {11912,32279}, {11951,32295}, {11952,32296}, {13904,32303}, {13962,32304}, {22766,32270}

X(32307) = midpoint of X(67) and X(32309)
X(32307) = reflection of X(32289) in X(495)
X(32307) = X(67)-of-inner-Yff-triangle
X(32307) = X(32309)-of-outer-Yff-triangle
X(32307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 67, 32308), (3295, 32306, 32297)


X(32308) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TO WALSMITH

Barycentrics    (3*R^2*(3*SA+SW)-4*SA*SW)*S^2+(SB+SC)*(SA^2-SB*SC-(9*R^2-2*SW)*b*c)*SW : :

The reciprocal orthologic center of these triangles is X(125).

X(32308) lies on these lines: {1,67}, {3,32297}, {5,32289}, {11,9970}, {36,32233}, {56,542}, {125,611}, {141,10088}, {265,1469}, {496,32290}, {497,32247}, {498,6698}, {499,6593}, {511,12904}, {999,32243}, {1350,12896}, {1352,3028}, {1478,32274}, {1479,2781}, {1503,10081}, {1737,32278}, {2330,15061}, {3086,11061}, {3299,32253}, {3301,32252}, {3818,12373}, {5433,15462}, {5622,26955}, {5663,12589}, {10046,32262}, {10047,32268}, {10048,32280}, {10049,32281}, {10071,14984}, {10523,32288}, {10802,32242}, {10896,32271}, {11399,32239}, {11508,32256}, {11879,32265}, {11880,32266}, {11913,32279}, {11953,32295}, {11954,32296}, {13905,32303}, {13963,32304}, {14982,19470}, {22767,32270}

X(32308) = midpoint of X(67) and X(32310)
X(32308) = reflection of X(32290) in X(496)
X(32308) = X(67)-of-outer-Yff-triangle
X(32308) = X(32310)-of-inner-Yff-triangle
X(32308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 67, 32307), (999, 32306, 32243)


X(32309) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TANGENTS TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32309) lies on these lines: {1,67}, {12,32287}, {511,12905}, {542,10679}, {1503,12381}, {2781,12115}, {5552,6593}, {9970,10942}, {10528,11061}, {10531,32274}, {10803,32242}, {10805,32247}, {10834,32262}, {10878,32268}, {10915,32278}, {10929,32280}, {10930,32281}, {10955,32288}, {10956,32289}, {10958,32290}, {10965,32297}, {11248,32233}, {11400,32239}, {11509,32243}, {11881,32265}, {11882,32266}, {11914,32279}, {11955,32295}, {11956,32296}, {12430,14984}, {13906,32303}, {13964,32304}, {18542,32271}, {19047,32252}, {19048,32253}, {22768,32270}

X(32309) = reflection of X(67) in X(32307)
X(32309) = X(67)-of-inner-Yff-tangents-triangle
X(32309) = {X(67), X(32298)}-harmonic conjugate of X(32310)


X(32310) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TANGENTS TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(32310) lies on these lines: {1,67}, {11,32288}, {511,12906}, {542,10680}, {1503,12382}, {2781,12116}, {6593,10527}, {9970,10943}, {10529,11061}, {10532,32274}, {10804,32242}, {10806,32247}, {10835,32262}, {10879,32268}, {10916,32278}, {10931,32280}, {10932,32281}, {10949,32287}, {10957,32289}, {10959,32290}, {10966,32270}, {11249,32233}, {11401,32239}, {11510,32256}, {11883,32265}, {11884,32266}, {11915,32279}, {11957,32295}, {11958,32296}, {12001,32306}, {12431,14984}, {13907,32303}, {13965,32304}, {18544,32271}, {18967,32243}, {19049,32252}, {19050,32253}

X(32310) = reflection of X(67) in X(32308)
X(32310) = X(67)-of-outer-Yff-tangents-triangle
X(32310) = {X(67), X(32298)}-harmonic conjugate of X(32309)


X(32311) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: REFLECTION TO WALSMITH

Barycentrics
4*a^12-(b^2+c^2)*a^10-14*(b^4-b^2*c^2+c^4)*a^8+(b^2+c^2)*(12*b^4-17*b^2*c^2+12*c^4)*a^6+2*(4*b^8+4*c^8-(8*b^4-9*b^2*c^2+8*c^4)*b^2*c^2)*a^4-(b^2+c^2)*(11*b^8+11*c^8-5*(5*b^4-6*b^2*c^2+5*c^4)*b^2*c^2)*a^2+2*(b^4-4*b^2*c^2+c^4)*(b^4-c^4)^2 : :
X(32311) = X(110)-3*X(9829) = X(3448)+3*X(6031) = 2*X(5972)-3*X(10163) = 3*X(6032)-5*X(15059) = 4*X(6723)-3*X(10162) = 3*X(23515)-2*X(31749)

See preamble just before X(31353).

X(32311) lies on these lines: {74,12505}, {110,599}, {113,31606}, {125,3849}, {2777,14866}, {3448,6031}, {5663,31744}, {5972,10163}, {6032,15059}, {6699,12506}, {6723,10162}, {11594,32269}, {17702,31729}, {23515,31749}

X(32311) = midpoint of X(74) and X(12505)
X(32311) = reflection of X(i) in X(j) for these (i,j): (113, 31606), (12506, 6699)


X(32312) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st PARRY TO WALSMITH

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

The reciprocal parallelogic center of these triangles is X(125).

X(32312) lies on these lines: {351,690}, {512,13290}, {525,9138}, {3566,15139}, {9131,9517}, {9208,13291}

X(32312) = reflection of X(i) in X(j) for these (i,j): (13291, 9208), (32313, 351)
X(32312) = X(67)-of-1st-Parry-triangle
X(32312) = X(32233)-of-2nd-Parry-triangle


X(32313) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd PARRY TO WALSMITH

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

The reciprocal parallelogic center of these triangles is X(125).

X(32313) lies on these lines: {67,18310}, {110,525}, {113,1560}, {351,690}, {512,13291}, {542,1640}, {1499,1551}, {1648,14114}, {2780,14698}, {3288,19140}, {3566,5653}, {5027,13290}, {5095,9033}, {6593,18311}, {8429,18332}, {9209,9759}, {9517,9979}, {11061,14977}, {22105,22255}

X(32313) = midpoint of X(11061) and X(14977)
X(32313) = reflection of X(i) in X(j) for these (i,j): (67, 18310), (3569, 14697), (13290, 5027), (18311, 6593), (32312, 351)
X(32313) = X(67)-of-2nd-Parry-triangle
X(32313) = X(32233)-of-1st-Parry-triangle


X(32314) = CENTER OF INVERSE SIMILITUDE OF THESE TRIANGLES: CIRCUMMEDIAL AND WALSMITH

Barycentrics    2*(9*R^2-2*SW)^2*S^4+(216*R^4*SW+3*R^2*(9*SA^2-12*SA*SW-35*SW^2)-2*SW*(3*SA^2-3*SA*SW-7*SW^2))*SW*S^2+6*(3*R^2-SW)*SB*SC*SW^3 : :

X(32314) lies on these lines: {1316,14682}, {5642,9463}, {9140,15080}, {9745,15484}


X(32315) = CENTER OF INVERSE SIMILITUDE OF THESE TRIANGLES: 1st EHRMANN AND WALSMITH

Barycentrics    (SB+SC)*((54*R^2*(3*R^2-SW)+3*SW^2)*S^2+(SW^2*(4*SW+3*SA)+9*R^2*(9*(3*SA-SW)*R^2-SW*(9*SA-SW)))*SA) : :

X(32315) lies on these lines: {1511,5651}, {1995,5476}, {6800,32305}, {9125,14270}, {16510,32225}


X(32316) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH TO HATZIPOLAKIS-MOSES

Barycentrics    (5*R^4*(24*R^2-5*SA)-R^2*SW*(97*R^2-14*SA-25*SW)-2*SW^2*(SW+SA))*S^2+(2*R^2-SW)*R^2*SB*SC*SW : :

The reciprocal orthologic center of these triangles is X(32317).

X(32316) lies on these lines: {68,1658}, {74,6145}, {110,343}, {113,1209}, {161,3448}, {973,11746}, {1154,32123}, {6293,12281}, {7703,23315}, {7730,26917}, {10117,31383}, {15068,17824}, {18400,32110}


X(32317) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO WALSMITH

Barycentrics    (6*(15*SA-SW)*R^4-9*(7*SA-2*SW)*SW*R^2+2*(5*SA-2*SW)*SW^2)*S^2-(7*R^2-2*SW)*SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(32316).

X(32317) lies on these lines: {6,67}, {542,6102}, {1511,5965}, {2781,13403}, {3564,11561}, {9925,9932}, {11061,19136}, {16511,32244}, {32154,32257}

X(32317) = reflection of X(67) in X(32283)
X(32317) = {X(125), X(5095)}-harmonic conjugate of X(15140)


X(32318) = X(1)X(389)∩X(3)X(2262)

Barycentrics    a*(2*S^4+a*((SA+SB)*b+(SA+SC)*c)*S^2-(SB+SC)*(S^2+2*(4*R^2-SW)*SA)*b*c) : :

See Tran Quang Hung and César Lozada, Hyacinthos 28999.

X(32318) lies on these lines: {1, 389}, {3, 2262}


X(32319) = X(4)X(19209)∩X(20)X(2979)

Barycentrics    a^2 (b^2 c^2 (b^2 - c^2)^6 - 10 a^10 (b^2 - c^2)^2 (b^2 + c^2) - 2 a^2 (b^2 - c^2)^4 (b^2 + c^2)^3 + a^12 (2 b^4 - 5 b^2 c^2 + 2 c^4) + 5 a^8 (b^2 - c^2)^2 (4 b^4 + 7 b^2 c^2 + 4 c^4) - 4 a^6 (b^2 - c^2)^2 (5 b^6 + 9 b^4 c^2 + 9 b^2 c^4 + 5 c^6) + a^4 (b^2 - c^2)^2 (10 b^8 + 13 b^6 c^2 + 18 b^4 c^4 + 13 b^2 c^6 + 10 c^8)) : :

See Angel Montesdeoca, Hyacinthos 29000 and HG020519

X(32319) lies on these lines: {4,19209}, {20,2979}, {51,3087}, {97,6759}, {154,160}, {217,3172}, {512,23613}, {3198,11190}

X(32319) = isogonal conjugate of X(20477)
X(32319) = isogonal of the anticomplement of X(53)
X(32319) = isogonal of the isotomic of X(15318)
X(32319) = polar conjugate of the isotomic of X(18890)
X(32319) = X(i)-Ceva conjugate of X(j) for these (i,j): {14371, 6}, {15318, 18890}
X(32319) = X(3199)-cross conjugate of X(6)
X(32319) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20477}, {75, 6759}, {799, 30442}
X(32319) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 18890}, {6, 15318}, {53, 14371}, {512, 30441}
X(32319) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 20477}, {32, 6759}, {669, 30442}, {3199, 14363}, {15318, 76}, {18890, 69}, {30441, 670}


X(32320) = REFLECTION OF X(17434) IN X(647)

Barycentrics    a^4 (a^2 - b^2 - c^2)^3 (b^2 - c^2) : :
Barycentrics    (sin^2 2A)(sin 2B - sin 2C) : :
X(32320) = 2X[647]-3X[1636] = 3X[1636]-X[17434] = 4X[2501]-3X[14391] = 4X[3265]-3X[23616] = 8X[6587]-9X[14401]

See Angel Montesdeoca, Hyacinthos 29000 and HG020519

X(32320) lies on these lines: {6,2430}, {112,6080}, {323,401}, {394,3265}, {416,23090}, {418,23613}, {450,2451}, {520,647}, {651,2639}, {1640,23128}, {3569,6753}, {9033,12077}

X(32320) = reflection of X(17434) and X(647)
X(32320) = isogonal conjugate of X(15352)
X(32320) = isogonal of the polar conjugate of X(520)
X(32320) = X(i)-Ceva conjugate of X(j) for these (i,j): {110, 418}, {394, 2972}, {648, 3}, {651, 408}, {1625, 22052}, {2430, 1636}, {2986, 1650}, {4558, 417}, {4563, 426}, {15316, 20975}
X(32320) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15352}, {4, 823}, {19, 6528}, {75, 6529}, {92, 107}, {99, 6520}, {110, 6521}, {158, 648}, {162, 2052}, {264, 24019}, {393, 811}, {525, 24021}, {653, 1896}, {662, 1093}, {799, 6524}, {1096, 6331}, {1577, 32230}, {1784, 15459}, {2501, 23999}, {2617, 8794}, {3267, 24022}, {6330, 24024}, {6335, 8747}, {8748, 18026}, {14208, 23590}, {14618, 24000}, {17926, 24032}, {23582, 24006}
X(32320) = crosspoint of X(i) and X(j) for these (i,j): {3, 648}, {97, 110}
X(32320) = crosssum of X(i) and X(j) for these (i,j): {4, 647}, {53, 523}, {107, 6529}, {133, 1637}, {235, 2501}, {1896, 17926}, {2052, 14618}, {6750, 12077}
X(32320) = crosssum of Jerabek-hyperbola-intercepts of orthic axis
X(32320) = crossdifference of every pair of points on line {4, 51}
X(32320) = pole of Euler line wrt MacBeath circumconic
X(32320) = perspector of hyperbola {{A,B,C,X(3),X(95)}}
X(32320) = barycentric product X(i) X(j) for these lines: {i,j}: {3, 520}, {32, 4143}, {48, 24018}, {63, 822}, {71, 4091}, {72, 23224}, {97, 17434}, {110, 2972}, {184, 3265}, {217, 15414}, {228, 4131}, {255, 656}, {326, 810}, {394, 647}, {512, 3964}, {521, 22341}, {523, 1092}, {525, 577}, {661, 6507}, {669, 4176}, {684, 17974}, {798, 1102}, {850, 23606}, {905, 3990}, {924, 16391}, {1364, 23067}, {1459, 3682}, {1577, 4100}, {1636, 14919}, {1783, 16730}, {2200, 30805}, {2584, 2585}, {2632, 4575}, {3049, 3926}, {3267, 14585}, {3269, 4558}, {3733, 4158}, {3998, 22383}, {4025, 4055}, {4557, 7215}, {5562, 23286}, {6056, 17094}, {6368, 19210}, {7066, 23189}, {7125, 8611}, {8057, 14379}, {14642, 20580}, {23103, 32230}, {23107, 23963}, {23357, 23616}
X(32320) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {3, 6528}, {6, 15352}, {32, 6529}, {48, 823}, {184, 107}, {255, 811}, {394, 6331}, {512, 1093}, {520, 264}, {525, 18027}, {577, 648}, {647, 2052}, {661, 6521}, {669, 6524}, {798, 6520}, {810, 158}, {822, 92}, {1092, 99}, {1102, 4602}, {1363, 17094}, {1576, 32230}, {1946, 1896}, {2623, 8794}, {2972, 850}, {3049, 393}, {3265, 18022}, {3269, 14618}, {3964, 670}, {3990, 6335}, {4055, 1897}, {4100, 662}, {4143, 1502}, {4158, 27808}, {4176, 4609}, {4575, 23999}, {6507, 799}, {9247, 24019}, {14533, 16813}, {14585, 112}, {14600, 20031}, {15451, 13450}, {16730, 15413}, {17434, 324}, {17974, 22456}, {18877, 15459}, {19210, 18831}, {22341, 18026}, {23224, 286}, {23286, 8795}, {23606, 110}, {23613, 2972}, {23616, 23962}, {24018, 1969}, {30451, 11547}
X(32320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 6587, 30442}, {647, 30451, 3049}, {1636, 17434, 647}


X(32321) = MIDPOINT OF X(9914) AND X(12085)

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 + 10*a^10*b^2*c^2 - 13*a^8*b^4*c^2 + 8*a^6*b^6*c^2 - a^4*b^8*c^2 - 2*a^2*b^10*c^2 + b^12*c^2 + a^10*c^4 - 13*a^8*b^2*c^4 + 2*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 + 5*a^8*c^6 + 8*a^6*b^2*c^6 + 2*a^4*b^4*c^6 - 12*a^2*b^6*c^6 - 3*b^8*c^6 - 5*a^6*c^8 - a^4*b^2*c^8 + 5*a^2*b^4*c^8 - 3*b^6*c^8 - a^4*c^10 - 2*a^2*b^2*c^10 + 3*b^4*c^10 + 3*a^2*c^12 + b^2*c^12 - c^14) : :
X(32321) = (1 + J^2) X[3] - 2 X[64], (7 - J^2) X[3] - 6 X[154], (7 - J^2) X[64] - 3 (1 + J^2) X[154]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29002

X(32321) lies on these lines: {3, 64}, {4, 18532}, {22, 9833}, {24, 14216}, {25, 13419}, {26, 1503}, {30, 9938}, {159, 2918}, {161, 2937}, {186, 12324}, {265, 7517}, {378, 5878}, {511, 9908}, {542, 9937}, {1216, 1660}, {1593, 18388}, {1598, 18383}, {1853, 7506}, {2071, 12250}, {2777, 9914}, {2781, 16266}, {2883, 7526}, {3515, 13171}, {3517, 14864}, {3518, 32064}, {3520, 6225}, {3818, 6642}, {5073, 9919}, {5198, 18376}, {5656, 14118}, {5893, 31861}, {6053, 13293}, {6247, 6644}, {6293, 18445}, {6640, 32125}, {7387, 12293}, {7512, 11206}, {7514, 16252}, {7516, 10192}, {7525, 15577}, {7529, 23325}, {7555, 15581}, {9934, 12292}, {10249, 15805}, {10628, 12164}, {11413, 20427}, {12083, 17845}, {12084, 15311}, {22658, 22978}

X(32321) = midpoint of X(9914) and X(12085)
X(32321) = crosspoint of X(1288) and X(15384)
X(32321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1619, 6759}, {64, 1498, 18439}, {3357, 6759, 5907}

leftri

Centers related to the Hatzipolakis-Moses triangle: X(32322)-X(32413)

rightri

This preamble and centers X(32322)-X(32413) were contributed by César Eliud Lozada, May 4, 2019.

Hatzipolakis-Moses triangle is defined in X(6145).

The appearance of (T,i) in the following list means that triangles Hatizpolakis-Moses and T are perspective with perspector X(i) (an asterisk * means they are homothetic):

(ABC, 54), (2nd anti-extouch, 32322), (anti-inner-Grebe, 32323), (anti-outer-Grebe, 32324), (anti-orthocentroidal, 32325), (1st excosine, 32326), (inner-Grebe, 32327), (outer-Grebe, 32328), (3rd Hatzipolakis, 54), (2nd Hyacinth, 6146), (Kosnita, 54), (midheight, 389), (orthic, 1986), (orthocentroidal, 32329), (reflection, 6241)

The appearance of (T,i,j) in the following list means that triangles Hatizpolakis-Moses and T are orthologic with orthologic centers X(i) and X(j):

(ABC, 6146, 6145), (ABC-X3 reflections, 6146, 32330), (anti-Aquila, 6146, 32331), (anti-Ara, 6146, 32332), (anti-Ascella, 389, 32333), (anti-Atik, 389, 32334), (5th anti-Brocard, 6146, 32335), (2nd anti-circumperp-tangential, 6146, 32336), (1st anti-circumperp, 389, 7691), (anti-Conway, 389, 54), (2nd anti-Conway, 389, 973), (anti-Euler, 6146, 32337), (3rd anti-Euler, 389, 32338), (4th anti-Euler, 389, 32339), (anti-excenters-reflections, 389, 32340), (2nd anti-extouch, 389, 32341), (anti-inner-Grebe, 6146, 32342), (anti-outer-Grebe, 6146, 32343), (anti-Honsberger, 389, 32344), (anti-Hutson intouch, 389, 32345), (anti-incircle-circles, 389, 9920), (anti-inverse-in-incircle, 389, 32346), (anti-Mandart-incircle, 6146, 32347), (6th anti-mixtilinear, 389, 32348), (anti-orthocentroidal, 1986, 32349), (1st anti-Sharygin, 389, 54), (anti-tangential-midarc, 389, 32350), (anti-Ursa minor, 389, 32351), (anti-Wasat, 389, 32352), (antiAOA, 10114, 32353), (anticomplementary, 6146, 32354), (AOA, 10114, 32355), (Aquila, 6146, 32356), (Ara, 6146, 32357), (Aries, 32358, 32359), (1st Auriga, 6146, 32360), (2nd Auriga, 6146, 32361), (5th Brocard, 6146, 32362), (circumorthic, 389, 54), (2nd circumperp tangential, 6146, 32363), (Ehrmann-mid, 6146, 32364), (Ehrmann-side, 389, 6288), (Ehrmann-vertex, 389, 32365), (1st Ehrmann, 32366, 32367), (2nd Ehrmann, 389, 32368), (Euler, 6146, 32369), (2nd Euler, 389, 1209), (1st excosine, 389, 17824), (extangents, 389, 32370), (outer-Garcia, 6146, 32371), (Gossard, 6146, 32372), (inner-Grebe, 6146, 32373), (outer-Grebe, 6146, 32374), (3rd Hatzipolakis, 32375, 32376), (1st Hyacinth, 10114, 10115), (2nd Hyacinth, 32358, 32377), (intangents, 389, 32378), (Johnson, 6146, 32379), (inner-Johnson, 6146, 32380), (outer-Johnson, 6146, 32381), (1st Johnson-Yff, 6146, 32382), (2nd Johnson-Yff, 6146, 32383), (1st Kenmotu diagonals, 389, 32384), (2nd Kenmotu diagonals, 389, 32385), (Kosnita, 389, 23358), (Lucas antipodal tangents, 389, 32386), (Lucas homothetic, 6146, 32388), (Lucas(-1) antipodal tangents, 389, 32387), (Lucas(-1) homothetic, 6146, 32389), (Mandart-incircle, 6146, 32390), (medial, 6146, 32391), (midheight, 32392, 32393), (5th mixtilinear, 6146, 32394), (orthic, 389, 3574), (orthocentroidal, 1986, 32395), (reflection, 54, 17824), (submedial, 389, 32396), (tangential, 389, 2917), (inner tri-equilateral, 389, 32397), (outer tri-equilateral, 389, 32398), (3rd tri-squares-central, 6146, 32399), (4th tri-squares-central, 6146, 32400), (Trinh, 389, 32401), (Walsmith, 32317, 32316), (X3-ABC reflections, 6146, 32402), (inner-Yff, 6146, 32403), (outer-Yff, 6146, 32404), (inner-Yff tangents, 6146, 32405), (outer-Yff tangents, 6146, 32406)

The appearance of (T,i,j) in the following list means that triangles Hatizpolakis-Moses and T are parallelogic with parallelogic centers X(i) and X(j): (1st Parry, 6146, 32407), (2nd Parry, 6146, 32408).

The appearance of (T,i,j) in the following list means that triangles Hatizpolakis-Moses and T are cyclologic with cyclologic centers X(i) and X(j): (2nd anti-Conway, 389, 32409), (orthic, 32410, 1986).

The appearance of (T,i,j) in the following list means that triangles Hatizpolakis-Moses and T are eulerologic with eulorologic centers X(i) and X(j): (2nd anti-Conway, 32411, x), (Lucas(-1) reflection, 0, x), where x means "not-existing-eulerologic center" and 0 means "not calculated center".


X(32322) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND 2nd ANTI-EXTOUCH

Barycentrics    (S^2-SB*SC)*((4*R^2-SW)*S^2-72*R^6-6*(SA-10*SW)*R^4+(4*SA+9*SW)*(SA-2*SW)*R^2-(SA^2-2*SW^2)*SW) : :

X(32322) lies on these lines: {26,1181}, {182,32251}, {184,2931}, {389,10274}, {567,19361}, {568,19362}, {1533,18534}, {1593,13403}, {1899,10264}, {6146,32345}, {8479,21331}, {9932,19357}, {10620,10938}, {12022,22533}, {12168,21243}, {14805,19348}, {19468,32358}


X(32323) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ANTI-INNER-GREBE

Barycentrics    (SB+SC)*(2*(18*R^2-5*SW)*S^2+(3*S^2+4*R^2*(40*R^2-SA-26*SW)+SA^2-2*SB*SC+16*SW^2)*S-2*(4*R^2-SW)*(SA-2*SW)*SA) : :

X(32323) lies on these lines: {389,19095}, {1588,13403}, {3312,6102}, {6146,32342}, {6241,19087}


X(32324) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ANTI-OUTER-GREBE

Barycentrics    (SB+SC)*(2*(18*R^2-5*SW)*S^2-(3*S^2+4*R^2*(40*R^2-SA-26*SW)+SA^2-2*SB*SC+16*SW^2)*S-2*(4*R^2-SW)*(SA-2*SW)*SA) : :

X(32324) lies on these lines: {389,19096}, {1587,13403}, {3311,6102}, {6146,32343}, {6241,19088}


X(32325) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ANTI-ORTHOCENTROIDAL

Barycentrics    (SB+SC)*((431*R^4-2*(21*SA+92*SW)*R^2+4*(3*SA+5*SW)*SW)*S^2+3*(7*R^2-2*SW)*(84*R^4+(5*SA-34*SW)*R^2-2*SA^2+4*SW^2+2*SB*SC)*SA) : :

X(32325) lies on these lines: {74,13403}, {389,2914}, {399,6102}, {1986,32349}, {6241,17812}, {10114,12380}


X(32326) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND 1st EXCOSINE

Barycentrics    (SB+SC)*((72*R^4-3*(2*SA+11*SW)*R^2+2*(SA+2*SW)*SW)*S^2+2*(3*R^2-SW)*(48*R^4-16*R^2*SW-SA^2+SB*SC+2*SW^2)*SA) : :

X(32326) lies on these lines: {3,32276}, {64,13403}, {389,15139}, {1498,6102}, {6759,17837}, {9932,17821}, {14677,17835}, {17846,32358}


X(32327) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND INNER-GREBE

Barycentrics    (SB+SC)*(3*S^4+(4*R^2*(40*R^2-SA-4*SW)+SA^2-2*SB*SC)*S^2-(2*(18*R^2-SA-3*SW)*S^2-2*(4*R^2*SA+SA^2-SB*SC-2*SW^2)*SA)*S-16*R^2*SB*SC*SW) : :

X(32327) lies on these lines: {389,6277}, {1161,6102}, {5871,13403}, {6146,32373}, {6241,6267}


X(32328) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND OUTER-GREBE

Barycentrics    (SB+SC)*(3*S^4+(4*R^2*(40*R^2-SA-4*SW)+SA^2-2*SB*SC)*S^2+(2*(18*R^2-SA-3*SW)*S^2-2*(4*R^2*SA+SA^2-SB*SC-2*SW^2)*SA)*S-16*R^2*SB*SC*SW) : :

X(32328) lies on these lines: {389,6276}, {1160,6102}, {5870,13403}, {6146,32374}, {6241,6266}


X(32329) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ORTHOCENTROIDAL

Barycentrics    (SB+SC)*((43*R^2-10*SW)*S^2+(7*R^2-2*SW)*(28*R^2-SA-6*SW)*SA) : :

X(32329) lies on these lines: {74,19361}, {195,1511}, {381,3567}, {389,6143}, {1986,32395}, {2777,22949}, {5890,13403}, {7730,10114}, {11561,12280}, {15033,32210}, {25739,32392}


X(32330) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ABC-X3 REFLECTIONS TO HATZIPOLAKIS-MOSES

Barycentrics    (R^2*(32*R^2+3*SA-23*SW)-(SA-4*SW)*SW)*S^2-(8*R^2*(7*R^2-5*SW)+7*SW^2)*SB*SC : :
X(32330) = 3*X(3)-X(32402) = 2*X(20)+X(32359) = 3*X(165)-X(32356) = 3*X(376)-X(32337) = 3*X(3576)-2*X(32331) = 4*X(6689)-3*X(32395) = 5*X(17821)-2*X(32340) = 3*X(18405)-4*X(32393)

The reciprocal orthologic center of these triangles is X(6146).

X(32330) lies on these lines: {2,32369}, {3,161}, {4,32391}, {20,32354}, {30,32372}, {35,32403}, {36,32404}, {54,6240}, {55,32336}, {56,32390}, {110,12225}, {154,5448}, {165,32356}, {182,32335}, {371,32343}, {372,32342}, {376,32337}, {382,32364}, {515,32371}, {517,32394}, {973,18533}, {1154,12118}, {1593,32332}, {3098,32362}, {3428,32363}, {3574,11425}, {3576,32331}, {4549,5876}, {5925,11820}, {6000,18442}, {6242,6776}, {6284,32383}, {6689,32395}, {7354,32382}, {7487,11743}, {7507,17821}, {7691,15138}, {9540,32399}, {9630,32350}, {10274,13352}, {10282,31724}, {10310,32347}, {10619,32341}, {10625,10628}, {11248,32405}, {11249,32406}, {11414,32357}, {11824,32373}, {11825,32374}, {11826,32380}, {11827,32381}, {11828,32388}, {11829,32389}, {13160,32351}, {13935,32400}, {17818,17846}, {18405,32393}, {18569,32171}

X(32330) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 32354}, {17845, 32345}
X(32330) = reflection of X(i) in X(j) for these (i,j): (4, 32391), (382, 32364), (6145, 3), (6288, 23358), (32359, 32354)
X(32330) = anticomplement of X(32369)
X(32330) = X(6145)-of-ABC-X3-reflections-triangle


X(32331) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-AQUILA TO HATZIPOLAKIS-MOSES

Barycentrics
(b+c)*a^15-2*b*c*a^14-(b+c)*(3*b^2-2*b*c+3*c^2)*a^13+(b^4+c^4+2*(2*b^2-b*c+2*c^2)*b*c)*a^12+(b+c)*(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^11-2*(2*b^6+2*c^6-(b^4+c^4+(b^2-3*b*c+c^2)*b*c)*b*c)*a^10+(b+c)*(5*b^6+5*c^6-(2*b^4+2*c^4+3*(b-c)^2*b*c)*b*c)*a^9+(5*b^6+5*c^6+(2*b^4+2*c^4+(b+c)^2*b*c)*b*c)*(b-c)^2*a^8-(b^2-c^2)*(b-c)*(5*b^6+5*c^6+(2*b^2+b*c+c^2)*(b^2+b*c+2*c^2)*b*c)*a^7+2*(b^2-c^2)^2*(b^4+c^4-(b^2-3*b*c+c^2)*b*c)*b*c*a^6-(b^2-c^2)^2*(b+c)*(b^6+c^6+(2*b^2-b*c+c^2)*(b^2-b*c+2*c^2)*b*c)*a^5-(5*b^8+5*c^8-2*(2*b^2-b*c+2*c^2)*(b^4+c^4-(b^2+b*c+c^2)*b*c)*b*c)*(b^2-c^2)^2*a^4+(b^2-c^2)*(b-c)^2*(b^3+c^3)*(b^4-c^4)*(3*b^2+5*b*c+3*c^2)*a^3+2*(b^4-c^4)*(b^2-c^2)^3*(2*b^4+2*c^4-(b-c)^2*b*c)*a^2-(b^2-c^2)^5*(b-c)*(b^2+c^2)^2*a-(b^2+c^2)^2*(b^2-c^2)^6 : :
X(32331) = 3*X(3576)-X(32330) = 5*X(3616)-X(32354) = 3*X(5603)+X(32337) = 3*X(5886)-X(32379) = 7*X(9624)-X(32359) = 3*X(10246)+X(32402)

The reciprocal orthologic center of these triangles is X(6146).

X(32331) lies on these lines: {1,6145}, {2,32371}, {515,32369}, {960,1209}, {999,32363}, {1125,32391}, {1154,12259}, {1319,32336}, {1385,18400}, {2646,32390}, {3295,32347}, {3576,32330}, {3616,32354}, {5603,32337}, {5886,32379}, {9624,32359}, {9955,32364}, {10246,32402}, {10628,12261}, {11363,32332}, {11364,32335}, {11365,32357}, {11368,32362}, {11370,32373}, {11371,32374}, {11373,32380}, {11374,32381}, {11375,32382}, {11376,32383}, {11377,32388}, {11378,32389}, {11831,32372}, {13883,32399}, {13936,32400}, {18991,32342}, {18992,32343}

X(32331) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 6145}, {32356, 32394}
X(32331) = reflection of X(i) in X(j) for these (i,j): (32364, 9955), (32391, 1125)
X(32331) = complement of X(32371)
X(32331) = X(6145)-of-anti-Aquila-triangle
X(32331) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32356, 32394), (6145, 32394, 32356)


X(32332) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ARA TO HATZIPOLAKIS-MOSES

Barycentrics    S^4-(R^2*(12*R^2+3*SA-10*SW)-SA^2+SB*SC+2*SW^2)*S^2+(R^2*(16*R^2-19*SW)+5*SW^2)*SB*SC : :
X(32332) = 3*X(428)-2*X(11743) = 4*X(6756)-X(32377)

The reciprocal orthologic center of these triangles is X(6146).

X(32332) lies on these lines: {4,54}, {25,6145}, {26,1209}, {33,32390}, {34,32336}, {66,1204}, {159,32333}, {235,32369}, {427,32391}, {428,11743}, {539,7540}, {973,6756}, {1154,11819}, {1352,7691}, {1593,32330}, {1598,32402}, {1843,32352}, {5090,32371}, {5410,32343}, {5411,32342}, {5576,6689}, {5965,12272}, {6288,7517}, {7487,32337}, {7488,32348}, {7564,11750}, {7713,32356}, {10628,12140}, {11363,32331}, {11380,32335}, {11383,32347}, {11386,32362}, {11388,32373}, {11389,32374}, {11390,32380}, {11391,32381}, {11392,32382}, {11393,32383}, {11394,32388}, {11395,32389}, {11396,32394}, {11398,32403}, {11399,32404}, {11400,32405}, {11401,32406}, {11572,32393}, {11832,32372}, {12133,16621}, {13884,32399}, {13937,32400}, {15761,22804}, {18563,32062}, {22479,32363}, {32341,32359}

X(32332) = reflection of X(i) in X(j) for these (i,j): (973, 6756), (32377, 973)
X(32332) = X(6145)-of-anti-Ara-triangle
X(32332) = {X(4), X(32379)}-harmonic conjugate of X(3574)


X(32333) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ASCELLA TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(R^2*S^2+(2*SW^2+R^2*(16*R^2-SA-11*SW))*SA) : :
X(32333) = 4*X(54)-3*X(11402) = 4*X(578)-X(12175) = X(1593)+2*X(19468) = 3*X(11402)-2*X(32341)

The reciprocal orthologic center of these triangles is X(389).

X(32333) lies on these lines: {3,54}, {4,9920}, {6,32352}, {25,2917}, {26,20424}, {159,32332}, {184,6293}, {378,12254}, {427,32346}, {539,12166}, {578,12175}, {973,9777}, {1181,10628}, {1209,7395}, {1398,32350}, {1593,18400}, {1658,22051}, {2888,7503}, {2937,31815}, {3515,12242}, {3516,10619}, {3520,31804}, {5094,32351}, {5410,32384}, {5411,32385}, {6242,11426}, {6288,9818}, {6644,8254}, {7071,32378}, {7484,32348}, {7488,31802}, {7509,26869}, {7514,21230}, {7526,12168}, {9704,12412}, {10274,19357}, {10831,13079}, {10832,18984}, {10982,11808}, {11245,32334}, {11284,32396}, {11403,32340}, {11405,32368}, {11406,32370}, {11408,32397}, {11409,32398}, {11410,32401}, {11424,17846}, {11425,21660}, {12233,21284}, {13423,15033}, {14528,32226}, {15739,26864}, {18386,32365}, {19118,32344}, {19404,32386}, {19405,32387}

X(32333) = reflection of X(i) in X(j) for these (i,j): (12160, 195), (32341, 54)
X(32333) = X(21)-of-anti-Ascella-triangle if ABC is acute
X(32333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 32339, 7592), (54, 32341, 11402)


X(32334) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ATIK TO HATZIPOLAKIS-MOSES

Barycentrics    2*S^4+2*(R^2*(8*R^2-3*SA-3*SW)+SA^2-SB*SC)*S^2-(8*R^2-3*SW)*R^2*SB*SC : :

The reciprocal orthologic center of these triangles is X(389).

X(32334) lies on these lines: {2,32341}, {4,973}, {54,69}, {68,11802}, {195,3548}, {539,18934}, {1154,6643}, {1199,6143}, {1209,11411}, {1658,27552}, {1899,32346}, {2888,6815}, {2917,6776}, {3541,32251}, {3574,11433}, {6288,18917}, {6353,32379}, {6515,7691}, {7730,11457}, {9920,18914}, {10628,18933}, {11245,32333}, {11808,14216}, {12254,18910}, {12324,32340}, {13418,14528}, {13567,17824}, {15801,16051}, {18400,18909}, {18911,32338}, {18912,32339}, {18913,32345}, {18915,32350}, {18918,32365}, {18919,32368}, {18921,32370}, {18922,32378}, {18923,32384}, {18924,32385}, {18925,23358}, {18926,32386}, {18927,32387}, {18928,32396}, {18929,32397}, {18930,32398}, {18931,32401}, {19119,32344}, {19468,21844}, {22051,31283}, {23291,32351}, {32354,32377}

X(32334) = X(21)-of-anti-Atik-triangle if ABC is acute
X(32334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (973, 32337, 4), (1899, 32352, 32346)


X(32335) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th ANTI-BROCARD TO HATZIPOLAKIS-MOSES

Barycentrics
((72*R^2+3*SA-46*SW)*R^2-(SA-7*SW)*SW)*S^4+(8*(5*SA^2-12*SB*SC-6*SW^2)*R^4-(23*SA^2-63*SB*SC-29*SW^2)*SW*R^2+(3*SA^2-10*SB*SC-4*SW^2)*SW^2)*S^2-(2*R^2-SW)*(8*R^2-3*SW)*SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32335) lies on these lines: {32,6145}, {83,32391}, {98,32369}, {182,32330}, {1154,12193}, {3398,18400}, {7787,32354}, {10628,12201}, {10788,32337}, {10789,32356}, {10790,32357}, {10791,32371}, {10792,32373}, {10793,32374}, {10794,32380}, {10795,32381}, {10796,32379}, {10797,32382}, {10798,32383}, {10799,32390}, {10800,32394}, {10801,32403}, {10802,32404}, {10803,32405}, {10804,32406}, {11364,32331}, {11380,32332}, {11490,32347}, {11839,32372}, {11840,32388}, {11841,32389}, {11842,32402}, {12835,32336}, {13885,32399}, {13938,32400}, {18502,32364}, {18993,32342}, {18994,32343}, {22520,32363}

X(32335) = X(6145)-of-5th-anti-Brocard-triangle


X(32336) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL TO HATZIPOLAKIS-MOSES

Barycentrics    (3*R^2-SW)*(8*R^2-SA-3*SW)*S^2+(SB+SC)*((5*R^2-2*SW)*(4*R^2-SW)*b*c-(12*R^2-5*SW)*(3*R^2-SW)*SA) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32336) lies on these lines: {1,18400}, {3,32403}, {4,32383}, {11,32369}, {12,32391}, {34,32332}, {55,32330}, {56,6145}, {57,32356}, {388,32354}, {999,32402}, {1154,18970}, {1319,32331}, {1478,32379}, {2099,32394}, {2917,9659}, {3574,19365}, {3585,32364}, {4293,32337}, {5252,32371}, {9657,32359}, {9672,32345}, {10628,18968}, {11509,32347}, {12835,32335}, {18954,32357}, {18957,32362}, {18958,32372}, {18959,32373}, {18960,32374}, {18961,32380}, {18962,32381}, {18963,32388}, {18964,32389}, {18965,32399}, {18966,32400}, {18967,32406}, {18995,32342}, {18996,32343}

X(32336) = reflection of X(32390) in X(1)
X(32336) = X(6145)-of-2nd-anti-circumperp-tangential-triangle
X(32336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 32354, 32382), (999, 32402, 32404)


X(32337) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EULER TO HATZIPOLAKIS-MOSES

Barycentrics    S^4+(R^2*(8*R^2-3*SA-3*SW)+SA^2-SB*SC)*S^2-(R^2*(SW+4*R^2)-SW^2)*SB*SC : :
X(32337) = 3*X(4)-4*X(32369) = 3*X(376)-2*X(32330) = 5*X(631)-2*X(32359) = 5*X(631)-4*X(32391) = 3*X(1853)-X(17824) = 3*X(1853)-2*X(32351) = X(2888)+2*X(14216) = 5*X(3091)-4*X(32364) = 3*X(5603)-4*X(32331) = 3*X(5657)-2*X(32371) = X(6225)-4*X(22804) = 4*X(6247)-X(12254) = 2*X(6288)+X(12324) = 3*X(7967)-2*X(32394) = 3*X(11845)-2*X(32372) = 3*X(32064)-X(32346)

The reciprocal orthologic center of these triangles is X(6146).

X(32337) lies on these lines: {2,32379}, {3,32354}, {4,973}, {20,2888}, {24,32357}, {30,32402}, {54,66}, {64,12244}, {70,18533}, {104,32363}, {376,32330}, {388,32403}, {427,32341}, {497,32404}, {515,32356}, {631,32359}, {1154,11411}, {1209,3547}, {1352,32348}, {1503,2916}, {1853,7592}, {1899,3574}, {2892,8549}, {3085,32382}, {3086,32383}, {3088,32377}, {3091,32364}, {3410,9833}, {3448,5889}, {3520,6247}, {4293,32336}, {4294,32390}, {5012,10274}, {5189,14864}, {5596,32344}, {5603,32331}, {5657,32371}, {6143,15139}, {6146,30100}, {6225,22804}, {6288,12324}, {6759,14076}, {7487,32332}, {7581,32343}, {7582,32342}, {7967,32394}, {9862,32362}, {9920,21230}, {10783,32373}, {10784,32374}, {10785,32380}, {10786,32381}, {10788,32335}, {10805,32405}, {10806,32406}, {11431,18912}, {11491,32347}, {11550,32352}, {11845,32372}, {11846,32388}, {11847,32389}, {12300,18910}, {13423,32247}, {13886,32399}, {13939,32400}, {15033,32412}, {15801,31099}, {22533,25739}

X(32337) = reflection of X(i) in X(j) for these (i,j): (4, 6145), (5596, 32344), (6759, 14076), (9833, 23358), (9920, 21230), (10274, 20299), (12254, 32345), (17824, 32351), (32345, 6247), (32354, 3), (32359, 32391)
X(32337) = anticomplement of X(32379)
X(32337) = X(6145)-of-anti-Euler-triangle
X(32337) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32334, 973), (7691, 11442, 2888)


X(32338) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-EULER TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((7*R^2-2*SB-2*SC)*S^2+((32*R^2-7*SA-22*SW)*R^2+2*SA^2-2*SB*SC+4*SW^2)*SA) : :
X(32338) = 4*X(5)-3*X(7730) = 3*X(381)-2*X(32196) = 3*X(568)-4*X(8254) = 5*X(631)-4*X(11802) = 8*X(973)-9*X(5640) = 4*X(1209)-5*X(11444) = 3*X(2979)-2*X(7691) = 3*X(3060)-4*X(3574) = 5*X(3091)-4*X(11808) = 9*X(5055)-8*X(13365) = 4*X(5562)-X(12280) = X(5889)-4*X(12606) = 3*X(5890)-4*X(10610) = 3*X(5891)-2*X(6153) = 4*X(6152)-7*X(15056) = 2*X(6242)-5*X(11444) = 2*X(6288)-3*X(11459) = 5*X(10574)-8*X(12363) = X(11412)+2*X(22815) = 3*X(11459)-X(13423)

The reciprocal orthologic center of these triangles is X(389).

X(32338) lies on these lines: {2,32352}, {3,54}, {5,7730}, {20,10628}, {22,17824}, {30,15103}, {68,12319}, {110,2917}, {381,32196}, {539,12271}, {568,8254}, {631,11802}, {973,5640}, {1209,6242}, {1216,6143}, {1658,11597}, {2888,3153}, {2937,7731}, {3060,3574}, {3091,11808}, {3519,16000}, {5055,13365}, {5891,6153}, {5925,12279}, {5965,15073}, {6152,7547}, {6243,20424}, {6288,11459}, {6689,15043}, {7488,10274}, {7998,32348}, {9920,11441}, {10224,21230}, {10625,13619}, {11439,32340}, {11440,32345}, {11442,32346}, {11443,32368}, {11445,32370}, {11446,32378}, {11447,32384}, {11448,32385}, {11449,23358}, {11451,32396}, {11452,32397}, {11453,32398}, {11454,32401}, {11464,15091}, {11576,18386}, {11591,13368}, {11750,15100}, {12111,12226}, {12254,13754}, {12272,15069}, {12273,12281}, {12380,15068}, {13340,15332}, {15058,22804}, {18392,32365}, {18911,32334}, {19122,32344}, {19367,32350}, {19412,32386}, {19413,32387}, {19467,21660}, {23293,32351}, {26881,32379}

X(32338) = reflection of X(i) in X(j) for these (i,j): (54, 12606), (2888, 5562), (5889, 54), (6242, 1209), (6243, 20424), (12280, 2888), (12307, 6101), (13368, 11591), (13423, 6288), (32339, 3), (32341, 31807)
X(32338) = anticomplement of X(32352)
X(32338) = X(21)-of-3rd-anti-Euler-triangle if ABC is acute
X(32338) = {X(11459), X(13423)}-harmonic conjugate of X(6288)


X(32339) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-EULER TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((7*R^2-2*SB-2*SC)*S^2+((52*R^2-7*SA-30*SW)*R^2+2*SA^2-2*SB*SC+4*SW^2)*SA) : :
X(32339) = 3*X(2)-4*X(11802) = 2*X(4)-3*X(7730) = 3*X(4)-4*X(11808) = 2*X(54)-3*X(5890) = 4*X(185)-X(12291) = 3*X(568)-2*X(20424) = 8*X(973)-7*X(9781) = 4*X(1209)-3*X(11459) = 5*X(3567)-4*X(3574) = 7*X(3851)-8*X(13365) = 4*X(6152)-X(12290) = X(6241)+2*X(6242) = 8*X(6689)-9*X(15045) = 9*X(7730)-8*X(11808) = 3*X(7730)-4*X(32352) = 7*X(7999)-8*X(32348) = 7*X(9781)-4*X(12300) = 5*X(10574)-4*X(10610) = 5*X(10574)-2*X(22815) = 2*X(11808)-3*X(32352)

The reciprocal orthologic center of these triangles is X(389).

X(32339) lies on these lines: {2,11802}, {3,54}, {4,7730}, {24,17824}, {52,3153}, {74,6799}, {143,14644}, {185,12254}, {186,10274}, {382,32196}, {389,6143}, {539,12282}, {568,10224}, {973,7547}, {1204,16013}, {1209,5448}, {1614,2917}, {1986,2929}, {2888,13754}, {2914,11438}, {3060,18377}, {3432,14979}, {3567,3574}, {3851,13365}, {5498,22051}, {5663,13368}, {5895,6152}, {6145,16000}, {6153,12162}, {6241,6242}, {6288,12111}, {6689,15045}, {7999,32348}, {9905,31728}, {9920,11456}, {11271,22647}, {11455,32340}, {11457,32346}, {11458,32368}, {11460,32370}, {11461,32378}, {11462,32384}, {11463,32385}, {11464,23358}, {11465,32396}, {11466,32397}, {11467,32398}, {11468,32401}, {11557,21451}, {12270,12278}, {13565,15056}, {15305,22804}, {17855,22949}, {18394,32365}, {18436,21230}, {18912,32334}, {19123,32344}, {19368,32350}, {19414,32386}, {19415,32387}, {21357,31834}, {23294,32351}, {26882,32379}

X(32339) = midpoint of X(6241) and X(13423)
X(32339) = reflection of X(i) in X(j) for these (i,j): (4, 32352), (195, 6102), (382, 32196), (9905, 31728), (11412, 7691), (12111, 6288), (12162, 6153), (12254, 185), (12291, 12254), (12300, 973), (13423, 6242), (18436, 21230), (22815, 10610), (32338, 3)
X(32339) = anticomplement of the anticomplement of X(11802)
X(32339) = X(21)-of-4th-anti-Euler-triangle if ABC is acute
X(32339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32352, 7730), (7592, 32333, 54)


X(32340) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EXCENTERS-REFLECTIONS TO HATZIPOLAKIS-MOSES

Barycentrics    4*a^10-6*(b^2+c^2)*a^8-3*(b^2-c^2)^2*a^6+5*(b^4-c^4)*(b^2-c^2)*a^4+(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)*a^2-3*(b^4-c^4)*(b^2-c^2)^3 : :
X(32340) = 3*X(4)-X(54) = 4*X(4)-X(10619) = 5*X(4)-2*X(12242) = 5*X(4)-X(12254) = 3*X(51)-4*X(11743) = 2*X(54)-3*X(3574) = 4*X(54)-3*X(10619) = 5*X(54)-6*X(12242) = 5*X(54)-3*X(12254) = X(195)-5*X(5076) = 3*X(381)-2*X(6689) = 3*X(382)+X(12307) = X(1493)-4*X(12102) = X(2888)+3*X(3543) = 5*X(3574)-4*X(12242) = 5*X(3574)-2*X(12254) = 9*X(3830)-X(12316) = 3*X(6288)-X(12307) = 5*X(10619)-8*X(12242) = 5*X(10619)-4*X(12254)

The reciprocal orthologic center of these triangles is X(389).

X(32340) lies on these lines: {4,54}, {5,15432}, {20,15431}, {24,32401}, {25,32345}, {30,1209}, {33,32350}, {34,32378}, {51,11743}, {64,6145}, {125,3575}, {185,973}, {195,5076}, {235,32351}, {378,23358}, {381,6689}, {382,6288}, {468,20376}, {539,3830}, {546,10610}, {548,20584}, {550,13565}, {1112,11262}, {1154,3627}, {1493,12102}, {1495,23047}, {1498,32341}, {1539,3853}, {1568,18350}, {1593,2917}, {1597,9920}, {2888,3543}, {3091,32396}, {3146,7691}, {3527,18396}, {3861,8254}, {5921,5965}, {6000,11808}, {6152,10628}, {6564,8995}, {6565,13986}, {6756,13851}, {7507,17821}, {7576,18383}, {7730,12290}, {10594,18376}, {11381,11576}, {11403,32333}, {11439,32338}, {11455,32339}, {11470,32368}, {11471,32370}, {11473,32384}, {11474,32385}, {11475,32397}, {11476,32398}, {11802,14915}, {12060,16337}, {12063,13423}, {12101,22051}, {12266,18483}, {12315,32377}, {12324,32334}, {12606,18323}, {12943,12956}, {12946,12953}, {13473,16656}, {15004,18945}, {15687,20424}, {15739,21660}, {15811,17824}, {18559,20299}, {19095,23259}, {19096,23249}, {19124,32344}, {19416,32386}, {19417,32387}

X(32340) = midpoint of X(i) and X(j) for these lines: {i,j}: {382, 6288}, {3146, 7691}, {11381, 32352}
X(32340) = reflection of X(i) in X(j) for these (i,j): (20, 32348), (185, 973), (548, 20584), (550, 13565), (1209, 22804), (3574, 4), (8254, 3861), (10610, 546), (10619, 3574), (12254, 12242), (12266, 18483), (21660, 15739), (32345, 32393), (32352, 11576)
X(32340) = X(21)-of-anti-excenters-reflections-triangle if ABC is acute
X(32340) = {X(3575), X(11572)}-harmonic conjugate of X(125)


X(32341) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-EXTOUCH TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((3*R^2-SB-SC)*S^2+((8*R^2-3*SA-3*SW)*R^2+SA^2-SB*SC)*SA) : :
X(32341) = 2*X(54)-3*X(11402) = X(1181)+2*X(12234) = 3*X(11402)-X(32333)

The reciprocal orthologic center of these triangles is X(389).

X(32341) lies on these lines: {2,32334}, {3,54}, {4,19362}, {6,3574}, {25,973}, {155,1209}, {184,2917}, {185,32345}, {389,10274}, {394,32348}, {427,32337}, {539,19458}, {578,10628}, {1147,11802}, {1181,12173}, {1199,1594}, {1498,32340}, {1614,7730}, {1899,32351}, {1994,12225}, {2888,3564}, {2904,11426}, {2914,15106}, {3515,32391}, {3575,32354}, {5094,12242}, {5198,11743}, {6152,9920}, {6240,12254}, {6276,19352}, {6277,19351}, {6288,18445}, {6759,11808}, {6776,32346}, {7558,12325}, {8254,18916}, {9905,31811}, {10224,27552}, {10601,32396}, {10602,32368}, {10605,32401}, {10619,32330}, {10982,18376}, {11576,12167}, {11702,15132}, {11803,14791}, {12022,14627}, {12175,19459}, {13371,22051}, {13565,15068}, {15037,26879}, {15047,26917}, {18386,32369}, {18396,32365}, {18569,20424}, {18997,19095}, {18998,19096}, {19125,32344}, {19349,32350}, {19350,32370}, {19354,32378}, {19355,32384}, {19356,32385}, {19357,23358}, {19358,32386}, {19359,32387}, {19363,32397}, {19364,32398}, {19468,21284}, {20376,26937}, {22804,32139}, {32332,32359}

X(32341) = reflection of X(i) in X(j) for these (i,j): (195, 12161), (9905, 31811), (12254, 31804), (32333, 54), (32338, 31807)
X(32341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7592, 12161, 11402), (11402, 32333, 54)
X(32341) = X(21)-of-2nd-anti-extouch-triangle if ABC is acute


X(32342) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GREBE TO HATZIPOLAKIS-MOSES

Barycentrics    ((8*R^2-3*SA-3*SW)*R^2+SA*SW)*S^2-2*(5*R^2-2*SW)*(4*R^2-SW)*(SB+SC)*S+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC : :

The reciprocal orthologic center of these triangles is X(6146).

X(32342) lies on these lines: {2,32400}, {6,3574}, {372,32330}, {973,19039}, {1154,19061}, {1587,32369}, {3069,32391}, {3299,32403}, {3301,32404}, {3312,18400}, {5411,32332}, {6146,32323}, {6293,19045}, {6418,32402}, {7582,32337}, {7584,32379}, {7585,32399}, {7586,32354}, {7968,32394}, {10628,19051}, {13785,32364}, {13936,32371}, {18991,32331}, {18993,32335}, {18995,32336}, {18997,32345}, {18999,32347}, {19003,32356}, {19005,32357}, {19011,32362}, {19013,32363}, {19017,32372}, {19023,32380}, {19025,32381}, {19027,32382}, {19029,32383}, {19031,32388}, {19033,32389}, {19037,32390}, {19047,32405}, {19049,32406}, {19096,32351}

X(32342) = X(6145)-of-anti-inner-Grebe-triangle
X(32342) = {X(6), X(6145)}-harmonic conjugate of X(32343)


X(32343) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-GREBE TO HATZIPOLAKIS-MOSES

Barycentrics    ((8*R^2-3*SA-3*SW)*R^2+SA*SW)*S^2+2*(5*R^2-2*SW)*(4*R^2-SW)*(SB+SC)*S+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC : :

The reciprocal orthologic center of these triangles is X(6146).

X(32343) lies on these lines: {2,32399}, {6,3574}, {371,32330}, {973,19040}, {1154,19062}, {1588,32369}, {3068,32391}, {3299,32404}, {3301,32403}, {3311,18400}, {5410,32332}, {6146,32324}, {6293,19046}, {6417,32402}, {7581,32337}, {7583,32379}, {7585,32354}, {7586,32400}, {7969,32394}, {10628,19052}, {13665,32364}, {13883,32371}, {18992,32331}, {18994,32335}, {18996,32336}, {18998,32345}, {19000,32347}, {19004,32356}, {19006,32357}, {19012,32362}, {19014,32363}, {19018,32372}, {19024,32380}, {19026,32381}, {19028,32382}, {19030,32383}, {19032,32388}, {19034,32389}, {19038,32390}, {19048,32405}, {19050,32406}, {19095,32351}

X(32343) = X(6145)-of-anti-outer-Grebe-triangle
X(32343) = {X(6), X(6145)}-harmonic conjugate of X(32342)


X(32344) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-HONSBERGER TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((10*R^2*(2*R^2-SW)+SW^2)*S^2+(2*R^2-SW)*(4*R^2+SA-2*SW)*SA*SW) : :
X(32344) = 2*X(2917)+X(32368) = 5*X(3618)-X(32346) = 3*X(5050)+X(9920) = 3*X(5085)-X(32345) = X(9972)+2*X(32367) = X(9977)+2*X(10282) = X(10274)-3*X(23042) = X(17824)-5*X(19132) = 3*X(23041)-2*X(32391)

The reciprocal orthologic center of these triangles is X(389).

X(32344) lies on these lines: {6,24}, {110,343}, {159,9827}, {161,5012}, {182,18400}, {206,1209}, {511,23358}, {539,19141}, {569,9815}, {1154,19139}, {1176,1503}, {1177,10628}, {1428,32350}, {1974,3574}, {2330,32378}, {3589,32351}, {3618,32346}, {5050,9920}, {5085,32345}, {5092,32401}, {5596,32337}, {5965,10274}, {6288,19129}, {7691,19121}, {9967,15462}, {9972,32367}, {9977,10282}, {17824,19132}, {19118,32333}, {19119,32334}, {19122,32338}, {19123,32339}, {19124,32340}, {19125,32341}, {19126,32348}, {19127,19149}, {19130,32365}, {19133,32370}, {19134,32386}, {19135,32387}, {19137,32396}, {21637,32352}

X(32344) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 2917}, {5596, 32337}
X(32344) = reflection of X(i) in X(j) for these (i,j): (32351, 3589), (32365, 19130), (32368, 6), (32379, 206), (32401, 5092)
X(32344) = X(21)-of-anti-Honsberger-triangle if ABC is acute


X(32345) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-HUTSON INTOUCH TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((3*R^2-SA-SW)*S^2-(2*(16*R^2-SA-9*SW)*R^2+SA^2-SB*SC+2*SW^2)*SA) : :
X(32345) = 3*X(2)-4*X(20376) = 3*X(3)-X(9920) = 3*X(3)-2*X(23358) = 2*X(4)-3*X(32395) = 2*X(54)+X(64) = 3*X(154)-4*X(32391) = X(195)+2*X(3357) = X(1498)-4*X(10610) = X(2888)-4*X(6696) = 3*X(2917)-2*X(9920) = 3*X(2917)-4*X(23358) = X(2917)-4*X(32401) = 3*X(3060)-4*X(11262) = 4*X(3574)-X(5895) = 3*X(5085)-2*X(32344) = X(5878)-4*X(8254) = 2*X(6247)+X(12254) = 2*X(7691)-5*X(8567) = X(9914)-3*X(32357) = 4*X(32351)-3*X(32395)

The reciprocal orthologic center of these triangles is X(389).

X(32345) lies on these lines: {2,20376}, {3,161}, {4,10117}, {20,32346}, {24,11704}, {25,32340}, {26,18379}, {40,12341}, {54,64}, {55,32350}, {56,32378}, {74,6799}, {125,2929}, {154,7503}, {185,32341}, {195,2935}, {221,32382}, {382,32365}, {389,19361}, {539,12301}, {578,6293}, {973,9786}, {1147,19376}, {1151,32384}, {1152,32385}, {1154,10606}, {1192,11576}, {1204,1205}, {1350,7691}, {1498,7526}, {1503,32354}, {1593,3574}, {2070,18383}, {2071,2888}, {2192,32383}, {2883,7527}, {3060,11262}, {3516,10619}, {3518,23324}, {3520,6247}, {3522,15578}, {5085,32344}, {5448,12412}, {5584,32370}, {5646,7509}, {5878,8254}, {5894,12086}, {5898,25564}, {6000,10274}, {6102,17835}, {6146,32322}, {6644,22804}, {6689,9818}, {7514,17821}, {7730,17823}, {7973,12266}, {9659,32390}, {9672,32336}, {9905,12262}, {9934,32137}, {10282,14926}, {10625,12307}, {11250,12118}, {11438,11808}, {11440,32338}, {11456,32349}, {11468,13423}, {11477,32368}, {11479,32396}, {11480,32397}, {11481,32398}, {11597,18439}, {11743,17810}, {12041,13368}, {13021,32386}, {13022,32387}, {13366,32392}, {13367,15139}, {14216,18570}, {14864,18364}, {14865,15311}, {15100,17847}, {15579,16010}, {15622,32347}, {17822,17846}, {18376,18378}, {18382,31304}, {18431,20424}, {18913,32334}, {18997,32342}, {18998,32343}, {19351,32373}, {19352,32374}, {19460,31978}, {22467,23332}, {23292,30100}, {26937,32316}

X(32345) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 32346}, {64, 17824}, {12254, 32337}
X(32345) = reflection of X(i) in X(j) for these (i,j): (3, 32401), (4, 32351), (382, 32365), (1498, 32379), (2917, 3), (9920, 23358), (11477, 32368), (17824, 54), (17845, 32330), (32337, 6247), (32340, 32393), (32379, 10610), (32402, 18381)
X(32345) = anticomplement of the anticomplement of X(20376)
X(32345) = X(21)-of-anti-Hutson-intouch-triangle if ABC is acute
X(32345) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 9920, 23358), (9920, 23358, 2917)


X(32346) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INVERSE-IN-INCIRCLE TO HATZIPOLAKIS-MOSES

Barycentrics    (4*R^2+SA-2*SW)*R^2*S^2+2*(2*R^2-SW)^2*SB*SC : :
X(32346) = 3*X(2)-4*X(32351) = 3*X(4)-4*X(32365) = 3*X(376)-4*X(32401) = 5*X(631)-4*X(23358) = 3*X(1992)-4*X(32368) = 5*X(3091)-6*X(32395) = 7*X(3523)-8*X(20376) = 5*X(3618)-4*X(32344) = 3*X(11206)-4*X(32379) = X(12325)-4*X(18381) = 3*X(32064)-2*X(32337)

The reciprocal orthologic center of these triangles is X(389).

X(32346) lies on these lines: {2,2917}, {4,54}, {5,9920}, {20,32345}, {69,1225}, {159,7566}, {195,31723}, {376,32401}, {388,32350}, {427,32333}, {497,32378}, {539,12318}, {631,23358}, {973,11433}, {1154,11411}, {1209,6643}, {1370,7691}, {1503,17824}, {1899,32334}, {1992,32368}, {2550,32370}, {3068,32384}, {3069,32385}, {3091,15582}, {3153,14516}, {3523,20376}, {3618,32344}, {5189,6247}, {6193,12319}, {6288,11487}, {6689,7401}, {6776,32341}, {6816,15435}, {7386,32348}, {7391,12324}, {7392,32396}, {7544,32391}, {7730,18912}, {8254,11818}, {10610,18420}, {10628,12284}, {11382,11576}, {11412,12325}, {11442,32338}, {11457,32339}, {11488,32397}, {11489,32398}, {13423,25739}, {14791,21230}, {18489,22804}, {19420,32386}, {19421,32387}

X(32346) = reflection of X(i) in X(j) for these (i,j): (20, 32345), (2888, 6145), (2917, 32351), (9833, 10274), (9920, 5), (32354, 54)
X(32346) = anticomplement of X(2917)
X(32346) = X(21)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(32346) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 12254, 18925), (2917, 32351, 2)


X(32347) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE TO HATZIPOLAKIS-MOSES

Barycentrics    a*(((5*R^2-2*SW)*(4*R^2-SW)*(b+c)*a-((8*R^2-3*SA-3*SW)*R^2+SA*SW)*b*c-(5*R^2-2*SW)*(4*R^2-SW)*(SB+SC))*S^2-(2*R^2-SW)*(8*R^2-3*SW)*SB*SC*b*c) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32347) lies on these lines: {3,32363}, {35,32356}, {55,6145}, {56,32394}, {100,32354}, {197,32357}, {1154,12328}, {1376,32380}, {3295,32331}, {5687,32371}, {10310,32330}, {10628,12334}, {11248,18400}, {11383,32332}, {11490,32335}, {11491,32337}, {11494,32362}, {11496,32369}, {11497,32373}, {11498,32374}, {11499,32379}, {11500,32381}, {11501,32382}, {11502,32383}, {11503,32388}, {11504,32389}, {11507,32403}, {11508,32404}, {11509,32336}, {11510,32406}, {11848,32372}, {11849,32402}, {13887,32399}, {13940,32400}, {15622,32345}, {18491,32364}, {18999,32342}, {19000,32343}

X(32347) = reflection of X(i) in X(j) for these (i,j): (32363, 3), (32380, 32391)
X(32347) = X(6145)-of-anti-Mandart-incircle-triangle


X(32348) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR TO HATZIPOLAKIS-MOSES

Barycentrics    2*a^10-4*(b^2+c^2)*a^8-(b^4+c^4)*a^6+(b^2+c^2)*(7*b^4-2*b^2*c^2+7*c^4)*a^4-(b^2-c^2)^2*(5*b^4+8*b^2*c^2+5*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3 : :
X(32348) = 3*X(2)+X(7691) = 3*X(3)+X(6288) = X(54)-5*X(631) = 5*X(54)-X(11271) = 3*X(54)+X(12325) = 3*X(140)-X(8254) = 7*X(140)-X(11803) = 4*X(140)-X(12242) = 5*X(140)-X(22051) = 15*X(631)+X(12325) = 3*X(1209)-X(6288) = 3*X(5892)-X(10115) = 3*X(6689)-2*X(8254) = 7*X(6689)-2*X(11803) = 5*X(6689)-2*X(22051) = X(7691)+2*X(32396) = 7*X(8254)-3*X(11803) = 4*X(8254)-3*X(12242) = 5*X(8254)-3*X(22051) = 3*X(11271)+5*X(12325) = 4*X(11803)-7*X(12242) = 5*X(11803)-7*X(22051) = 5*X(12242)-4*X(22051) = 3*X(13565)-2*X(20584) = X(18381)+3*X(23358)

The reciprocal orthologic center of these triangles is X(389).

X(32348) lies on these lines: {2,3574}, {3,161}, {5,32223}, {20,15431}, {24,24206}, {30,13565}, {54,69}, {140,389}, {141,32391}, {185,7495}, {195,5054}, {343,10112}, {394,32341}, {511,973}, {539,549}, {550,22804}, {569,11225}, {632,20424}, {1038,32350}, {1040,32378}, {1352,32337}, {1368,32351}, {1493,14869}, {1899,2888}, {3098,3541}, {3153,18428}, {3519,14528}, {3524,12254}, {3526,5646}, {3530,6699}, {3547,5878}, {3549,32364}, {3567,25555}, {3576,12785}, {3628,13566}, {3818,9715}, {3917,32352}, {5204,12946}, {5217,12956}, {5418,8995}, {5420,13986}, {5432,18984}, {5433,13079}, {5657,7979}, {5894,6823}, {5907,6676}, {5972,7542}, {6153,23336}, {6745,9940}, {7386,32346}, {7484,32333}, {7488,32332}, {7494,12324}, {7499,9729}, {7502,13419}, {7512,29012}, {7516,9932}, {7568,13754}, {7998,32338}, {7999,32339}, {9306,11487}, {9540,19096}, {9827,11808}, {10018,12300}, {10020,10170}, {10165,12266}, {10257,12363}, {10303,15801}, {10319,32370}, {10516,16195}, {11017,25338}, {11438,14542}, {11511,32368}, {11513,32384}, {11514,32385}, {11515,32397}, {11516,32398}, {11548,11745}, {11574,16196}, {11576,13348}, {11743,13598}, {12108,20585}, {12362,32393}, {13347,26937}, {13365,13391}, {13367,32377}, {13474,16618}, {13564,18488}, {13935,19095}, {14389,14531}, {14862,18435}, {15559,29317}, {15712,21357}, {16976,22581}, {17811,17824}, {17821,32359}, {18531,32365}, {19126,32344}, {19422,32386}, {19423,32387}, {21167,23300}

X(32348) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 1209}, {20, 32340}, {550, 22804}, {1216, 11802}, {2888, 10619}, {3574, 7691}, {10610, 21230}, {11808, 15644}, {13564, 18488}
X(32348) = reflection of X(i) in X(j) for these (i,j): (3574, 32396), (6689, 140), (12242, 6689), (13598, 11743), (15605, 21230)
X(32348) = anticomplement of X(32396)
X(32348) = complement of X(3574)
X(32348) = X(21)-of-6th-anti-Mixtilinear-triangle if ABC is acute
X(32348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3574, 32396), (2, 7691, 3574)


X(32349) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ORTHOCENTROIDAL TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((R^2*(11*R^2-18*SA-10*SW)+2*(3*SA+SW)*SW)*S^2-6*(3*R^2-SW)*((8*R^2-3*SA-3*SW)*R^2+SA^2-SB*SC)*SA) : :

The reciprocal orthologic center of these triangles is X(1986).

X(32349) lies on these lines: {6,3574}, {64,32401}, {195,18405}, {399,15091}, {1986,32325}, {2917,15068}, {3581,10628}, {6000,11597}, {10274,14805}, {11441,12226}, {11456,32345}, {11750,32359}, {15032,32351}


X(32350) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC TO HATZIPOLAKIS-MOSES

Barycentrics    a*((12*R^2-5*SW)*SB*SC*b*c-((4*R^2+SA-2*SW)*b*c-4*(5*R^2-2*SW)*(4*R^2-SW))*S^2) : :
X(32350) = X(7355)+2*X(13079)

The reciprocal orthologic center of these triangles is X(389).

X(32350) lies on these lines: {1,18400}, {12,32351}, {33,32340}, {34,3574}, {35,32401}, {36,23358}, {54,65}, {55,32345}, {56,2917}, {73,6145}, {221,17824}, {388,32346}, {539,19471}, {973,19366}, {999,9920}, {1038,32348}, {1060,1209}, {1154,7352}, {1398,32333}, {1425,32352}, {1428,32344}, {1469,18984}, {2067,32384}, {3468,4551}, {3585,32365}, {4296,7691}, {5432,20376}, {6284,10118}, {6286,10628}, {6288,18447}, {6502,32385}, {7051,32397}, {7355,13079}, {9630,32330}, {10082,26888}, {10535,32383}, {10895,32395}, {18915,32334}, {18970,19469}, {19349,32341}, {19367,32338}, {19368,32339}, {19369,32368}, {19370,32386}, {19371,32387}, {19372,32396}, {19373,32398}

X(32350) = reflection of X(32378) in X(1)
X(32350) = X(21)-of-anti-tangential-midarc-triangle if ABC is acute


X(32351) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-URSA MINOR TO HATZIPOLAKIS-MOSES

Barycentrics    (R^2*(24*R^2+SA-15*SW)+2*SW^2)*S^2+2*(2*R^2-SW)^2*SB*SC : :
X(32351) = 3*X(2)+X(32346) = X(4)-3*X(32395) = 5*X(1656)-X(9920) = 3*X(1853)+X(17824) = 3*X(1853)-X(32337) = 2*X(3574)+X(6247) = 2*X(8254)+X(18381) = 2*X(11804)+X(23315) = 2*X(20299)+X(20424) = 3*X(23324)-2*X(32369) = 3*X(23324)-4*X(32393) = X(32345)+3*X(32395)

The reciprocal orthologic center of these triangles is X(389).

X(32351) lies on these lines: {2,2917}, {3,20376}, {4,10117}, {5,5944}, {11,32378}, {12,32350}, {30,32365}, {52,11262}, {54,1594}, {125,6746}, {140,23358}, {141,1209}, {161,7569}, {185,427}, {195,15141}, {235,32340}, {394,2888}, {524,32368}, {539,23307}, {590,32384}, {615,32385}, {858,7691}, {973,13567}, {1147,10224}, {1154,12359}, {1216,14076}, {1368,32348}, {1498,5169}, {1503,5576}, {1656,9920}, {1853,7592}, {1899,32341}, {2072,6288}, {2883,32137}, {3549,18382}, {3589,32344}, {3925,32370}, {5094,32333}, {5133,16252}, {5965,23326}, {6102,10115}, {7577,12254}, {7730,26917}, {8254,10274}, {8550,12242}, {10066,32404}, {10082,32403}, {11743,15873}, {13160,32330}, {13406,18376}, {15032,32349}, {15311,15559}, {19095,32343}, {19096,32342}, {19176,32181}, {21243,31807}, {23291,32334}, {23293,32338}, {23294,32339}, {23298,32386}, {23299,32387}, {23302,32397}, {23303,32398}, {23328,23335}

X(32351) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32345}, {54, 6145}, {2917, 32346}, {10274, 18381}, {17824, 32337}, {32365, 32401}
X(32351) = reflection of X(i) in X(j) for these (i,j): (3, 20376), (52, 11262), (2883, 32364), (10274, 8254), (21230, 14076), (23358, 140), (32344, 3589), (32369, 32393), (32391, 6689)
X(32351) = complement of X(2917)
X(32351) = X(21)-of-anti-Ursa-minor-triangle if ABC is acute
X(32351) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 32346, 2917), (32345, 32395, 4)


X(32352) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-WASAT TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(S^2+SB*SC)*((3*R^2-SW)*S^2-(4*R^2-SW)*SA^2) : :
X(32352) = X(4)-3*X(7730) = 3*X(5)-4*X(13365) = 3*X(51)-4*X(973) = 3*X(51)-2*X(3574) = 9*X(51)-4*X(15739) = X(185)+2*X(6152) = X(195)-3*X(568) = 9*X(373)-8*X(32396) = 2*X(389)+X(6242) = 4*X(389)-X(21660) = 3*X(568)-2*X(10115) = 3*X(973)-X(15739) = 3*X(3574)-2*X(15739) = 3*X(5891)-4*X(13565) = 2*X(6242)+X(21660) = 3*X(7730)-2*X(11808) = 3*X(7730)+X(32339) = 2*X(11597)-3*X(16223) = 2*X(11808)+X(32339) = X(15801)-4*X(16625)

The reciprocal orthologic center of these triangles is X(389).

Let HAHBHC be as described in Anapolis #2471 (March 19, 2015, Antreas Hatzipolakis). X(32352) is the intersection of the Euler lines of the orthic triangle and HAHBHC. (Randy Hutson, June 7, 2019)

X(32352) lies on these lines: {2,32338}, {3,11802}, {4,7730}, {5,51}, {6,32333}, {24,10274}, {25,17824}, {30,32196}, {54,186}, {125,6746}, {184,2917}, {185,6152}, {195,568}, {373,32396}, {511,7691}, {539,14831}, {1181,9920}, {1204,1205}, {1425,32350}, {1495,32379}, {1594,14076}, {1843,32332}, {1899,32334}, {2888,5889}, {3270,32378}, {3292,15801}, {3567,14940}, {3611,32370}, {3917,32348}, {5446,18403}, {5462,22815}, {5890,12254}, {5946,8254}, {6101,15426}, {6102,11562}, {6145,11572}, {6153,6288}, {6243,11424}, {6403,32354}, {6467,8550}, {6689,12606}, {9729,12226}, {9730,10610}, {9786,12175}, {10018,12242}, {10296,13598}, {11262,13567}, {11381,11576}, {11550,32337}, {11561,14049}, {12162,22804}, {12280,32248}, {12380,15032}, {12897,18563}, {13382,13433}, {13451,25402}, {13568,21652}, {13851,32365}, {14449,16657}, {15060,20584}, {16227,22249}, {16881,22051}, {21637,32344}, {21639,32368}, {21640,32384}, {21641,32385}, {21642,32386}, {21643,32387}, {21647,32397}, {21648,32398}, {21663,32401}

X(32352) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32339}, {54, 6242}, {2888, 5889}, {6102, 13368}, {6243, 12307}, {12254, 13423}
X(32352) = reflection of X(i) in X(j) for these (i,j): (3, 11802), (4, 11808), (54, 389), (195, 10115), (3574, 973), (5562, 1209), (6288, 6153), (11381, 32340), (12162, 22804), (12606, 6689), (20424, 143), (21660, 54), (22051, 16881), (32340, 11576)
X(32352) = complement of X(32338)
X(32352) = X(21)-of-anti-Wasat-triangle if ABC is acute
X(32352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 7730, 11808), (7730, 32339, 4)


X(32353) = ORTHOLOGIC CENTER OF THESE TRIANGLES: antiAOA TO HATZIPOLAKIS-MOSES

Barycentrics    (96*R^6-21*R^4*(SA+3*SW)+R^2*SW*(10*SW+13*SA)-2*SA*SW^2)*S^2+(R^2*(72*R^4-104*R^2*SW+45*SW^2)-6*SW^3)*SB*SC : :

The reciprocal orthologic center of these triangles is X(10114)

X(32353) lies on these lines: {3,161}, {265,19402}, {1154,15133}, {5094,32355}, {6143,32391}, {7574,10628}, {10115,15134}, {10224,32379}, {11202,18432}, {15131,19381}

X(32353) = X(11604)-of-AAOA-triangle if ABC is acute


X(32354) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO HATZIPOLAKIS-MOSES

Barycentrics    S^4-(R^2*(12*R^2+3*SA-10*SW)-SA^2+SB*SC+2*SW^2)*S^2+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC : :
X(32354) = 3*X(2)-4*X(32391) = 3*X(4)-4*X(32364) = X(20)+2*X(32359) = 3*X(1853)-4*X(20376) = 5*X(3091)-4*X(32369) = 5*X(3616)-4*X(32331) = 2*X(9833)+X(12254) = 3*X(11202)-2*X(14076) = 2*X(32364)-3*X(32379)

The reciprocal orthologic center of these triangles is X(6146).

X(32354) lies on these lines: {2,6145}, {3,32337}, {4,54}, {5,32402}, {8,32371}, {10,32356}, {20,32330}, {22,32357}, {26,9920}, {69,7691}, {70,21844}, {100,32347}, {145,32394}, {146,1498}, {193,31304}, {195,31802}, {343,1601}, {388,32336}, {497,32383}, {973,7487}, {1154,6193}, {1270,32374}, {1271,32373}, {1503,32345}, {1853,20376}, {1993,17824}, {2892,11413}, {2896,32362}, {2975,32363}, {3085,32403}, {3086,32404}, {3091,32369}, {3434,32380}, {3436,32381}, {3549,6288}, {3575,32341}, {3616,32331}, {4240,32372}, {6403,32352}, {6462,32388}, {6463,32389}, {6995,11743}, {7564,8254}, {7585,32343}, {7586,32342}, {7787,32335}, {8972,32399}, {10528,32405}, {10529,32406}, {10628,11412}, {11202,14076}, {11271,14531}, {12363,18439}, {13941,32400}, {14216,32401}, {14389,32395}, {32334,32377}

X(32354) = midpoint of X(i) and X(j) for these lines: {i,j}: {17824, 17845}, {32330, 32359}
X(32354) = reflection of X(i) in X(j) for these (i,j): (4, 32379), (8, 32371), (20, 32330), (145, 32394), (2888, 2917), (4240, 32372), (6145, 32391), (14216, 32401), (32337, 3), (32346, 54), (32356, 10), (32402, 5)
X(32354) = anticomplementary conjugate of the anticomplement of X(7488)
X(32354) = anticomplement of X(6145)
X(32354) = X(6145)-of-anticomplementary-triangle
X(32354) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 3574, 11427), (6145, 32391, 2)


X(32355) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AOA TO HATZIPOLAKIS-MOSES

Barycentrics    (528*R^6+6*(7*SA-79*SW)*R^4-(19*SA-134*SW)*SW*R^2+2*(SA-6*SW)*SW^2)*S^2-(144*R^6-31*R^2*SW*(4*R^2-SW)-2*SW^3)*SB*SC : :

The reciprocal orthologic center of these triangles is X(10114).

X(32355) lies on these lines: {5,5944}, {1154,15115}, {5094,32353}, {5965,23296}, {10115,15120}, {10274,18281}, {10628,15122}, {11597,15116}

X(32355) = X(11604)-of-AOA-triangle if ABC is acute


X(32356) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AQUILA TO HATZIPOLAKIS-MOSES

Barycentrics
3*a^16-(b+c)*a^15-(9*b^2-2*b*c+9*c^2)*a^14+(b+c)*(3*b^2-2*b*c+3*c^2)*a^13+(5*b^4+5*c^4-(4*b-c)*(b-4*c)*b*c)*a^12-(b+c)*(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^11+(7*b^6+7*c^6-(2*b^4+2*c^4+(5*b^2-6*b*c+5*c^2)*b*c)*b*c)*a^10-(b+c)*(5*b^6+5*c^6-(2*b^4+2*c^4+3*(b-c)^2*b*c)*b*c)*a^9-(5*b^6+5*c^6+(2*b^4+2*c^4+7*(b+c)^2*b*c)*b*c)*(b-c)^2*a^8+(b^2-c^2)*(b-c)*(5*b^6+5*c^6+(2*b^2+b*c+c^2)*(b^2+b*c+2*c^2)*b*c)*a^7-(3*b^6+3*c^6+(2*b^2-b*c+2*c^2)*(b-c)^2*b*c)*(b^2-c^2)^2*a^6+(b^2-c^2)^2*(b+c)*(b^6+c^6+(2*b^2-b*c+c^2)*(b^2-b*c+2*c^2)*b*c)*a^5-(b^8+c^8+(4*b^6+4*c^6+(3*b^4+3*c^4+2*(b^2+6*b*c+c^2)*b*c)*b*c)*b*c)*(b^2-c^2)^2*a^4-(b^2-c^2)*(b-c)^2*(b^3+c^3)*(b^4-c^4)*(3*b^2+5*b*c+3*c^2)*a^3+(b^4-c^4)*(b^2-c^2)^3*(5*b^4+5*c^4+2*(b^2+b*c+c^2)*b*c)*a^2+(b^2-c^2)^5*(b-c)*(b^2+c^2)^2*a-2*(b^2+c^2)^2*(b^2-c^2)^6 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32356) lies on these lines: {1,6145}, {10,32354}, {35,32347}, {36,32363}, {40,12785}, {57,32336}, {165,32330}, {515,32337}, {517,32402}, {1154,9896}, {1697,32390}, {1698,32391}, {1699,32369}, {3099,32362}, {3679,32371}, {5587,32379}, {5588,32374}, {5589,32373}, {7713,32332}, {8185,32357}, {8188,32388}, {8189,32389}, {9578,32382}, {9581,32383}, {10628,12407}, {10789,32335}, {10826,32380}, {10827,32381}, {11852,32372}, {13888,32399}, {13942,32400}, {16473,17824}, {18492,32364}, {19003,32342}, {19004,32343}

X(32356) = reflection of X(i) in X(j) for these (i,j): (1, 6145), (32354, 10), (32394, 32331)
X(32356) = X(6145)-of-Aquilla-triangle
X(32356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6145, 32394, 32331), (32331, 32394, 1)


X(32357) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARA TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((2*R^2-SW)*R^2*S^2+(8*(4*R^2+SA-6*SW)*R^4-SW*((3*SA-19*SW)*R^2+2*SW^2))*SA) : :
X(32357) = X(9914)+2*X(32345)

The reciprocal orthologic center of these triangles is X(6146).

X(32357) lies on these lines: {3,32379}, {22,32354}, {24,32337}, {25,6145}, {64,13171}, {155,10628}, {159,2917}, {184,6293}, {197,32347}, {382,9919}, {1154,9908}, {1593,3574}, {1598,32369}, {2937,9833}, {3556,5693}, {5562,22658}, {5594,32374}, {5595,32373}, {7387,12293}, {7517,32402}, {8185,32356}, {8192,32394}, {8193,32371}, {8194,32388}, {8195,32389}, {9818,32364}, {10037,32403}, {10046,32404}, {10790,32335}, {10828,32362}, {10829,32380}, {10830,32381}, {10831,32382}, {10832,32383}, {10833,32390}, {10834,32405}, {10835,32406}, {11365,32331}, {11414,32330}, {11477,32262}, {11853,32372}, {13889,32399}, {13943,32400}, {14130,15311}, {18954,32336}, {19005,32342}, {19006,32343}, {22654,32363}

X(32357) = X(6145)-of-Ara-triangle


X(32358) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO ARIES

Barycentrics    (R^2-2*SA+SW)*S^2+(R^2-SW)*SB*SC : :
X(32358) = 3*X(5)-2*X(31831) = 2*X(140)-3*X(11245) = 4*X(143)-3*X(13490) = 3*X(568)-X(14516) = 3*X(568)-2*X(31830) = X(1216)-3*X(11232) = 2*X(5462)-3*X(11225) = 3*X(5889)+X(12289) = 3*X(6102)-2*X(13568) = 5*X(6146)-4*X(11565) = 3*X(6146)-2*X(13470) = 3*X(10112)-X(13403) = 3*X(11245)-4*X(32165) = 5*X(11264)-2*X(11565) = 3*X(11264)-X(13470) = 6*X(11565)-5*X(13470) = 3*X(12022)-X(18436) = 2*X(12134)-3*X(13490) = 3*X(12370)-2*X(13403) = 3*X(13292)-X(31831)

The reciprocal orthologic center of these triangles is X(32359).

Let A'B'C' be the reflection triangle. Let AB and AC be the orthogonal projections of A' on CA and AB, resp. Let A" = CAAC∩ABBA, and define B" and C" cyclically. Triangle A"B"C" is homothetic to ABC at X(6). X(32358) = X(5)-of-A"B"C". (Randy Hutson, March 29, 2020)

X(32358) lies on these lines: {5,6}, {26,6515}, {30,5889}, {49,3580}, {52,11819}, {54,140}, {69,7516}, {70,1993}, {143,12134}, {193,14790}, {195,1594}, {323,11271}, {343,7568}, {389,539}, {394,18952}, {427,18356}, {511,10116}, {524,6101}, {542,5446}, {550,10605}, {568,14516}, {1154,6146}, {1199,2888}, {1209,13366}, {1216,5965}, {1493,23292}, {1503,10263}, {1899,16266}, {1986,3575}, {1994,5576}, {3627,13142}, {3628,11422}, {3853,7728}, {5133,14627}, {5462,11225}, {5876,12241}, {6102,13568}, {6193,6644}, {6759,16619}, {7393,11898}, {7502,31804}, {7526,11411}, {7553,14449}, {7574,12316}, {8537,16198}, {8681,12585}, {9703,10018}, {10112,12370}, {10255,25740}, {10602,14791}, {11449,16531}, {11750,14531}, {12022,18436}, {12084,18917}, {12160,18569}, {12359,32166}, {13160,15087}, {13413,22051}, {15073,26926}, {15083,18390}, {15644,18128}, {15761,18445}, {15801,25739}, {17846,32326}, {18400,32392}, {19468,32322}, {22660,23323}

X(32358) = midpoint of X(6243) and X(34224)
X(32358) = midpoint of X(11750) and X(14531)
X(32358) = reflection of X(i) in X(j) for these (i,j): (5, 13292), (68, 22663), (140, 32165), (550, 18914), (3627, 13142), (5876, 12241), (6146, 11264), (7553, 14449), (11819, 52), (12134, 143), (12359, 32166), (12370, 10112), (14516, 31830), (15644, 18128)
X(32358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (49, 3580, 10020), (68, 12161, 5)


X(32359) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARIES TO HATZIPOLAKIS-MOSES

Barycentrics    3*S^4-(R^2*(16*R^2+9*SA-17*SW)-3*SA^2+3*SB*SC+4*SW^2)*S^2+(8*R^2*(R^2-2*SW)+5*SW^2)*SB*SC : :
X(32359) = 2*X(5)-3*X(32379) = 2*X(20)-3*X(32330) = X(20)-3*X(32354) = 3*X(154)-2*X(1209) = 5*X(631)-3*X(32337) = 5*X(631)-6*X(32391) = 3*X(1853)-4*X(6689) = X(2888)-3*X(11206) = 7*X(3832)-6*X(32369) = 5*X(3843)-6*X(32364) = 5*X(3843)-3*X(32402) = 7*X(9624)-6*X(32331) = 2*X(11362)-3*X(32371) = 2*X(15774)-3*X(32372) = 5*X(17821)-4*X(32348)

The reciprocal orthologic center of these triangles is X(32358).

X(32359) lies on these lines: {5,6145}, {20,32330}, {25,32377}, {54,1503}, {154,1209}, {159,2917}, {195,382}, {539,7387}, {548,15138}, {631,32337}, {973,9971}, {1154,6293}, {1593,10619}, {1619,9920}, {1853,6689}, {2888,11206}, {2937,3519}, {3574,11402}, {3832,32369}, {3843,32364}, {5596,11271}, {5965,9924}, {6152,9973}, {6278,32374}, {6281,32373}, {6288,6759}, {9624,32331}, {9657,32336}, {9670,32390}, {10535,12956}, {10610,14216}, {10628,23236}, {11362,32371}, {11576,31383}, {11750,32349}, {12234,13419}, {12242,17809}, {12254,15739}, {12946,26888}, {15774,32372}, {15888,32382}, {17821,32348}, {32332,32341}

X(32359) = reflection of X(i) in X(j) for these (i,j): (6145, 32379), (6288, 6759), (14216, 10610), (32330, 32354), (32337, 32391), (32402, 32364)


X(32360) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st AURIGA TO HATZIPOLAKIS-MOSES

Barycentrics    (2*a^16-(b+c)*a^15-2*(3*b^2-b*c+3*c^2)*a^14+(b+c)*(3*b^2-2*b*c+3*c^2)*a^13+(3*b^4+3*c^4-4*(b^2-3*b*c+c^2)*b*c)*a^12-(b+c)*(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^11+2*(3*b^6+3*c^6-(b^4+c^4+b*c*(2*b^2-3*b*c+2*c^2))*b*c)*a^10-(b+c)*(5*b^6+5*c^6-(2*b^4+2*c^4+3*b*c*(b-c)^2)*b*c)*a^9-(5*b^6+5*c^6+(2*b^4+2*c^4+5*b*c*(b+c)^2)*b*c)*(b-c)^2*a^8+(b^2-c^2)*(b-c)*(5*b^6+5*c^6+b*c*(2*b^2+b*c+c^2)*(b^2+b*c+2*c^2))*a^7-2*(b^2-c^2)^2*(b^6+c^6+b*c*(b^2-b*c+c^2)^2)*a^6+(b^2-c^2)^2*(b+c)*(b^6+c^6+b*c*(2*b^2-b*c+c^2)*(b^2-b*c+2*c^2))*a^5+(b^8+c^8-2*(b^2-b*c+c^2)*(2*b^4+2*c^4+b*c*(2*b^2+b*c+2*c^2))*b*c)*(b^2-c^2)^2*a^4-(b^2-c^2)*(b-c)^2*(b^3+c^3)*(b^4-c^4)*(3*b^2+5*b*c+3*c^2)*a^3+2*(b^3+c^3)*(b+c)*(b^2-c^2)^3*(b^4-c^4)*a^2+(b^2-c^2)^5*(b-c)*(b^2+c^2)^2*a-(b^2+c^2)^2*(b^2-c^2)^6)*D-4*S^2*(-a+b+c)*a^2*(-a^2+b^2+c^2)*(a^2+c^2-b^2)*(a^2-c^2+b^2)*(a^6-(b^2+c^2)*a^4-(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : : , where D=4*S*sqrt(R*(4*R+r))

The reciprocal orthologic center of these triangles is X(6146).

X(32360) lies on these lines: {}

X(32360) = X(6145)-of-1st-Auriga-triangle


X(32361) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd AURIGA TO HATZIPOLAKIS-MOSES

Barycentrics    (-2*a^16+(b+c)*a^15+2*(3*b^2-b*c+3*c^2)*a^14-(b+c)*(3*b^2-2*b*c+3*c^2)*a^13-(3*b^4+3*c^4-4*(b^2-3*b*c+c^2)*b*c)*a^12+(b+c)*(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^11-2*(3*b^6+3*c^6-(b^4+c^4+b*c*(2*b^2-3*b*c+2*c^2))*b*c)*a^10+(b+c)*(5*b^6+5*c^6-(2*b^4+2*c^4+3*b*c*(b-c)^2)*b*c)*a^9+(5*b^6+5*c^6+(2*b^4+2*c^4+5*b*c*(b+c)^2)*b*c)*(b-c)^2*a^8-(b^2-c^2)*(b-c)*(5*b^6+5*c^6+b*c*(2*b^2+b*c+c^2)*(b^2+b*c+2*c^2))*a^7+2*(b^2-c^2)^2*(b^6+c^6+b*c*(b^2-b*c+c^2)^2)*a^6-(b^2-c^2)^2*(b+c)*(b^6+c^6+b*c*(2*b^2-b*c+c^2)*(b^2-b*c+2*c^2))*a^5-(b^8+c^8-2*(b^2-b*c+c^2)*(2*b^4+2*c^4+b*c*(2*b^2+b*c+2*c^2))*b*c)*(b^2-c^2)^2*a^4+(b^2-c^2)*(b-c)^2*(b^3+c^3)*(b^4-c^4)*(3*b^2+5*b*c+3*c^2)*a^3-2*(b^3+c^3)*(b+c)*(b^2-c^2)^3*(b^4-c^4)*a^2-(b^2-c^2)^5*(b-c)*(b^2+c^2)^2*a+(b^2+c^2)^2*(b^2-c^2)^6)*D-4*S^2*(-a+b+c)*a^2*(-a^2+b^2+c^2)*(a^2+c^2-b^2)*(a^2-c^2+b^2)*(a^6-(b^2+c^2)*a^4-(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : : , where D=4*S*sqrt(R*(4*R+r))

The reciprocal orthologic center of these triangles is X(6146)

X(32361) lies on these lines: {}

X(32361) = X(6145)-of-2nd-Auriga-triangle


X(32362) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th BROCARD TO HATZIPOLAKIS-MOSES

Barycentrics    (3*R^2-SW)*(8*R^2-SA-3*SW)*S^4+(8*(7*SA^2-12*SA*SW+2*SW^2)*R^4-(40*SA^2-75*SA*SW+17*SW^2)*SW*R^2+(7*SA^2-14*SA*SW+4*SW^2)*SW^2)*S^2-3*(2*R^2-SW)*(8*R^2-3*SW)*SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32362) lies on these lines: {32,6145}, {1154,9923}, {2896,32354}, {3096,32391}, {3098,32330}, {3099,32356}, {9301,32402}, {9821,18400}, {9857,32371}, {9862,32337}, {9993,32369}, {9994,32373}, {9995,32374}, {9996,32379}, {9997,32394}, {10038,32403}, {10047,32404}, {10628,12501}, {10828,32357}, {10871,32380}, {10872,32381}, {10873,32382}, {10874,32383}, {10875,32388}, {10876,32389}, {10877,32390}, {10878,32405}, {10879,32406}, {11368,32331}, {11386,32332}, {11494,32347}, {11885,32372}, {13892,32399}, {13946,32400}, {18500,32364}, {18957,32336}, {19011,32342}, {19012,32343}, {22744,32363}

X(32362) = X(6145)-of-5th-Brocard-triangle


X(32363) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd CIRCUMPERP TANGENTIAL TO HATZIPOLAKIS-MOSES

Barycentrics    a*(a^18-(b+c)*a^17-2*(2*b^2-3*b*c+2*c^2)*a^16+4*(b^3+c^3)*a^15+(4*b^4+4*c^4-(18*b^2-17*b*c+18*c^2)*b*c)*a^14-(b+c)*(2*b^2-3*b*c+2*c^2)^2*a^13+(4*b^6+4*c^6+(8*b^4+8*c^4-19*(b-c)^2*b*c)*b*c)*a^12-(b+c)*(4*b^6+4*c^6+(4*b^4+4*c^4-(19*b^2-28*b*c+19*c^2)*b*c)*b*c)*a^11-2*(5*b^6+5*c^6-(b^4+c^4+2*(b-c)^2*b*c)*b*c)*(b-c)^2*a^10+2*(b^2-c^2)*(b-c)*(5*b^6+6*b^3*c^3+5*c^6)*a^9+2*(2*b^8+2*c^8-(6*b^6+6*c^6-(b^4+c^4-2*(b^2+5*b*c+c^2)*b*c)*b*c)*b*c)*(b-c)^2*a^8-2*(b^2-c^2)*(b-c)*(2*b^8+2*c^8-(6*b^6+6*c^6-(-4*b^2*c^2+(b^2-c^2)^2)*b*c)*b*c)*a^7+(b^2-c^2)^2*(b-c)^2*(4*b^6+4*c^6+(2*b^2-b*c+c^2)*(b^2-b*c+2*c^2)*b*c)*a^6-(b^2-c^2)^3*(b-c)*(4*b^6+4*c^6+(4*b^4+4*c^4+(b^2+10*b*c+c^2)*b*c)*b*c)*a^5-(b^2-c^2)^2*(4*b^10+4*c^10-(8*b^8+8*c^8-(15*b^6+15*c^6-(6*b^4+6*c^4-(5*b^2+12*b*c+5*c^2)*b*c)*b*c)*b*c)*b*c)*a^4+(b^4-c^4)*(b^2-c^2)^2*(b-c)^3*(4*b^4+4*c^4+(4*b^2+3*b*c+4*c^2)*b*c)*a^3+(b^4-c^4)*(b^2-c^2)^3*(b^6+c^6+(2*b^4+2*c^4+(7*b^2-4*b*c+7*c^2)*b*c)*b*c)*a^2-(b^2-c^2)^5*(b-c)^3*(b^2+c^2)^2*a-2*(b^2-c^2)^6*(b^2+c^2)^2*b*c) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32363) lies on these lines: {3,32347}, {36,32356}, {55,32394}, {56,6145}, {104,32337}, {956,32371}, {958,32381}, {999,32331}, {1154,22659}, {2917,23361}, {2975,32354}, {3428,32330}, {10628,19478}, {10966,32390}, {11249,18400}, {12114,32380}, {18761,32364}, {19013,32342}, {19014,32343}, {22479,32332}, {22520,32335}, {22654,32357}, {22744,32362}, {22753,32369}, {22755,32372}, {22756,32373}, {22757,32374}, {22758,32379}, {22759,32382}, {22760,32383}, {22761,32388}, {22762,32389}, {22763,32399}, {22764,32400}, {22765,32402}, {22766,32403}, {22767,32404}, {22768,32405}

X(32363) = reflection of X(i) in X(j) for these (i,j): (32347, 3), (32381, 32391)
X(32363) = X(6145)-of-2nd-circumperp-tangential-triangle


X(32364) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-MID TO HATZIPOLAKIS-MOSES

Barycentrics    S^4-(R^2*(12*R^2+3*SA-10*SW)-SA^2+SB*SC+2*SW^2)*S^2-(R^2*(44*R^2-25*SW)+3*SW^2)*SB*SC : :
X(32364) = 3*X(4)+X(32354) = X(1498)+3*X(32395) = 5*X(3091)-X(32337) = X(3357)-4*X(32396) = 5*X(3843)+X(32359) = 5*X(3843)-X(32402) = 2*X(5893)+X(10610) = 2*X(6689)+X(22802) = 5*X(18492)-X(32356) = X(32354)-3*X(32379)

The reciprocal orthologic center of these triangles is X(6146).

X(32364) lies on these lines: {4,54}, {26,5448}, {30,32391}, {113,1209}, {235,973}, {381,6145}, {382,32330}, {546,32369}, {1154,15761}, {1478,32383}, {1479,32382}, {1498,32395}, {1539,5893}, {1568,7488}, {1596,11743}, {2883,32137}, {2917,7517}, {3091,32337}, {3357,4846}, {3549,32348}, {3583,32390}, {3585,32336}, {3818,9977}, {3843,32359}, {5576,6000}, {6288,17824}, {6689,7526}, {7564,18128}, {7703,10574}, {9818,32357}, {9955,32331}, {10895,32403}, {10896,32404}, {11802,22800}, {11819,16252}, {12699,32371}, {13665,32343}, {13785,32342}, {14076,18504}, {15311,20376}, {18491,32347}, {18492,32356}, {18500,32362}, {18502,32335}, {18507,32372}, {18509,32373}, {18511,32374}, {18516,32380}, {18517,32381}, {18520,32388}, {18522,32389}, {18525,32394}, {18538,32399}, {18542,32405}, {18544,32406}, {18761,32363}, {18762,32400}, {20424,21850}

X(32364) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32379}, {382, 32330}, {2883, 32351}, {6288, 17824}, {6759, 32365}, {12699, 32371}, {18507, 32372}, {18525, 32394}, {22802, 32401}, {32359, 32402}
X(32364) = reflection of X(i) in X(j) for these (i,j): (18381, 32393), (32331, 9955), (32369, 546), (32401, 6689)
X(32364) = X(6145)-of-Ehrmann-mid-triangle


X(32365) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-VERTEX TO HATZIPOLAKIS-MOSES

Barycentrics    (4*R^2+SA-2*SW)*R^2*S^2+(68*R^4-47*R^2*SW+8*SW^2)*SB*SC : :
X(32365) = X(3)-3*X(32395) = 3*X(4)+X(32346) = 3*X(381)-X(2917) = 5*X(3843)-X(9920) = X(17824)+3*X(18405) = 3*X(18376)-2*X(32369) = 3*X(18405)-X(32402) = 3*X(23325)-4*X(32393)

The reciprocal orthologic center of these triangles is X(389).

X(32365) lies on these lines: {3,32395}, {4,54}, {5,18428}, {30,32351}, {52,265}, {381,2917}, {382,32345}, {539,18568}, {542,32368}, {550,20376}, {576,18382}, {973,18390}, {1154,9927}, {1209,18404}, {2888,18387}, {3153,7691}, {3357,31723}, {3583,32378}, {3585,32350}, {3627,11804}, {3818,22804}, {3843,9920}, {5449,18569}, {5907,6288}, {6102,11262}, {6564,32384}, {6565,32385}, {10113,32196}, {11204,14790}, {11576,18385}, {12370,20424}, {12893,13371}, {13851,32352}, {16808,32397}, {16809,32398}, {17824,18405}, {18386,32333}, {18392,32338}, {18394,32339}, {18396,32341}, {18406,32370}, {18414,32386}, {18415,32387}, {18420,32396}, {18531,32348}, {18567,19479}, {18572,21230}, {18918,32334}, {19130,32344}

X(32365) = midpoint of X(i) and X(j) for these lines: {i,j}: {382, 32345}, {17824, 32402}
X(32365) = reflection of X(i) in X(j) for these (i,j): (550, 20376), (6102, 11262), (6145, 18383), (6759, 32364), (7691, 14076), (10274, 3574), (23358, 5), (32344, 19130), (32401, 32351)
X(32365) = X(21)-of-Ehrmann-vertex-triangle if ABC is acute
X(32365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3574, 21659, 54), (18383, 31724, 19506)


X(32366) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO 1st EHRMANN

Barycentrics    a^2*((b^2+c^2)*a^4-6*b^2*c^2*a^2-(b^4-c^4)*(b^2-c^2)) : :
X(32366) = 5*X(6)-3*X(51) = 3*X(6)-X(1843) = 7*X(6)-3*X(9971) = 5*X(6)-X(9973) = 9*X(51)-5*X(1843) = 3*X(51)+5*X(6467) = 6*X(51)-5*X(9969) = 7*X(51)-5*X(9971) = 3*X(51)-X(9973) = 3*X(51)-10*X(22829) = 5*X(69)-9*X(7998) = X(69)+3*X(15531) = X(1843)+3*X(6467) = 2*X(1843)-3*X(9969) = 7*X(1843)-9*X(9971) = 5*X(1843)-3*X(9973) = X(1843)-6*X(22829) = 2*X(6467)+X(9969) = 7*X(6467)+3*X(9971) = 3*X(7998)+5*X(15531)

The reciprocal orthologic center of these triangles is X(32367).

X(32366) lies on these lines: {6,25}, {66,17040}, {69,3266}, {141,8681}, {157,5065}, {160,800}, {182,8548}, {193,3313}, {389,12007}, {511,550}, {524,6665}, {570,20975}, {597,9822}, {1216,5965}, {1503,13403}, {1511,5892}, {1992,12220}, {2386,15048}, {2854,3589}, {2929,13367}, {2979,11008}, {3003,20775}, {3564,11264}, {3618,12272}, {3631,3819}, {5097,5446}, {5140,5254}, {5181,26156}, {5421,23635}, {5943,6329}, {6146,15739}, {6241,6776}, {7668,14767}, {10574,27082}, {12235,32046}, {12283,14853}, {14778,23642}, {14912,15073}, {15126,23300}, {15140,32226}, {18583,18874}, {20583,21849}, {25320,32248}

X(32366) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 6467}, {193, 3313}, {1353, 15074}, {3629, 17710}, {15073, 19161}
X(32366) = reflection of X(i) in X(j) for these (i,j): (6, 22829), (389, 12007), (5446, 5097), (9969, 6), (14913, 3589), (21849, 20583)
X(32366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 159, 19136), (6, 19459, 206), (6467, 22829, 9969)


X(32367) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st EHRMANN TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(3*(2*R^2*(5*R^2-3*SW)+(SA+SW)*SW)*S^2-((16*R^2+9*SA-17*SW)*R^2-3*SA^2+3*SB*SC+4*SW^2)*SA*SW) : :
X(32367) = X(576)-3*X(10274) = X(9972)-3*X(32344) = 2*X(15579)-3*X(32401)

The reciprocal orthologic center of these triangles is X(32366).

X(32367) lies on these lines: {54,2393}, {159,3574}, {206,576}, {5965,9925}, {8542,32391}, {9970,32379}, {9972,32344}, {12584,23358}, {15579,32401}, {15581,18400}


X(32368) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd EHRMANN TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((6*R^2*(10*R^2-7*SW)+7*SW^2)*S^2-(2*R^2-SW)*(4*R^2+SA-2*SW)*SA*SW) : :
X(32368) = 3*X(6)-X(2917) = 3*X(1992)+X(32346) = 2*X(2917)-3*X(32344) = X(9920)-5*X(11482) = X(15069)-3*X(32395) = 3*X(17813)+X(17824) = 3*X(23049)-2*X(32369)

The reciprocal orthologic center of these triangles is X(389).

X(32368) lies on these lines: {6,24}, {68,5965}, {161,11422}, {511,32401}, {524,32351}, {539,9926}, {542,32365}, {575,23358}, {576,18400}, {895,6145}, {1154,8548}, {1209,8538}, {1992,32346}, {2393,32379}, {3574,8541}, {5486,12242}, {6288,18449}, {7691,11416}, {8539,32370}, {8540,32378}, {9813,32396}, {9920,11482}, {9976,10628}, {10602,32341}, {11405,32333}, {11443,32338}, {11458,32339}, {11470,32340}, {11477,32345}, {11511,32348}, {15069,32395}, {17813,17824}, {18919,32334}, {19369,32350}, {19426,32386}, {19427,32387}, {21639,32352}, {23049,32369}

X(32368) = midpoint of X(11477) and X(32345)
X(32368) = reflection of X(i) in X(j) for these (i,j): (23358, 575), (32344, 6)
X(32368) = X(21)-of-2nd-Ehrmann-triangle if ABC is acute


X(32369) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EULER TO HATZIPOLAKIS-MOSES

Barycentrics    S^4+(8*R^4-3*R^2*SA-3*R^2*SW+SA^2-SB*SC)*S^2+(56*R^4-40*R^2*SW+7*SW^2)*SB*SC : :
X(32369) = 3*X(4)+X(32337) = X(54)-3*X(32395) = 3*X(381)-X(32379) = 3*X(381)+X(32402) = 3*X(1699)+X(32356) = X(2917)+3*X(18405) = 5*X(3091)-X(32354) = 7*X(3832)-X(32359) = 3*X(5587)-X(32371) = 3*X(5603)-X(32394) = 3*X(11897)-X(32372) = 3*X(18376)-X(32365) = 2*X(18383)+X(22804) = 3*X(23049)-X(32368) = 3*X(23324)-X(32351) = 3*X(23324)-2*X(32393) = 3*X(23325)-X(32401)

The reciprocal orthologic center of these triangles is X(6146).

X(32369) lies on these lines: {2,32330}, {4,973}, {5,5944}, {11,32336}, {12,32390}, {24,11704}, {54,7547}, {98,32335}, {125,3575}, {235,32332}, {265,11262}, {371,32399}, {372,32400}, {381,32379}, {515,32331}, {546,32364}, {1154,9927}, {1209,12605}, {1352,6288}, {1478,32404}, {1479,32403}, {1587,32342}, {1588,32343}, {1598,32357}, {1658,23325}, {1699,32356}, {2917,7503}, {3091,32354}, {3574,12241}, {3832,32359}, {3861,27552}, {5446,10113}, {5587,32371}, {5603,32394}, {6152,15738}, {6201,32374}, {6202,32373}, {7542,20376}, {7569,17845}, {7691,18392}, {7706,13630}, {8212,32388}, {8213,32389}, {9993,32362}, {10531,32405}, {10532,32406}, {10893,32380}, {10894,32381}, {10895,32382}, {10896,32383}, {10982,17824}, {11496,32347}, {11897,32372}, {13565,23358}, {18386,32341}, {20191,23332}, {22753,32363}, {23049,32368}

X(32369) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 6145}, {32379, 32402}
X(32369) = reflection of X(i) in X(j) for these (i,j): (23358, 13565), (32351, 32393), (32364, 546), (32391, 5)
X(32369) = complement of X(32330)
X(32369) = X(6145)-of-Euler-triangle
X(32369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 32402, 32379), (23324, 32351, 32393)


X(32370) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EXTANGENTS TO HATZIPOLAKIS-MOSES

Barycentrics
a*(a^15+(b+c)*a^14-3*(b^2+c^2)*a^13-3*(b+c)*(b^2+c^2)*a^12+(b^2-b*c+c^2)^2*a^11+(b+c)*(b^2+b*c+c^2)^2*a^10+(5*b^4+5*c^4-3*(b-c)^2*b*c)*(b+c)^2*a^9+(b^2-c^2)*(b-c)*(5*b^4+5*c^4+3*(b+c)^2*b*c)*a^8-(b^2+c^2)*(5*b^4+5*c^4-2*(b^2+c^2)*b*c)*(b+c)^2*a^7-(b^4-c^4)*(b-c)*(5*b^4+5*c^4+2*(b^2+c^2)*b*c)*a^6-(b^4-c^4)*(b^2-c^2)*(b^4+c^4-2*(b^2+b*c+c^2)*b*c)*a^5-(b^4-c^4)*(b^2-c^2)*(b+c)*(b^4+c^4+2*(b^2-b*c+c^2)*b*c)*a^4+(b^2-c^2)^2*(b+c)^2*(3*b^6+3*c^6-2*(2*b^4+2*c^4-3*(b^2-b*c+c^2)*b*c)*b*c)*a^3+(b^2-c^2)^3*(b-c)*(3*b^6+3*c^6+2*(2*b^4+2*c^4+3*(b^2+b*c+c^2)*b*c)*b*c)*a^2-(b^3+c^3)*(b+c)*(b^2-c^2)^3*(b^4-c^4)*a-(b^3-c^3)*(b^2-c^2)^5*(b^2+c^2)) : :

The reciprocal orthologic center of these triangles is X(389).

X(32370) lies on these lines: {19,3574}, {40,12785}, {54,65}, {55,2917}, {71,6145}, {539,12417}, {973,11435}, {1154,6237}, {1209,8251}, {2550,32346}, {2888,9537}, {3101,7691}, {3197,17824}, {3611,32352}, {3925,32351}, {5415,32384}, {5416,32385}, {5584,32345}, {6288,18453}, {7688,32401}, {7724,10119}, {8274,9572}, {8539,32368}, {9816,32396}, {9920,10306}, {10319,32348}, {10536,32379}, {10636,32397}, {10637,32398}, {10901,12946}, {10902,23358}, {11406,32333}, {11445,32338}, {11460,32339}, {11471,32340}, {18406,32365}, {18921,32334}, {19133,32344}, {19350,32341}, {19432,32386}, {19433,32387}

X(32370) = reflection of X(32378) in X(2917)
X(32370) = X(21)-of-extangents-triangle if ABC is acute


X(32371) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GARCIA TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(2*R^2-3*SA-SW)*S^2+4*(5*R^2-2*SW)*(4*R^2-SW)*R*a*S-(SB+SC)*(2*R^2*(4*R^2-4*SA+SW)+3*SA^2-3*SB*SC-2*SW^2)*SA-2*(5*R^2-2*SW)*(4*R^2-SW)*(SB*b+SC*c)*a : :
X(32371) = 3*X(5587)-2*X(32369) = 3*X(5657)-X(32337) = 3*X(5790)-X(32402) = 2*X(11362)+X(32359)

The reciprocal orthologic center of these triangles is X(6146).

X(32371) lies on these lines: {1,32391}, {2,32331}, {8,32354}, {10,6145}, {54,65}, {72,32381}, {355,18400}, {515,32330}, {517,32379}, {519,32394}, {956,32363}, {1154,9928}, {1737,32404}, {1837,32390}, {3057,32383}, {3679,32356}, {3751,9905}, {5090,32332}, {5252,32336}, {5587,32369}, {5657,32337}, {5687,32347}, {5688,32374}, {5689,32373}, {5790,32402}, {7713,11743}, {8193,32357}, {8214,32388}, {8215,32389}, {9857,32362}, {10039,32403}, {10628,12778}, {10791,32335}, {10914,32380}, {10915,32405}, {10916,32406}, {11362,32359}, {11900,32372}, {12699,32364}, {13883,32343}, {13893,32399}, {13936,32342}, {13947,32400}

X(32371) = midpoint of X(8) and X(32354)
X(32371) = reflection of X(i) in X(j) for these (i,j): (1, 32391), (6145, 10), (12699, 32364)
X(32371) = anticomplement of X(32331)
X(32371) = X(6145)-of-outer-Garcia-triangle


X(32372) = ORTHOLOGIC CENTER OF THESE TRIANGLES: GOSSARD TO HATZIPOLAKIS-MOSES

Barycentrics
(S^2-3*SB*SC)*(S^4-(R^2*(10*R^2+3*SA-6*SW)-SA^2+SB*SC+SW^2)*S^2-16*(72*R^2+15*SA-98*SW)*R^6-2*(17*SA^2-107*SA*SW+378*SW^2)*R^4+(17*SA^2-59*SA*SW+153*SW^2)*SW*R^2-(2*SA^2-5*SA*SW+11*SW^2)*SW^2) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32372) lies on these lines: {30,32330}, {402,6145}, {1154,12418}, {1650,32391}, {4240,32354}, {10628,12790}, {11251,18400}, {11831,32331}, {11832,32332}, {11839,32335}, {11845,32337}, {11848,32347}, {11852,32356}, {11853,32357}, {11885,32362}, {11897,32369}, {11900,32371}, {11901,32373}, {11902,32374}, {11903,32380}, {11904,32381}, {11905,32382}, {11906,32383}, {11907,32388}, {11908,32389}, {11909,32390}, {11910,32394}, {11911,32402}, {11912,32403}, {11913,32404}, {11914,32405}, {11915,32406}, {13894,32399}, {13948,32400}, {15774,32359}, {18507,32364}, {18958,32336}, {19017,32342}, {19018,32343}, {22755,32363}

X(32372) = midpoint of X(4240) and X(32354)
X(32372) = reflection of X(i) in X(j) for these (i,j): (1650, 32391), (6145, 402), (18507, 32364)
X(32372) = X(6145)-of-Gossard-triangle


X(32373) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-GREBE TO HATZIPOLAKIS-MOSES

Barycentrics    (((8*R^2-3*SA-3*SW)*R^2+SA*SW)*S^2+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC)*S+2*(2*R^2-SW)*(3*S^4-(2*R^2*(5*SA-3*SW)-3*SA^2+3*SB*SC+2*SW^2)*S^2-(8*R^2-3*SW)*SB*SC*SW) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32373) lies on these lines: {6,3574}, {973,6218}, {1154,9929}, {1161,18400}, {1271,32354}, {2917,8903}, {5589,32356}, {5591,32391}, {5595,32357}, {5605,32394}, {5689,32371}, {6146,32327}, {6202,32369}, {6215,32379}, {6220,6293}, {6281,32359}, {8216,32388}, {8217,32389}, {8974,32399}, {9994,32362}, {10040,32403}, {10048,32404}, {10628,12803}, {10783,32337}, {10792,32335}, {10919,32380}, {10921,32381}, {10923,32382}, {10925,32383}, {10927,32390}, {10929,32405}, {10931,32406}, {11370,32331}, {11388,32332}, {11497,32347}, {11824,32330}, {11901,32372}, {11916,32402}, {13949,32400}, {18509,32364}, {18959,32336}, {19351,32345}, {22756,32363}

X(32373) = X(6145)-of-inner-Grebe-triangle


X(32374) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GREBE TO HATZIPOLAKIS-MOSES

Barycentrics    -(((8*R^2-3*SA-3*SW)*R^2+SA*SW)*S^2+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC)*S+2*(2*R^2-SW)*(3*S^4-(2*R^2*(5*SA-3*SW)-3*SA^2+3*SB*SC+2*SW^2)*S^2-(8*R^2-3*SW)*SB*SC*SW) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32374) lies on these lines: {6,3574}, {973,6217}, {1154,9930}, {1160,18400}, {1270,32354}, {2917,8904}, {5588,32356}, {5590,32391}, {5594,32357}, {5604,32394}, {5688,32371}, {6146,32328}, {6201,32369}, {6214,32379}, {6219,6293}, {6278,32359}, {8218,32388}, {8219,32389}, {8975,32399}, {9995,32362}, {10041,32403}, {10049,32404}, {10628,12804}, {10784,32337}, {10793,32335}, {10920,32380}, {10922,32381}, {10924,32382}, {10926,32383}, {10928,32390}, {10930,32405}, {10932,32406}, {11371,32331}, {11389,32332}, {11498,32347}, {11825,32330}, {11902,32372}, {11917,32402}, {13950,32400}, {18511,32364}, {18960,32336}, {19352,32345}, {22757,32363}

X(32374) = X(6145)-of-outer-Grebe-triangle


X(32375) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO 3rd HATZIPOLAKIS

Barycentrics    (2*R^4*(32*R^2-73*SA+39*SW)+(59*SA-38*SW)*R^2*SW-2*(3*SA-2*SW)*SW^2)*S^2+(16*R^2-3*SW)*(R^2*(16*R^2-13*SW)+2*SW^2)*SB*SC : :

The reciprocal orthologic center of these triangles is X(32376).

X(32375) lies on these lines: {6,17837}, {54,22533}, {3521,22979}, {9932,22962}, {19511,22834}

X(32375) = reflection of X(22466) in X(31985)


X(32376) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd HATZIPOLAKIS TO HATZIPOLAKIS-MOSES

Barycentrics    (64*R^6-2*(37*SA-3*SW)*R^4+(43*SA-22*SW)*SW*R^2-2*(3*SA-2*SW)*SW^2)*S^2+(8*R^2-3*SW)*(16*R^4-13*R^2*SW+2*SW^2)*SB*SC : :

The reciprocal orthologic center of these triangles is X(32375).

X(32376) lies on these lines: {6,3574}, {54,22533}, {368,20917}, {539,14076}, {13630,18128}

X(32376) = midpoint of X(i) and X(j) for these lines: {i,j}: {6145, 32412}, {32377, 32393}


X(32377) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HYACINTH TO HATZIPOLAKIS-MOSES

Barycentrics    SA*((12*R^2-SA-3*SW)*S^2+(SB+SC)*((8*R^2-3*SA-11*SW)*R^2+SA^2-SB*SC+3*SW^2)) : :
X(32377) = 3*X(973)-2*X(6756) = 4*X(6756)-3*X(32332) = 3*X(12022)-X(12300)

The reciprocal orthologic center of these triangles is X(32358).

X(32377) lies on these lines: {3,539}, {6,3574}, {25,32359}, {54,70}, {125,6689}, {184,1209}, {185,6152}, {542,13160}, {973,6756}, {974,18914}, {1154,6146}, {1181,6288}, {1493,13371}, {1503,11576}, {1594,12242}, {2888,6776}, {3088,32337}, {3542,32379}, {5965,6467}, {6243,10938}, {7691,19467}, {9827,12134}, {10112,12225}, {11271,18946}, {11416,15801}, {12022,12300}, {12234,18381}, {12254,18909}, {12315,32340}, {12946,19349}, {12956,19354}, {13367,32348}, {13431,14791}, {17818,17846}, {21230,31804}, {32334,32354}

X(32377) = reflection of X(i) in X(j) for these (i,j): (32332, 973), (32393, 32376)
X(32377) = {X(6145), X(32341)}-harmonic conjugate of X(3574)


X(32378) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INTANGENTS TO HATZIPOLAKIS-MOSES

Barycentrics    a*((4*R^2*(20*R^2-13*SW)+b*c*(4*R^2+SA-2*SW)+8*SW^2)*S^2-(12*R^2-5*SW)*SB*SC*b*c) : :
X(32378) = X(6285)+2*X(18984)

The reciprocal orthologic center of these triangles is X(389).

X(32378) lies on these lines: {1,18400}, {11,32351}, {33,3574}, {34,32340}, {35,23358}, {36,32401}, {54,6198}, {55,2917}, {56,32345}, {195,9642}, {497,32346}, {539,9931}, {973,11436}, {1040,32348}, {1062,1209}, {1154,6238}, {1250,32398}, {2066,32384}, {2192,17824}, {2330,32344}, {2888,9538}, {3056,13079}, {3057,7979}, {3100,7691}, {3270,32352}, {3295,9920}, {3583,32365}, {5414,32385}, {5433,20376}, {6145,9630}, {6285,18984}, {6288,18455}, {7071,32333}, {7354,19505}, {7356,7727}, {8540,32368}, {9577,9905}, {9627,12946}, {9641,12307}, {9817,32396}, {10066,10535}, {10149,22954}, {10638,32397}, {10896,32395}, {11446,32338}, {11461,32339}, {12428,12888}, {18922,32334}, {19354,32341}, {19434,32386}, {19435,32387}, {26888,32382}

X(32378) = reflection of X(i) in X(j) for these (i,j): (32350, 1), (32370, 2917)
X(32378) = X(21)-of-intangents-triangle if ABC is acute


X(32379) = ORTHOLOGIC CENTER OF THESE TRIANGLES: JOHNSON TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((2*R^2-3*SA-SW)*S^2-(2*(4*R^2-4*SA+SW)*R^2+3*SA^2-3*SB*SC-2*SW^2)*SA) : :
X(32379) = 2*X(5)+X(32359) = X(54)+2*X(6759) = 3*X(154)-X(2917) = 3*X(154)+X(17824) = 2*X(195)+X(9935) = X(195)+5*X(14530) = 3*X(381)-2*X(32369) = 3*X(381)-X(32402) = X(1498)+2*X(10610) = 2*X(3574)+X(9833) = 3*X(5587)-X(32356) = 3*X(5886)-2*X(32331) = X(6288)-4*X(16252) = 4*X(6689)-X(14216) = X(7691)-4*X(10282) = X(9920)-5*X(14530) = X(9934)+2*X(11597) = X(9935)-10*X(14530) = 3*X(11206)+X(32346) = X(32354)+2*X(32364)

The reciprocal orthologic center of these triangles is X(6146).

X(32379) lies on these lines: {1,32382}, {2,32337}, {3,32357}, {4,54}, {5,6145}, {11,32404}, {12,32403}, {23,15801}, {25,973}, {26,154}, {30,32330}, {110,5562}, {140,15139}, {159,195}, {161,12161}, {182,32396}, {206,1209}, {355,32380}, {381,32369}, {517,32371}, {569,32393}, {952,32394}, {1177,3519}, {1478,32336}, {1479,32390}, {1493,7530}, {1495,32352}, {1498,7526}, {1503,5576}, {1598,11743}, {1843,11808}, {2393,32368}, {2777,8718}, {2781,13564}, {2883,7728}, {2918,10117}, {3542,32377}, {5012,18381}, {5587,32356}, {5886,32331}, {5887,24301}, {6000,15062}, {6214,32374}, {6215,32373}, {6247,20376}, {6288,10024}, {6293,7502}, {6353,32334}, {6689,14216}, {7529,19153}, {7552,10203}, {7564,32046}, {7583,32343}, {7584,32342}, {8220,32388}, {8221,32389}, {8976,32399}, {9306,11487}, {9544,31304}, {9652,13079}, {9667,18984}, {9707,12300}, {9970,32367}, {9996,32362}, {10066,10535}, {10082,26888}, {10192,18350}, {10224,32353}, {10533,32384}, {10534,32385}, {10536,32370}, {10627,17847}, {10796,32335}, {10942,32405}, {10943,32406}, {11262,15087}, {11499,32347}, {11585,15462}, {11819,20424}, {12363,19149}, {13434,18383}, {13951,32400}, {15132,15331}, {15647,22815}, {15739,26864}, {18374,21841}, {21230,31831}, {22758,32363}, {26881,32338}, {26882,32339}, {30402,32397}, {30403,32398}

X(32379) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32354}, {195, 9920}, {1498, 32345}, {2917, 17824}, {6145, 32359}, {6759, 10274}, {32380, 32381}
X(32379) = reflection of X(i) in X(j) for these (i,j): (3, 32391), (4, 32364), (54, 10274), (6145, 5), (6247, 20376), (7691, 23358), (9935, 9920), (23358, 10282), (32344, 206), (32345, 10610), (32402, 32369)
X(32379) = complement of X(32337)
X(32379) = X(6145)-of-Johnson-triangle
X(32379) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (184, 3574, 54), (184, 6759, 9833), (32382, 32383, 1)


X(32380) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-JOHNSON TO HATZIPOLAKIS-MOSES

Barycentrics
a*(a^18-(b+c)*a^17-(5*b^2-6*b*c+5*c^2)*a^16+(b+c)*(5*b^2-4*b*c+5*c^2)*a^15+(9*b^4+9*c^4-(20*b^2-19*b*c+20*c^2)*b*c)*a^14-(b+c)*(9*b^4+9*c^4-(14*b^2-19*b*c+14*c^2)*b*c)*a^13-(5*b^6+5*c^6-(16*b^4+16*c^4-(21*b^2-38*b*c+21*c^2)*b*c)*b*c)*a^12+(b^2-c^2)*(b-c)*(5*b^4+5*c^4-2*(b^2-6*b*c+c^2)*b*c)*a^11-(5*b^6+5*c^6-2*(b^4+c^4+3*(b^2+c^2)*b*c)*b*c)*(b-c)^2*a^10+(b^2-c^2)*(b-c)*(5*b^6+5*c^6-2*(b-c)^2*b^2*c^2)*a^9+(b^2+c^2)*(9*b^6+9*c^6-(2*b^4+2*c^4+5*(b^2+c^2)*b*c)*b*c)*(b-c)^2*a^8-(b^2-c^2)*(b-c)*(9*b^8+9*c^8-2*(b^2-b*c+c^2)*(b^4+c^4-(b^2+3*b*c+c^2)*b*c)*b*c)*a^7-(b^2-c^2)^2*(5*b^8+5*c^8-(4*b^6+4*c^6-(13*b^4+13*c^4-4*(4*b^2-5*b*c+4*c^2)*b*c)*b*c)*b*c)*a^6+(b^3+c^3)*(b^2-c^2)^2*(5*b^6+5*c^6-(b^4+c^4-(7*b^2-6*b*c+7*c^2)*b*c)*b*c)*a^5+(b^2-c^2)^2*(b+c)^2*(b^8+c^8-2*(b^2+3*b*c+c^2)*(b^2-b*c+c^2)^2*b*c)*a^4-(b^4-c^4)*(b^2-c^2)^2*(b-c)*(b^6+c^6+(6*b^4+6*c^4+(5*b^2+4*b*c+5*c^2)*b*c)*b*c)*a^3+(b^4-c^4)*(b^2-c^2)^3*(4*b^4+4*c^4+(3*b^2+2*b*c+3*c^2)*b*c)*b*c*a^2+(b^2-c^2)^5*(b-c)*(b^2+c^2)*(2*b^2+b*c+2*c^2)*b*c*a-2*(b^2-c^2)^6*(b^2+c^2)^2*b*c) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32380) lies on these lines: {11,6145}, {12,32405}, {355,32379}, {1154,12422}, {1376,32347}, {3434,32354}, {10523,32403}, {10525,18400}, {10628,12889}, {10785,32337}, {10794,32335}, {10826,32356}, {10829,32357}, {10871,32362}, {10893,32369}, {10914,32371}, {10919,32373}, {10920,32374}, {10944,32382}, {10945,32388}, {10946,32389}, {10947,32390}, {10948,32404}, {10949,32406}, {11373,32331}, {11390,32332}, {11826,32330}, {11903,32372}, {11928,32402}, {12114,32363}, {13895,32399}, {13952,32400}, {18516,32364}, {18961,32336}, {19023,32342}, {19024,32343}

X(32380) = reflection of X(i) in X(j) for these (i,j): (32347, 32391), (32381, 32379)
X(32380) = X(6145)-of-inner-Johnson-triangle


X(32381) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-JOHNSON TO HATZIPOLAKIS-MOSES

Barycentrics
a*(a^18-(b+c)*a^17-(5*b^2+2*b*c+5*c^2)*a^16+5*(b+c)*(b^2+c^2)*a^15+(9*b^4+9*c^4+(4*b^2+11*b*c+4*c^2)*b*c)*a^14-(b^3+c^3)*(9*b^2+7*b*c+9*c^2)*a^13-(5*b^6+5*c^6-(4*b^4+4*c^4-5*(b+c)^2*b*c)*b*c)*a^12+(b+c)*(5*b^2-8*b*c+5*c^2)*(b^4+c^4)*a^11-(5*b^6+5*c^6+2*(b^4+c^4-(7*b^2-10*b*c+7*c^2)*b*c)*b*c)*(b+c)^2*a^10+(5*b^6+5*c^6-2*(5*b^2-8*b*c+5*c^2)*b^2*c^2)*(b+c)^3*a^9+3*(b^2-c^2)^2*(3*b^6+3*c^6+(b^2+4*b*c+c^2)*b^2*c^2)*a^8-(b^2-c^2)^2*(b+c)*(9*b^6+9*c^6+(3*b^2+8*b*c+3*c^2)*b^2*c^2)*a^7-(b^2-c^2)^2*(5*b^8+5*c^8-(4*b^2-7*b*c+4*c^2)*(3*b^4+3*c^4+4*(b^2+b*c+c^2)*b*c)*b*c)*a^6+(b^2-c^2)^2*(b+c)*(5*b^8+5*c^8-(2*b^2-b*c+2*c^2)*(5*b^4-4*b^2*c^2+5*c^4)*b*c)*a^5+(b^10+c^10-(b^2-b*c+c^2)*(4*b^6+4*c^6-(7*b^4+7*c^4+3*(3*b^2+2*b*c+3*c^2)*b*c)*b*c)*b*c)*(b^2-c^2)^2*a^4-(b^4-c^4)*(b^2-c^2)^2*(b-c)*(b^6+c^6-3*(2*b^4+2*c^4+(b^2+c^2)*b*c)*b*c)*a^3-(b^4-c^4)*(b^2-c^2)^3*(4*b^4+4*c^4+(5*b^2-2*b*c+5*c^2)*b*c)*b*c*a^2-(b^2-c^2)^5*(b-c)*(b^2+c^2)*(2*b^2-b*c+2*c^2)*b*c*a+2*(b^2-c^2)^6*(b^2+c^2)^2*b*c) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32381) lies on these lines: {11,32406}, {12,6145}, {54,15232}, {72,32371}, {355,32379}, {958,32363}, {1154,12423}, {3436,32354}, {10523,32404}, {10526,18400}, {10628,12890}, {10786,32337}, {10795,32335}, {10827,32356}, {10830,32357}, {10872,32362}, {10894,32369}, {10921,32373}, {10922,32374}, {10950,32383}, {10951,32388}, {10952,32389}, {10953,32390}, {10954,32403}, {10955,32405}, {11374,32331}, {11391,32332}, {11500,32347}, {11827,32330}, {11904,32372}, {11929,32402}, {13896,32399}, {13953,32400}, {18517,32364}, {18962,32336}, {19025,32342}, {19026,32343}

X(32381) = reflection of X(i) in X(j) for these (i,j): (32363, 32391), (32380, 32379)
X(32381) = X(6145)-of-outer-Johnson-triangle


X(32382) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JOHNSON-YFF TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(-2*(5*R^2-2*SW)*(4*R^2-SW)*b*c+2*(4*R^2*SA-S^2-4*SA^2+SA*SW)*R^2+SW*(S^2+3*SA^2-2*SA*SW)) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32382) lies on these lines: {1,32379}, {4,32390}, {5,32404}, {12,6145}, {54,65}, {56,32391}, {221,32345}, {388,32336}, {495,32403}, {973,11398}, {1154,3157}, {1478,10066}, {1479,32364}, {2917,18984}, {3085,32337}, {3574,11393}, {7354,32330}, {9578,32356}, {9654,32402}, {10082,10274}, {10088,10628}, {10797,32335}, {10831,32357}, {10873,32362}, {10895,32369}, {10923,32373}, {10924,32374}, {10944,32380}, {10956,32405}, {10957,32406}, {11375,32331}, {11392,32332}, {11501,32347}, {11905,32372}, {11930,32388}, {11931,32389}, {13079,17824}, {13897,32399}, {13954,32400}, {15888,32359}, {19027,32342}, {19028,32343}, {22759,32363}, {26888,32378}

X(32382) = reflection of X(32403) in X(495)
X(32382) = X(6145)-of-1st-Johnson-Yff-triangle
X(32382) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32379, 32383), (388, 32354, 32336)


X(32383) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd JOHNSON-YFF TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(2*(5*R^2-2*SW)*(4*R^2-SW)*b*c+2*(4*R^2*SA-S^2-4*SA^2+SA*SW)*R^2+SW*(S^2+3*SA^2-2*SA*SW)) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32383) lies on these lines: {1,32379}, {4,32336}, {5,32403}, {11,6145}, {54,6198}, {55,32391}, {496,32404}, {497,32354}, {973,11399}, {1069,1154}, {1478,32364}, {1479,10082}, {2192,32345}, {2917,13079}, {3057,32371}, {3086,32337}, {3574,11392}, {6284,32330}, {9581,32356}, {9669,32402}, {10066,10274}, {10091,10628}, {10535,32350}, {10798,32335}, {10832,32357}, {10874,32362}, {10896,32369}, {10925,32373}, {10926,32374}, {10950,32381}, {10958,32405}, {10959,32406}, {11376,32331}, {11393,32332}, {11502,32347}, {11906,32372}, {11932,32388}, {11933,32389}, {13898,32399}, {13955,32400}, {17824,18984}, {19029,32342}, {19030,32343}, {22760,32363}

X(32383) = reflection of X(32404) in X(496)
X(32383) = X(6145)-of-2nd-Johnson-Yff-triangle
X(32383) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32379, 32382), (497, 32354, 32390)


X(32384) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU DIAGONALS TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((3*R^2-SW)*S^2+(5*R^2-2*SW)*(4*R^2-SW)*S+(2*R^2-SW)*(4*R^2+SA-2*SW)*SA) : :

The reciprocal orthologic center of these triangles is X(389).

X(32384) lies on these lines: {6,24}, {371,18400}, {372,23358}, {539,12424}, {590,32351}, {1151,32345}, {1154,10665}, {1209,10897}, {2066,32378}, {2067,32350}, {3068,32346}, {3311,9920}, {3574,5412}, {5410,32333}, {5415,32370}, {6145,6413}, {6200,32401}, {6288,18457}, {6564,32365}, {7691,11417}, {10274,12971}, {10533,32379}, {10628,12375}, {10961,32396}, {11447,32338}, {11462,32339}, {11473,32340}, {11513,32348}, {17819,17824}, {18923,32334}, {19355,32341}, {19436,32386}, {19438,32387}, {21640,32352}

X(32384) = X(21)-of-1st-Kenmotu-diagonals-triangle if ABC is acute
X(32384) = {X(6), X(2917)}-harmonic conjugate of X(32385)


X(32385) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU DIAGONALS TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((3*R^2-SW)*S^2-(5*R^2-2*SW)*(4*R^2-SW)*S+(2*R^2-SW)*(4*R^2+SA-2*SW)*SA) : :

The reciprocal orthologic center of these triangles is X(389).

X(32385) lies on these lines: {6,24}, {371,23358}, {372,18400}, {539,12425}, {615,32351}, {1152,32345}, {1154,10666}, {1209,10898}, {3069,32346}, {3312,9920}, {3574,5413}, {5411,32333}, {5414,32378}, {5416,32370}, {6145,6414}, {6288,18459}, {6396,32401}, {6502,32350}, {6565,32365}, {7691,11418}, {10274,12965}, {10534,32379}, {10628,12376}, {10963,32396}, {11448,32338}, {11463,32339}, {11474,32340}, {11514,32348}, {17820,17824}, {18924,32334}, {19356,32341}, {19437,32387}, {19439,32386}, {21641,32352}

X(32385) = X(21)-of-2nd-Kenmotu-diagonals-triangle if ABC is acute
X(32385) = {X(6), X(2917)}-harmonic conjugate of X(32384)


X(32386) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS ANTIPODAL TANGENTIAL TO HATZIPOLAKIS-MOSES

Barycentrics
(SB+SC)*(4*S^4-(R^2*(20*R^2+10*SA-11*SW)-4*SA^2+4*SB*SC+SW^2)*S^2-(2*(2*R^2-SA-SW)*S^2-2*(R^2*(8*R^2-3*SA-8*SW)+SA^2-SB*SC+2*SW^2)*SA)*S+(2*R^2-SW)*(4*R^2+SA-2*SW)*SA*SW) : :

The reciprocal orthologic center of these triangles is X(389).

X(32386) lies on these lines: {54,19186}, {539,19486}, {973,19410}, {1154,18939}, {1209,19428}, {2917,8939}, {3574,19446}, {6288,18462}, {7691,19406}, {9723,32387}, {9920,19418}, {10628,19484}, {12590,12998}, {13021,32345}, {17824,19430}, {18400,18980}, {18414,32365}, {18926,32334}, {19134,32344}, {19358,32341}, {19370,32350}, {19404,32333}, {19412,32338}, {19414,32339}, {19416,32340}, {19420,32346}, {19422,32348}, {19426,32368}, {19432,32370}, {19434,32378}, {19436,32384}, {19439,32385}, {19440,23358}, {19448,32396}, {19450,32397}, {19452,32398}, {19454,32401}, {21642,32352}, {23298,32351}

X(32386) = X(21)-of-Lucas-antipodal-tangents-triangle if ABC is acute


X(32387) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) ANTIPODAL TANGENTIAL TO HATZIPOLAKIS-MOSES

Barycentrics
(SB+SC)*(4*S^4-(R^2*(20*R^2+10*SA-11*SW)-4*SA^2+4*SB*SC+SW^2)*S^2+(2*(2*R^2-SA-SW)*S^2-2*(R^2*(8*R^2-3*SA-8*SW)+SA^2-SB*SC+2*SW^2)*SA)*S+(2*R^2-SW)*(4*R^2+SA-2*SW)*SA*SW) : :

The reciprocal orthologic center of these triangles is X(389).

X(32387) lies on these lines: {54,19187}, {539,19487}, {973,19411}, {1154,18940}, {1209,19429}, {2917,8943}, {3574,19447}, {6288,18463}, {7691,19407}, {9723,32386}, {9920,19419}, {10628,19485}, {12591,12999}, {13022,32345}, {17824,19431}, {18400,18981}, {18415,32365}, {18927,32334}, {19135,32344}, {19359,32341}, {19371,32350}, {19405,32333}, {19413,32338}, {19415,32339}, {19417,32340}, {19421,32346}, {19423,32348}, {19427,32368}, {19433,32370}, {19435,32378}, {19437,32385}, {19438,32384}, {19441,23358}, {19449,32396}, {19451,32397}, {19453,32398}, {19455,32401}, {21643,32352}, {23299,32351}

X(32387) = X(21)-of-Lucas(-1)-antipodal-tangents-triangle if ABC is acute


X(32388) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS HOMOTHETIC TO HATZIPOLAKIS-MOSES

Barycentrics
(8*(5*SA^2-4*SW^2)*R^4-(SA+SW)*(26*SA-23*SW)*R^2*SW+(4*SA^2+SA*SW-4*SW^2)*SW^2)*S^2+(-2*(48*R^6-4*(2*SA+5*SW)*R^4+(9*SA-5*SW)*SW*R^2-2*(SA-SW)*SW^2)*S^2+8*(2*R^2-SW)*(8*R^2-3*SW)*R^2*SB*SC)*S+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32388) lies on these lines: {493,6145}, {1154,12426}, {6461,32389}, {6462,32354}, {8188,32356}, {8194,32357}, {8210,32394}, {8212,32369}, {8214,32371}, {8216,32373}, {8218,32374}, {8220,32379}, {8222,32391}, {10628,12894}, {10669,18400}, {10875,32362}, {10945,32380}, {10951,32381}, {11377,32331}, {11394,32332}, {11503,32347}, {11828,32330}, {11840,32335}, {11846,32337}, {11907,32372}, {11930,32382}, {11932,32383}, {11947,32390}, {11949,32402}, {11951,32403}, {11953,32404}, {11955,32405}, {11957,32406}, {13899,32399}, {13956,32400}, {18520,32364}, {18963,32336}, {19031,32342}, {19032,32343}, {22761,32363}

X(32388) = X(6145)-of-Lucas-homothetic-triangle


X(32389) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) HOMOTHETIC TO HATZIPOLAKIS-MOSES

Barycentrics
(8*(5*SA^2-4*SW^2)*R^4-(SA+SW)*(26*SA-23*SW)*R^2*SW+(4*SA^2+SA*SW-4*SW^2)*SW^2)*S^2-(-2*(48*R^6-4*(2*SA+5*SW)*R^4+(9*SA-5*SW)*SW*R^2-2*(SA-SW)*SW^2)*S^2+8*(2*R^2-SW)*(8*R^2-3*SW)*R^2*SB*SC)*S+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC*SW^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32389) lies on these lines: {494,6145}, {1154,12427}, {6461,32388}, {6463,32354}, {8189,32356}, {8195,32357}, {8211,32394}, {8213,32369}, {8215,32371}, {8217,32373}, {8219,32374}, {8221,32379}, {8223,32391}, {10628,12895}, {10673,18400}, {10876,32362}, {10946,32380}, {10952,32381}, {11378,32331}, {11395,32332}, {11504,32347}, {11829,32330}, {11841,32335}, {11847,32337}, {11908,32372}, {11931,32382}, {11933,32383}, {11948,32390}, {11950,32402}, {11952,32403}, {11954,32404}, {11956,32405}, {11958,32406}, {13900,32399}, {13957,32400}, {18522,32364}, {18964,32336}, {19033,32342}, {19034,32343}, {22762,32363}

X(32389) = X(6145)-of-Lucas(-1)-homothetic-triangle


X(32390) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MANDART-INCIRCLE TO HATZIPOLAKIS-MOSES

Barycentrics    (3*R^2-SW)*(8*R^2-SA-3*SW)*S^2-(SB+SC)*((5*R^2-2*SW)*(4*R^2-SW)*b*c+(12*R^2-5*SW)*(3*R^2-SW)*SA) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32390) lies on these lines: {1,18400}, {3,32404}, {4,32382}, {11,32391}, {12,32369}, {33,32332}, {55,6145}, {56,32330}, {497,32354}, {1154,12428}, {1479,32379}, {1697,32356}, {1837,32371}, {1858,6152}, {2098,32394}, {2646,32331}, {2917,9672}, {3295,32402}, {3574,11429}, {3583,32364}, {4294,32337}, {9659,32345}, {9670,32359}, {10628,12896}, {10799,32335}, {10833,32357}, {10877,32362}, {10927,32373}, {10928,32374}, {10947,32380}, {10953,32381}, {10965,32405}, {10966,32363}, {11909,32372}, {11947,32388}, {11948,32389}, {13901,32399}, {13958,32400}, {19037,32342}, {19038,32343}

X(32390) = reflection of X(32336) in X(1)
X(32390) = X(6145)-of-Mandart-incircle-triangle
X(32390) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 32354, 32383), (3295, 32402, 32403)


X(32391) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO HATZIPOLAKIS-MOSES

Barycentrics    a^2*(a^8-2*(b^2+c^2)*a^6+b^2*c^2*a^4+2*(b^6+c^6)*a^2-(b^6-c^6)*(b^2-c^2))*(2*a^6-3*(b^2+c^2)*a^4+(b^4-c^4)*(b^2-c^2)) : :
X(32391) = 3*X(2)+X(32354) = X(54)+5*X(17821) = 5*X(54)+X(17846) = 3*X(154)+X(32345) = 5*X(631)-X(32337) = 5*X(631)+X(32359) = 5*X(1656)-X(32402) = 5*X(1698)-X(32356) = X(2917)-5*X(17821) = 5*X(2917)-X(17846) = 3*X(10182)-X(14076) = X(10274)+3*X(11202) = 2*X(10282)+X(10610) = 3*X(11202)-X(23358) = X(17845)+3*X(32395) = 3*X(23041)-X(32344)

The reciprocal orthologic center of these triangles is X(6146).

X(32391) lies on these lines: {1,32371}, {2,6145}, {3,32357}, {4,32330}, {5,5944}, {6,24}, {8,32394}, {11,32390}, {12,32336}, {25,11743}, {30,32364}, {55,32383}, {56,32382}, {64,15080}, {83,32335}, {113,12605}, {141,32348}, {154,7503}, {389,15872}, {394,7691}, {427,32332}, {468,10619}, {498,32403}, {499,32404}, {590,32399}, {615,32400}, {631,32337}, {942,12266}, {958,32363}, {1125,32331}, {1147,1154}, {1209,7542}, {1216,1511}, {1376,32347}, {1493,7575}, {1495,23047}, {1503,20376}, {1650,32372}, {1656,32402}, {1698,32356}, {2781,7512}, {3068,32343}, {3069,32342}, {3096,32362}, {3515,32341}, {3574,3575}, {4550,6759}, {5552,32405}, {5590,32374}, {5591,32373}, {6143,32353}, {6288,6639}, {6696,22352}, {6750,8146}, {7505,12254}, {7506,9920}, {7544,32346}, {7547,26882}, {8222,32388}, {8223,32389}, {8254,31830}, {8542,32367}, {10182,14076}, {10527,32406}, {11597,12606}, {15116,16196}, {16195,19153}, {17845,32395}, {22249,27552}

X(32391) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 32371}, {3, 32379}, {4, 32330}, {8, 32394}, {54, 2917}, {1650, 32372}, {6145, 32354}, {6759, 32401}, {7691, 17824}, {10274, 23358}, {32337, 32359}, {32347, 32380}, {32363, 32381}
X(32391) = reflection of X(i) in X(j) for these (i,j): (32331, 1125), (32351, 6689), (32369, 5), (32393, 32396)
X(32391) = complement of X(6145)
X(32391) = complementary conjugate of X(1594)
X(32391) = X(6145)-of-medial-triangle
X(32391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 32354, 6145), (6689, 18475, 10610)


X(32392) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO MIDHEIGHT

Barycentrics    (SB+SC)*(2*R^2*S^2+(8*R^2-3*SW)*(8*R^2-SA-SW)*SA) : :
X(32392) = X(64)-3*X(185) = X(64)+3*X(6293) = 5*X(64)-9*X(7729) = 2*X(64)-3*X(31978) = 5*X(185)-3*X(7729) = 3*X(185)-2*X(22967) = 3*X(5562)-5*X(17821) = 5*X(6293)+3*X(7729) = 3*X(6293)+2*X(22967) = 2*X(6293)+X(31978) = 9*X(7729)-10*X(22967) = 6*X(7729)-5*X(31978) = 4*X(15012)-3*X(23332) = 4*X(22967)-3*X(31978)

The reciprocal orthologic center of these triangles is X(32393).

X(32392) lies on these lines: {6,64}, {26,6759}, {369,11761}, {389,32393}, {1216,1511}, {1660,12164}, {2393,5889}, {2929,15139}, {3627,5446}, {5562,17821}, {5878,18917}, {5892,32396}, {5895,16879}, {6053,16252}, {6144,14531}, {6241,18945}, {6247,13382}, {12315,18534}, {13366,32345}, {13367,17824}, {13403,15311}, {15012,23332}, {18400,32358}, {22802,32140}, {25739,32329}

X(32392) = midpoint of X(i) and X(j) for these lines: {i,j}: {185, 6293}, {14531, 17845}
X(32392) = reflection of X(i) in X(j) for these (i,j): (64, 22967), (6247, 13382), (31978, 185)
X(32392) = X(6145)-of-5th-mixtilinear-triangle
X(32392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (64, 185, 22967), (64, 22967, 31978)


X(32393) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MIDHEIGHT TO HATZIPOLAKIS-MOSES

Barycentrics    S^4+(2*R^2*(16*R^2-SA-9*SW)+SA^2-SB*SC+2*SW^2)*S^2+(8*R^2-3*SW)^2*SB*SC : :
X(32393) = 3*X(3574)-X(17824) = X(3574)-3*X(32395) = X(6689)+2*X(18383) = X(17824)-9*X(32395) = 3*X(18376)+X(32401) = 3*X(18405)+X(32330) = 3*X(23324)+X(32351) = 3*X(23324)-X(32369) = 3*X(23325)+X(32365)

The reciprocal orthologic center of these triangles is X(32392).

X(32393) lies on these lines: {4,11747}, {5,5944}, {6,3574}, {25,32340}, {26,18376}, {54,18945}, {206,3091}, {389,32392}, {569,32379}, {1154,12235}, {1209,18531}, {2917,7395}, {5449,18569}, {6676,20376}, {6756,7687}, {6816,15435}, {7514,23358}, {7564,18128}, {9969,11743}, {10628,12236}, {11431,18912}, {11572,32332}, {11576,32246}, {12362,32348}, {15077,15801}, {18405,32330}

X(32393) = midpoint of X(i) and X(j) for these lines: {i,j}: {3574, 6145}, {18381, 32364}, {32340, 32345}, {32351, 32369}
X(32393) = reflection of X(i) in X(j) for these (i,j): (32377, 32376), (32391, 32396)
X(32393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6145, 32395, 3574), (23324, 32351, 32369)


X(32394) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th MIXTILINEAR TO HATZIPOLAKIS-MOSES

Barycentrics
3*a^16-2*(b+c)*a^15-(9*b^2-4*b*c+9*c^2)*a^14+2*(b+c)*(3*b^2-2*b*c+3*c^2)*a^13+(4*b^4+4*c^4-(8*b^2-19*b*c+8*c^2)*b*c)*a^12-2*(b+c)*(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^11+(11*b^6+11*c^6-(4*b^4+4*c^4+(7*b^2-12*b*c+7*c^2)*b*c)*b*c)*a^10-2*(b+c)*(5*b^6+5*c^6-(2*b^4+2*c^4+3*(b-c)^2*b*c)*b*c)*a^9-2*(b^2-b*c+c^2)*(5*b^4+5*c^4+(7*b^2+6*b*c+7*c^2)*b*c)*(b-c)^2*a^8+2*(b^2-c^2)*(b-c)*(5*b^6+5*c^6+(2*b^2+b*c+c^2)*(b^2+b*c+2*c^2)*b*c)*a^7-(3*b^6+3*c^6+(4*b^4+4*c^4-(7*b^2-12*b*c+7*c^2)*b*c)*b*c)*(b^2-c^2)^2*a^6+2*(b^2-c^2)^2*(b+c)*(b^6+c^6+(2*b^2-b*c+c^2)*(b^2-b*c+2*c^2)*b*c)*a^5+(b^2-c^2)^2*(4*b^8+4*c^8-(8*b^6+8*c^6-(3*b^4+3*c^4-2*(2*b^2+3*b*c+2*c^2)*b*c)*b*c)*b*c)*a^4-2*(b^2-c^2)*(b-c)^2*(b^3+c^3)*(b^4-c^4)*(3*b^2+5*b*c+3*c^2)*a^3+(b^4-c^4)*(b^2-c^2)^3*(b^4+c^4+2*(2*b^2-b*c+2*c^2)*b*c)*a^2+2*(b^2-c^2)^5*(b-c)*(b^2+c^2)^2*a-(b^2+c^2)^2*(b^2-c^2)^6 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32394) lies on these lines: {1,6145}, {8,32391}, {55,32363}, {56,32347}, {145,32354}, {517,32330}, {519,32371}, {952,32379}, {1154,9933}, {1482,18400}, {2098,32390}, {2099,32336}, {5603,32369}, {5604,32374}, {5605,32373}, {7718,11743}, {7967,32337}, {7968,32342}, {7969,32343}, {8192,32357}, {8210,32388}, {8211,32389}, {9997,32362}, {10247,32402}, {10628,12898}, {10800,32335}, {10944,32380}, {10950,32381}, {11396,32332}, {11910,32372}, {13902,32399}, {13959,32400}, {18525,32364}

X(32394) = midpoint of X(145) and X(32354)
X(32394) = reflection of X(i) in X(j) for these (i,j): (8, 32391), (6145, 1), (18525, 32364), (32356, 32331)
X(32394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32356, 32331), (32331, 32356, 6145), (32405, 32406, 6145)


X(32395) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ORTHOCENTROIDAL TO HATZIPOLAKIS-MOSES

Barycentrics    (R^2*(24*R^2+SA-15*SW)+2*SW^2)*S^2+2*(8*R^2-3*SW)*(3*R^2-SW)*SB*SC : :
X(32395) = X(3)+2*X(32365) = 2*X(4)+X(32345) = X(4)+2*X(32351) = 4*X(5)-X(2917) = X(20)-4*X(20376) = X(54)+2*X(32369) = X(382)+2*X(32401) = X(1498)-4*X(32364) = 5*X(1656)-2*X(23358) = 5*X(3091)+X(32346) = 4*X(3574)-X(17824) = X(3574)+2*X(32393) = 7*X(3851)-X(9920) = X(5889)-4*X(11262) = 4*X(6689)-X(32330) = X(10274)+2*X(18383) = 2*X(10274)+X(32402) = X(17824)+8*X(32393) = 4*X(18383)-X(32402) = X(32345)-4*X(32351)

The reciprocal orthologic center of these triangles is X(1986).

X(32395) lies on these lines: {3,32365}, {4,10117}, {5,2917}, {6,3574}, {20,20376}, {54,7547}, {154,381}, {195,265}, {382,32401}, {567,10274}, {568,10628}, {1154,14852}, {1498,32364}, {1503,7565}, {1656,23358}, {1853,5890}, {1986,32329}, {2931,10224}, {3091,15582}, {3851,9920}, {5889,11262}, {6288,17814}, {6689,32330}, {7564,32046}, {7730,14644}, {10516,11188}, {10539,11597}, {10895,32350}, {10896,32378}, {12022,23324}, {12307,14076}, {14389,32354}, {15069,32368}, {17835,20299}, {17845,32391}

X(32395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32351, 32345), (3574, 6145, 17824), (3574, 32393, 6145)


X(32396) = ORTHOLOGIC CENTER OF THESE TRIANGLES: SUBMEDIAL TO HATZIPOLAKIS-MOSES

Barycentrics    (24*R^2+SA-10*SW)*S^2+(8*R^2-3*SW)*SB*SC : :
X(32396) = 3*X(2)+X(3574) = 9*X(2)-X(7691) = 3*X(5)+X(10610) = 5*X(5)-X(22804) = X(195)+3*X(1209) = X(195)+15*X(1656) = 5*X(195)+3*X(3519) = X(195)-3*X(12242) = 7*X(195)-3*X(13431) = 19*X(195)-3*X(13432) = X(1209)-5*X(1656) = 5*X(1209)-X(3519) = 7*X(1209)+X(13431) = 19*X(1209)+X(13432) = 3*X(1209)-X(15605) = 5*X(1656)+X(12242) = 15*X(1656)-X(15605) = X(3519)+5*X(12242) = 7*X(3519)+5*X(13431) = 3*X(3519)-5*X(15605) = 3*X(3574)+X(7691) = 3*X(6689)-X(10610) = 5*X(6689)+X(22804) = X(7691)-3*X(32348) = 5*X(10610)+3*X(22804) = 7*X(12242)-X(13431) = 19*X(12242)-X(13432)

The reciprocal orthologic center of these triangles is X(389).

X(32396) lies on these lines: {2,3574}, {5,5944}, {6,17}, {54,3090}, {182,32379}, {373,32352}, {485,13986}, {486,8995}, {539,547}, {973,5943}, {1154,3628}, {1493,16254}, {2888,7486}, {2917,5020}, {3091,32340}, {3357,4846}, {3549,19130}, {3818,14530}, {5055,6288}, {5056,10619}, {5071,12254}, {5449,32068}, {5576,29012}, {5892,32392}, {5893,20376}, {5972,14788}, {6642,23358}, {6723,9826}, {7392,32346}, {7569,7592}, {8889,13347}, {9813,32368}, {9816,32370}, {9817,32378}, {9818,32401}, {9920,11484}, {10109,20584}, {10112,14389}, {10115,10170}, {10175,12266}, {10601,32341}, {10643,32397}, {10644,32398}, {10961,32384}, {10963,32385}, {11284,32333}, {11451,32338}, {11465,32339}, {11479,32345}, {11597,23515}, {11808,12363}, {12046,15350}, {12900,15088}, {13469,25339}, {15699,21230}, {17824,17825}, {18420,32365}, {18928,32334}, {19137,32344}, {19372,32350}, {19448,32386}, {19449,32387}

X(32396) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 6689}, {195, 15605}, {1209, 12242}, {3574, 32348}, {8254, 13565}, {11808, 12363}, {32391, 32393}
X(32396) = complement of X(32348)
X(32396) = X(21)-of-submedial-triangle if ABC is acute
X(32396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3574, 32348), (195, 1209, 15605), (12242, 15605, 195)


X(32397) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER TRI-EQUILATERAL TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(sqrt(3)*(5*R^2-2*SW)*(4*R^2-SW)*S+3*(3*R^2-SW)*S^2+3*SA*(2*R^2-SW)*(4*R^2+SA-2*SW)) : :

The reciprocal orthologic center of these triangles is X(389).

X(32397) lies on these lines: {6,24}, {15,18400}, {16,23358}, {539,10659}, {1154,10661}, {1209,8837}, {3166,10635}, {3574,10641}, {6288,18468}, {7051,32350}, {7691,11420}, {9920,11485}, {10274,10678}, {10628,10657}, {10636,32370}, {10638,32378}, {10643,32396}, {10645,32401}, {11408,32333}, {11452,32338}, {11466,32339}, {11475,32340}, {11480,32345}, {11488,32346}, {11515,32348}, {16808,32365}, {17824,17826}, {18929,32334}, {19363,32341}, {19450,32386}, {19451,32387}, {21647,32352}, {23302,32351}, {30402,32379}

X(32397) = X(21)-of-inner-tri-equilateral-triangle if ABC is acute
X(32397) = {X(6), X(2917)}-harmonic conjugate of X(32398)


X(32398) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER TRI-EQUILATERAL TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(-sqrt(3)*(5*R^2-2*SW)*(4*R^2-SW)*S+3*(3*R^2-SW)*S^2+3*SA*(2*R^2-SW)*(4*R^2+SA-2*SW)) : :

The reciprocal orthologic center of these triangles is X(389).

X(32398) lies on these lines: {6,24}, {15,23358}, {16,18400}, {539,10660}, {1154,10662}, {1209,8839}, {1250,32378}, {3165,10634}, {3574,10642}, {6288,18470}, {7691,11421}, {9920,11486}, {10274,10677}, {10628,10658}, {10637,32370}, {10644,32396}, {10646,32401}, {11409,32333}, {11453,32338}, {11467,32339}, {11476,32340}, {11481,32345}, {11489,32346}, {11516,32348}, {16809,32365}, {17824,17827}, {18930,32334}, {19364,32341}, {19373,32350}, {19452,32386}, {19453,32387}, {21648,32352}, {23303,32351}, {30403,32379}

X(32398) = X(21)-of-outer-tri-equilateral-triangle if ABC is acute
X(32398) = {X(6), X(2917)}-harmonic conjugate of X(32397)


X(32399) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES-CENTRAL TO HATZIPOLAKIS-MOSES

Barycentrics    S^4+(R^2*(48*R^2-3*SA-29*SW)+SA^2-SB*SC+4*SW^2)*S^2+2*(5*R^2-2*SW)*(4*R^2-SW)*(SB+SC)*S+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC : :

The reciprocal orthologic center of these triangles is X(6146).

X(32399) lies on these lines: {2,32343}, {6,32400}, {371,32369}, {590,32391}, {1154,13909}, {3068,6145}, {7585,32342}, {8972,32354}, {8974,32373}, {8976,32379}, {8981,18400}, {9540,32330}, {10628,13915}, {13883,32331}, {13884,32332}, {13885,32335}, {13886,32337}, {13887,32347}, {13888,32356}, {13889,32357}, {13893,32371}, {13894,32372}, {13895,32380}, {13897,32382}, {13898,32383}, {13899,32388}, {13900,32389}, {13901,32390}, {13902,32394}, {13903,32402}, {13904,32403}, {13905,32404}, {13906,32405}, {13907,32406}, {18538,32364}, {18965,32336}, {22763,32363}

X(32399) = X(6145)-of-3rd-tri-squares-central-triangle


X(32400) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES-CENTRAL TO HATZIPOLAKIS-MOSES

Barycentrics    S^4+(R^2*(48*R^2-3*SA-29*SW)+SA^2-SB*SC+4*SW^2)*S^2-2*(5*R^2-2*SW)*(4*R^2-SW)*(SB+SC)*S+(2*R^2-SW)*(8*R^2-3*SW)*SB*SC : :

The reciprocal orthologic center of these triangles is X(6146).

X(32400) lies on these lines: {2,32342}, {6,32399}, {372,32369}, {615,32391}, {1154,13970}, {3069,6145}, {7586,32343}, {10628,13979}, {13935,32330}, {13936,32331}, {13937,32332}, {13938,32335}, {13939,32337}, {13940,32347}, {13941,32354}, {13942,32356}, {13943,32357}, {13946,32362}, {13947,32371}, {13948,32372}, {13949,32373}, {13950,32374}, {13951,32379}, {13952,32380}, {13953,32381}, {13954,32382}, {13955,32383}, {13956,32388}, {13957,32389}, {13958,32390}, {13959,32394}, {13961,32402}, {13962,32403}, {13963,32404}, {13964,32405}, {13965,32406}, {13966,18400}, {18762,32364}, {18966,32336}, {22764,32363}

X(32400) = X(6145)-of-4th-tri-squares-central-triangle


X(32401) = ORTHOLOGIC CENTER OF THESE TRIANGLES: TRINH TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*((3*R^2-SA-SW)*S^2-((52*R^2-2*SA-31*SW)*R^2+SA^2-SB*SC+4*SW^2)*SA) : :
X(32401) = 3*X(3)-X(2917) = 5*X(3)-X(9920) = X(195)+5*X(8567) = 3*X(376)+X(32346) = X(382)-3*X(32395) = 3*X(1853)-X(32402) = 5*X(2917)-3*X(9920) = 2*X(2917)-3*X(23358) = X(2917)+3*X(32345) = X(3357)+2*X(10610) = X(5894)+2*X(8254) = 4*X(6689)-X(22802) = 3*X(10606)+X(17824) = 2*X(15579)+X(32367) = 3*X(18376)-4*X(32393) = 3*X(23325)-2*X(32369) = 4*X(32184)-X(32196)

The reciprocal orthologic center of these triangles is X(389).

X(32401) lies on these lines: {3,161}, {5,13289}, {24,32340}, {26,18376}, {30,32351}, {35,32350}, {36,32378}, {49,19402}, {54,74}, {64,32349}, {186,11572}, {195,8567}, {376,32346}, {378,3574}, {382,32395}, {511,32368}, {539,9938}, {973,11438}, {1154,7689}, {1204,12234}, {1658,23325}, {2071,7691}, {2777,3521}, {3098,15578}, {3357,10274}, {3516,12242}, {4550,6759}, {5092,32344}, {5894,8254}, {6000,15062}, {6200,32384}, {6293,14805}, {6396,32385}, {6689,7526}, {6699,22962}, {7488,18383}, {7688,32370}, {9818,32396}, {9977,11802}, {10226,12901}, {10263,11262}, {10605,32341}, {10606,17824}, {10645,32397}, {10646,32398}, {11410,32333}, {11454,32338}, {11457,12254}, {11468,32339}, {11793,22955}, {12038,15132}, {12107,23324}, {12893,13561}, {13403,19457}, {14216,32354}, {15331,23332}, {15579,32367}, {16003,25564}, {18128,32412}, {18931,32334}, {19454,32386}, {19455,32387}, {21230,22978}, {21663,32352}, {32184,32196}

X(32401) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32345}, {3357, 10274}, {14216, 32354}
X(32401) = reflection of X(i) in X(j) for these (i,j): (5, 20376), (6145, 20299), (6288, 14076), (6759, 32391), (10263, 11262), (10274, 10610), (14076, 25563), (22802, 32364), (23358, 3), (32344, 5092), (32364, 6689), (32365, 32351), (32412, 18128)
X(32401) = circumtangential-isogonal conjugate of X(7488)
X(32401) = X(21)-of-Trinh-triangle if ABC is acute
X(32401) = {X(11750), X(20299)}-harmonic conjugate of X(18381)


X(32402) = ORTHOLOGIC CENTER OF THESE TRIANGLES: X3-ABC REFLECTIONS TO HATZIPOLAKIS-MOSES

Barycentrics    (R^2*(4*R^2+6*SA-7*SW)+2*(SB+SC)*SW)*S^2-(R^2*(52*R^2-41*SW)+8*SW^2)*SB*SC : :
X(32402) = 3*X(3)-2*X(32330) = 3*X(381)-4*X(32369) = 3*X(381)-2*X(32379) = 5*X(1656)-4*X(32391) = 3*X(1853)-2*X(32401) = 5*X(3843)-2*X(32359) = 5*X(3843)-4*X(32364) = 3*X(5790)-2*X(32371) = 3*X(10246)-4*X(32331) = 3*X(10247)-2*X(32394) = 2*X(10274)-3*X(32395) = 3*X(11911)-2*X(32372) = X(12315)-4*X(32340) = X(17824)-3*X(18405) = 4*X(18383)-3*X(32395) = 3*X(18405)-2*X(32365)

The reciprocal orthologic center of these triangles is X(6146).

X(32402) lies on these lines: {3,161}, {4,19362}, {5,32354}, {30,32337}, {54,7507}, {195,31724}, {381,32369}, {517,32356}, {567,10274}, {973,18494}, {999,32336}, {1154,12429}, {1594,12254}, {1598,32332}, {1656,32391}, {2888,12225}, {3295,32390}, {3574,11426}, {3843,32359}, {5790,32371}, {6193,12319}, {6241,7730}, {6243,10628}, {6417,32343}, {6418,32342}, {7517,32357}, {9301,32362}, {9654,32382}, {9669,32383}, {10246,32331}, {10247,32394}, {10620,14216}, {11842,32335}, {11849,32347}, {11911,32372}, {11916,32373}, {11917,32374}, {11928,32380}, {11929,32381}, {11949,32388}, {11950,32389}, {12000,32405}, {12001,32406}, {12315,32340}, {13903,32399}, {13961,32400}, {17824,18405}, {22765,32363}

X(32402) = reflection of X(i) in X(j) for these (i,j): (3, 6145), (9920, 6288), (10274, 18383), (17824, 32365), (17845, 23358), (32345, 18381), (32354, 5), (32359, 32364), (32379, 32369)
X(32402) = X(6145)-of-X3-ABC-reflections-triangle
X(32402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (10274, 18383, 32395), (32369, 32379, 381)


X(32403) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TO HATZIPOLAKIS-MOSES

Barycentrics    (3*R^2-SW)*(8*R^2-SA-3*SW)*S^2+(SB+SC)*((5*R^2-2*SW)*(4*R^2-SW)*b*c-(2*R^2-SW)*(8*R^2-3*SW)*SA) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32403) lies on these lines: {1,6145}, {3,32336}, {5,32383}, {12,32379}, {35,32330}, {55,12946}, {388,32337}, {495,32382}, {498,32391}, {973,11392}, {1154,10055}, {1479,32369}, {3295,32390}, {3299,32342}, {3301,32343}, {6288,18455}, {10037,32357}, {10038,32362}, {10039,32371}, {10040,32373}, {10041,32374}, {10082,32351}, {10523,32380}, {10628,12903}, {10801,32335}, {10895,32364}, {10954,32381}, {11398,32332}, {11507,32347}, {11912,32372}, {11951,32388}, {11952,32389}, {13904,32399}, {13962,32400}, {22766,32363}

X(32403) = midpoint of X(6145) and X(32405)
X(32403) = reflection of X(32382) in X(495)
X(32403) = X(6145)-of-inner-Yff-triangle
X(32403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6145, 32404), (3295, 32402, 32390)


X(32404) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TO HATZIPOLAKIS-MOSES

Barycentrics    (3*R^2-SW)*(8*R^2-SA-3*SW)*S^2+(SB+SC)*(-(5*R^2-2*SW)*(4*R^2-SW)*b*c-(2*R^2-SW)*(8*R^2-3*SW)*SA) : :

The reciprocal orthologic center of these triangles is X(6146).

X(32404) lies on these lines: {1,6145}, {3,32390}, {5,32382}, {11,32379}, {36,32330}, {56,12956}, {496,32383}, {497,32337}, {499,32391}, {973,11393}, {999,32336}, {1154,10071}, {1478,32369}, {1737,32371}, {3086,32354}, {3299,32343}, {3301,32342}, {6288,18447}, {10046,32357}, {10047,32362}, {10048,32373}, {10049,32374}, {10066,32351}, {10523,32381}, {10628,12904}, {10802,32335}, {10896,32364}, {10948,32380}, {11399,32332}, {11508,32347}, {11913,32372}, {11953,32388}, {11954,32389}, {13905,32399}, {13963,32400}, {22767,32363}

X(32404) = midpoint of X(6145) and X(32406)
X(32404) = reflection of X(32383) in X(496)
X(32404) = X(6145)-of-outer-Yff-triangle
X(32404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6145, 32403), (999, 32402, 32336)


X(32405) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TANGENTS TO HATZIPOLAKIS-MOSES

Barycentrics
a^19-(b+c)*a^18-4*(b-c)^2*a^17+2*(b+c)*(2*b^2-3*b*c+2*c^2)*a^16+(5*b^4+5*c^4-(24*b^2-19*b*c+24*c^2)*b*c)*a^15-(b+c)*(5*b^2-3*b*c+5*c^2)*(b^2-3*b*c+c^2)*a^14-(b^6+c^6-12*(b^4+c^4-2*(b-c)^2*b*c)*b*c)*a^13+(b+c)*(b^6+c^6-2*(4*b^4+4*c^4-(12*b^2-19*b*c+12*c^2)*b*c)*b*c)*a^12-(b^8+c^8-2*(12*b^6+12*c^6-(5*b^4+5*c^4+(8*b^2-15*b*c+8*c^2)*b*c)*b*c)*b*c)*a^11+(b+c)*(b^8+c^8-2*(11*b^6+11*c^6-(5*b^4+5*c^4+(7*b^2-15*b*c+7*c^2)*b*c)*b*c)*b*c)*a^10-(b^8+c^8+2*(11*b^6+11*c^6+(3*b^4+3*c^4+(7*b^2+17*b*c+7*c^2)*b*c)*b*c)*b*c)*(b-c)^2*a^9+(b^2-c^2)*(b-c)*(b^8+c^8+2*(11*b^6+11*c^6+(3*b^4+3*c^4+(5*b^2+13*b*c+5*c^2)*b*c)*b*c)*b*c)*a^8-(b^8+c^8+(8*b^6+8*c^6+(11*b^4+11*c^4-16*(b-c)^2*b*c)*b*c)*b*c)*(b^2-c^2)^2*a^7+(b^2-c^2)^2*(b+c)*(b^8+c^8+(6*b^6+6*c^6+(11*b^4+11*c^4-2*(7*b^2-16*b*c+7*c^2)*b*c)*b*c)*b*c)*a^6+(b^2-c^2)^2*(b+c)*(b^3+c^3)*(5*b^6+5*c^6-(b^4+c^4+(11*b^2-6*b*c+11*c^2)*b*c)*b*c)*a^5-(b^2-c^2)^3*(b-c)*(5*b^8+5*c^8+(18*b^6+18*c^6+(19*b^4+19*c^4+2*(13*b^2+16*b*c+13*c^2)*b*c)*b*c)*b*c)*a^4-4*(b^4-c^4)*(b^2-c^2)^3*(b^6+c^6-(2*b^4+2*c^4+(b^2+c^2)*b*c)*b*c)*a^3+2*(b^2-c^2)^6*(b+c)*(b^2+c^2)*(2*b^2-b*c+2*c^2)*a^2+(b^2-4*b*c+c^2)*(b^2+c^2)^2*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32405) lies on these lines: {1,6145}, {12,32380}, {1154,12430}, {5552,32391}, {10528,32354}, {10531,32369}, {10628,12905}, {10679,18400}, {10803,32335}, {10805,32337}, {10834,32357}, {10878,32362}, {10915,32371}, {10929,32373}, {10930,32374}, {10942,32379}, {10955,32381}, {10956,32382}, {10958,32383}, {10965,32390}, {11248,32330}, {11400,32332}, {11509,32336}, {11914,32372}, {11955,32388}, {11956,32389}, {12000,32402}, {13906,32399}, {13964,32400}, {18542,32364}, {19047,32342}, {19048,32343}, {22768,32363}

X(32405) = reflection of X(6145) in X(32403)
X(32405) = X(6145)-of-inner-Yff-tangents-triangle
X(32405) = {X(6145), X(32394)}-harmonic conjugate of X(32406)


X(32406) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TANGENTS TO HATZIPOLAKIS-MOSES

Barycentrics
a^19-(b+c)*a^18-4*(b^2+b*c+c^2)*a^17+2*(b+c)*(2*b^2+b*c+2*c^2)*a^16+(5*b^4+5*c^4+3*(4*b^2+b*c+4*c^2)*b*c)*a^15-(b+c)*(5*b^4+5*c^4+3*(2*b^2+b*c+2*c^2)*b*c)*a^14-(b^6+c^6+4*(b^4+c^4-(2*b^2-7*b*c+2*c^2)*b*c)*b*c)*a^13+(b+c)*(b^6+c^6-2*(4*b^2-9*b*c+4*c^2)*b^2*c^2)*a^12-(b^8+c^8+2*(10*b^6+10*c^6-3*(b^4+c^4+(2*b^2-3*b*c+2*c^2)*b*c)*b*c)*b*c)*a^11+(b+c)*(b^8+c^8+2*(9*b^6+9*c^6-(3*b^4+3*c^4+(5*b^2-9*b*c+5*c^2)*b*c)*b*c)*b*c)*a^10-(b^8+c^8-2*(9*b^6+9*c^6+(5*b^4+5*c^4+3*(3*b^2+5*b*c+3*c^2)*b*c)*b*c)*b*c)*(b-c)^2*a^9+(b^4-c^4)*(b-c)*(b^6+c^6-(18*b^4+18*c^4+(11*b^2-4*b*c+11*c^2)*b*c)*b*c)*a^8-(b^8+c^8-(4*b^6+4*c^6+(5*b^4+5*c^4-4*(3*b^2-4*b*c+3*c^2)*b*c)*b*c)*b*c)*(b^2-c^2)^2*a^7+(b^2-c^2)^2*(b+c)*(b^8+c^8-(2*b^2-3*b*c+2*c^2)*(b^4+c^4+4*(b^2+c^2)*b*c)*b*c)*a^6+(b^4-c^4)*(b^2-c^2)*(5*b^8+5*c^8-3*(4*b^6+4*c^6-5*(b^4+c^4)*b*c)*b*c)*a^5-(b^2-c^2)^3*(b-c)*(5*b^8+5*c^8-3*(2*b^2-b*c+2*c^2)*(b^4+c^4)*b*c)*a^4-4*(b-c)*(b^3+c^3)*(b^4-c^4)^3*a^3+2*(b^2-c^2)^5*(b-c)*(b^2+c^2)*(2*b^4+2*c^4-(b-c)^2*b*c)*a^2+(b^2+c^2)^3*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(32406) lies on these lines: {1,6145}, {11,32381}, {1154,12431}, {10527,32391}, {10529,32354}, {10532,32369}, {10628,12906}, {10680,18400}, {10804,32335}, {10806,32337}, {10835,32357}, {10879,32362}, {10916,32371}, {10931,32373}, {10932,32374}, {10943,32379}, {10949,32380}, {10957,32382}, {10959,32383}, {10966,32363}, {11249,32330}, {11401,32332}, {11510,32347}, {11915,32372}, {11957,32388}, {11958,32389}, {12001,32402}, {13907,32399}, {13965,32400}, {18544,32364}, {18967,32336}, {19049,32342}, {19050,32343}

X(32406) = reflection of X(6145) in X(32404)
X(32406) = X(6145)-of-outer-Yff-tangents-triangle
X(32406) = {X(6145), X(32394)}-harmonic conjugate of X(32405)


X(32407) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st PARRY TO HATZIPOLAKIS-MOSES

Barycentrics    SA*(SB-SC)*((18*R^2-6*SW)*S^4+(20*(3*SA-4*SW)*R^4+(9*SA^2-48*SA*SW+49*SW^2)*R^2-(3*SA^2-9*SA*SW+7*SW^2)*SW)*S^2-(8*R^2-3*SW)*SB*SC*SW^2) : :

The reciprocal parallelogic center of these triangles is X(6146).

X(32407) lies on these lines: {351,6368}, {1510,13223}

X(32407) = reflection of X(32408) in X(351)
X(32407) = X(6145)-of-1st-Parry-triangle


X(32408) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd PARRY TO HATZIPOLAKIS-MOSES

Barycentrics    SA*(SB-SC)*((-18*R^2+6*SW)*S^4+(20*(3*SA-4*SW)*R^4-(9*SA^2+30*SA*SW-55*SW^2)*R^2+3*(SA^2+SA*SW-3*SW^2)*SW)*S^2-(2*R^2-SW)*SB*SC*SW^2) : :

The reciprocal parallelogic center of these triangles is X(6146).

X(32408) lies on these lines: {110,16039}, {351,6368}, {1510,13224}

X(32408) = reflection of X(32407) in X(351)
X(32408) = X(6145)-of-2nd-Parry-triangle


X(32409) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CONWAY TO HATZIPOLAKIS-MOSES

Barycentrics    (SB+SC)*(S^2+SB*SC)*(3*S^4-(R^2*(16*R^2-13*SW)+SA^2+3*SW^2)*S^2+(3*R^2-SW)*(4*R^2-SW)*SA^2) : :
X(32409) = 3*X(51)-X(16337) = 3*X(568)+X(19552) = X(1157)-5*X(3567) = 3*X(5946)-X(6150)

The reciprocal cyclologic center of these triangles is X(389).

X(32409) lies on these lines: {5,51}, {54,3432}, {568,19552}, {1157,3567}, {5462,10615}, {5946,6150}, {11077,15401}, {18400,32410}

X(32409) = midpoint of X(52) and X(16336)
X(32409) = reflection of X(10615) in X(5462)
X(32409) = complement of X(16337) wrt orthic triangle
X(32409) = X(1325)-of-2nd-anti-Conway-triangle if ABC is acute


X(32410) = CYCLOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO ORTHIC

Barycentrics    (4*S^2-R^2*(24*R^2+5*SA-19*SW)+2*SA^2-2*SB*SC-4*SW^2)*((2*R^2-SA)*S^2+(3*R^2-SW)*SB*SC) : :

The reciprocal cyclologic center of these triangles is X(1986).

X(32410) lies on these lines: {5,49}, {137,12241}, {12370,25150}, {15959,19467}, {18400,32409}

X(32410) = reflection of X(137) in X(12241)


X(32411) = EULEROLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO 2nd ANTI-CONWAY

Barycentrics    (SB+SC)*((13*R^2-3*SW)*S^2+(4*R^2-SW)*(3*R^2+SA-2*SW)*SA) : :
X(32411) = 3*X(51)-X(403) = X(186)-5*X(3567) = 3*X(568)+X(18403) = X(2070)-9*X(13321) = X(2071)+3*X(3060) = 3*X(5946)-X(15646) = X(10297)+2*X(16625)

X(32411) lies on these lines: {6,2070}, {30,143}, {51,403}, {52,2072}, {186,578}, {468,973}, {511,10257}, {568,18390}, {1112,6000}, {1154,11746}, {1986,13851}, {2071,3060}, {5899,11432}, {5946,11430}, {6746,10110}, {7687,12236}, {7722,23043}, {9786,18859}, {10114,11557}, {10297,13376}, {10540,12227}, {11262,11745}, {11431,20063}, {11563,12233}, {11807,15311}, {15473,18400}, {15644,16976}

X(32411) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 2072}, {1986, 13851}, {13376, 16625}
X(32411) = reflection of X(i) in X(j) for these (i,j): (10151, 10110), (10297, 13376), (15644, 16976)
X(32411) = {X(12241), X(16881)}-harmonic conjugate of X(389)


X(32412) = ORTHOCENTER OF THE HATZIPOLAKIS-MOSES TRIANGLE

Barycentrics    (32*R^6-2*(31*SA-9*SW)*R^4+(39*SA-22*SW)*SW*R^2-2*(3*SA-2*SW)*SW^2)*S^2+(8*R^2-3*SW)*(R^2*(8*R^2-9*SW)+2*SW^2)*SB*SC : :
X(32412) = 3*X(11225)-2*X(11262) = 3*X(11225)-4*X(32413)

X(32412) lies on these lines: {6,3574}, {539,9932}, {1511,21230}, {5449,10274}, {6102,10116}, {6689,14076}, {11225,11262}, {15033,32337}, {18128,32401}

X(32412) = reflection of X(i) in X(j) for these (i,j): (6145, 32376), (11262, 32413), (32401, 18128)
X(32412) = {X(11262), X(32413)}-harmonic conjugate of X(11225)


X(32413) = X(5)-OF-HATZIPOLAKIS-MOSES TRIANGLE

Barycentrics    (96*R^6-(81*SA+23*SW)*R^4+4*(13*SA-4*SW)*SW*R^2-4*(2*SA-SW)*SW^2)*S^2+2*(R^2*(16*R^4-29*R^2*SW+14*SW^2)-2*SW^3)*SB*SC : :
X(32413) = 3*X(11225)-X(11262) = 3*X(11225)+X(32412) = 3*X(11245)-X(20376)

X(32413) lies on these lines: {11225,11262}, {11245,20376}, {12242,15118}, {18400,32165}

X(32413) = midpoint of X(11262) and X(32412)
X(32413) = {X(11225), X(32412)}-harmonic conjugate of X(11262)


X(32414) = X(2)X(1495)∩X(5)X(26614)

Barycentrics    24*S^4+(3*SA-4*SW)*SW*S^2+9*SB*SC*SW^2 : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32414) lies on these lines: {2, 1495}, {5, 26614}, {30, 1153}, {381, 5215}, {511, 7610}, {542, 9771}, {575, 6055}, {3830, 8588}, {6054, 10486}, {7603, 14830}, {13355, 21358}, {15597, 19924}, {23053, 31670}


X(32415) = X(2)X(32401)∩X(140)X(6000)

Barycentrics    (R^2*(188*R^2+SA-96*SW)+12*SW^2)*S^2-(R^2*(52*R^2-31*SW)+4*SW^2)*SB*SC : :
X(32415) = 15*X(15694)+X(32321)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004

X(32415) lies on these lines: {2, 32401}, {140, 6000}, {2777, 5498}, {6143, 13289}, {6288, 11202}, {10018, 18383}, {10125, 18400}, {10182, 14076}, {13363, 15426}, {15694, 32321}, {16532, 32351}


X(32416) = X(511)X(25488)∩X(3589)X(5066)

Barycentrics    4*S^4-(3*R^2*(3*SA-4*SW)-4*SA^2+4*SB*SC+12*SW^2)*S^2-27*R^2*SB*SC*SW : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32416) lies on these lines: {511, 25488}, {3589, 5066}, {3818, 5012}, {6676, 10219}, {7605, 32305}, {14389, 25561}


X(32417) = X(3)X(31378)∩X(4)X(5627)

Barycentrics    5*S^4+3*(3*R^2*(12*R^2-3*SA-4*SW)+2*SA^2-SB*SC+SW^2)*S^2-3*(9*R^2*(12*R^2-5*SW)+5*SW^2)*SB*SC : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32417) lies on these lines: {3, 31378}, {4, 5627}, {20, 14480}, {30, 511}, {74, 3258}, {107, 18809}, {113, 22104}, {133, 1552}, {146, 476}, {381, 18279}, {477, 1138}, {550, 18285}, {1304, 5667}, {3154, 20417}, {3233, 6053}, {5502, 20128}, {7471, 15063}, {7687, 12079}, {7728, 14993}, {10096, 16244}, {10620, 20957}, {10745, 16177}, {12041, 31379}, {13382, 14895}, {14508, 14731}, {14611, 16163}, {14934, 16111}, {15054, 17511}, {16978, 21649}

X(32417) = isogonal conjugate of X(32418}

X(32418) = X(107)X(12121)∩X(476)X(16163)

Barycentrics    (SB+SC)*(5*S^4+3*(3*R^2*(12*R^2-3*SB-4*SW)+2*SB^2-SA*SC+SW^2)*S^2-3*(9*R^2*(12*R^2-5*SW)+5*SW^2)*SC*SA)*(5*S^4+3*(3*R^2*(12*R^2-3*SC-4*SW)+2*SC^2-SA*SB+SW^2)*S^2-3*(9*R^2*(12*R^2-5*SW)+5*SW^2)*SA*SB) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32418) lies on the circumcircle and these lines: {107, 12121}, {476, 16163}, {1304, 1511}, {2132, 15035}

X(32418) = isogonal conjugate of X(32417}

X(32419) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES, 4th TRI-SQUARES, AND INNER-VECTEN

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

Centers X(32419) to X(32441) were contributed by César Lozada, May 5, 2019.

X(32419) lies on these lines: {2,371}, {3,591}, {4,5861}, {6,13644}, {13,22607}, {14,22608}, {20,26288}, {30,511}, {69,6561}, {187,13989}, {193,6560}, {298,22601}, {299,22603}, {323,12376}, {372,489}, {376,5860}, {381,1991}, {395,6307}, {396,6306}, {428,12147}, {485,12322}, {488,13712}, {491,6565}, {492,6200}, {551,12268}, {615,9675}, {640,3071}, {641,1151}, {1161,13748}, {1270,9541}, {1271,23259}, {1327,2996}, {1328,5491}, {1504,5309}, {1651,12799}, {2462,5182}, {2858,32422}, {3058,13081}, {3068,13650}, {3069,13770}, {3102,8356}, {3241,7980}, {3543,12296}, {3592,11313}, {3679,9906}, {3830,22809}, {3845,22596}, {4421,12343}, {5434,18989}, {5591,23273}, {5875,14230}, {6118,8981}, {6231,9892}, {6278,13710}, {6289,12313}, {6337,13701}, {6419,7389}, {6420,11293}, {6425,11315}, {6459,26619}, {6463,13798}, {7811,9986}, {7833,9991}, {7837,22613}, {7840,22501}, {9732,9766}, {9742,13681}, {9758,9770}, {9909,9921}, {10008,13684}, {10056,10067}, {10072,10083}, {10653,22612}, {10654,22611}, {11194,22595}, {11207,12484}, {11208,12485}, {11235,12928}, {11236,12938}, {11237,12948}, {11238,12958}, {11239,13132}, {11240,13133}, {12150,12210}, {12152,13002}, {12153,13003}, {12222,22644}, {12237,21849}, {12323,22615}, {12962,13846}, {12963,13821}, {12972,14070}, {13926,13927}, {16267,22602}, {16268,22604}, {19053,19104}, {19054,19105}, {19493,32060}, {21653,21969}, {23267,26339}

X(32419) = isogonal conjugate of X(32420)


X(32420) = ISOGONAL CONJUGATE OF X(32419)

Barycentrics    (SB+SC)*(S^2+(SW-3*SB)*S-3*SA*SC)*(S^2+(SW-3*SC)*S-3*SA*SB) : :

X(32420) lies on the circumcircle and these lines: {99,491}, {110,372}, {112,5412}, {485,925}, {691,2460}, {1307,6396}, {2858,32421}, {2872,9142}, {3565,6200}

X(32420) = isogonal conjugate of X(32419)
X(32420) = reflection of X(98) in the line X(3)X(9892)


X(32421) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES, 3rd TRI-SQUARES, AND OUTER-VECTEN

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

X(32421) lies on these lines: {2,372}, {3,1991}, {4,5860}, {6,13763}, {13,22636}, {14,22637}, {20,26289}, {30,511}, {69,6560}, {187,8997}, {193,6561}, {298,22630}, {299,22632}, {323,12375}, {371,490}, {376,5861}, {381,591}, {395,6303}, {396,6302}, {428,12148}, {486,12323}, {487,13835}, {491,6396}, {492,6564}, {551,12269}, {639,3070}, {642,1152}, {1160,13749}, {1270,23249}, {1327,5490}, {1328,2996}, {1505,5309}, {1651,12800}, {2461,5182}, {2858,32420}, {3058,13082}, {3068,13651}, {3069,13771}, {3103,8356}, {3241,7981}, {3543,12297}, {3594,11314}, {3679,9907}, {3830,22810}, {3845,22625}, {4421,12344}, {5434,18988}, {5590,23267}, {5874,14233}, {6119,13966}, {6230,9894}, {6281,13830}, {6290,12314}, {6337,13821}, {6419,11294}, {6420,7388}, {6426,11316}, {6460,26620}, {6462,13678}, {7811,9987}, {7833,9992}, {7837,22642}, {7840,22502}, {8989,12973}, {8996,9909}, {9733,9766}, {9742,13801}, {9757,9770}, {10008,13804}, {10056,10068}, {10072,10084}, {10653,22641}, {10654,22640}, {11194,22624}, {11207,12486}, {11208,12487}, {11235,12929}, {11236,12939}, {11237,12949}, {11238,12959}, {11239,13134}, {11240,13135}, {12150,12211}, {12152,13004}, {12153,13005}, {12221,22615}, {12238,21849}, {12322,22644}, {12968,13701}, {12969,13847}, {13873,13874}, {16267,22631}, {16268,22633}, {19053,19102}, {19054,19103}, {19492,32059}, {21654,21969}, {23273,26340}

X(32421) = isogonal conjugate of X(32422)


X(32422) = ISOGONAL CONJUGATE OF X(32421)

Barycentrics    (SB+SC)*(S^2-(SW-3*SB)*S-3*SA*SC)*(S^2-(SW-3*SC)*S-3*SA*SB) : :

X(32422) lies on the circumcircle and these lines: {99,492}, {110,371}, {112,5413}, {486,925}, {691,2459}, {1306,6200}, {2858,32419}, {2872,9142}, {3565,6396}

X(32422) = isogonal conjugate of X(32421)
X(32422) = reflection of X(98) in the line X(3)X(9894)


X(32423) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: AOA, AAOA, AND 1st HYACINTH

Barycentrics    (3*R^2+2*SA-2*SW)*S^2-(9*R^2-4*SW)*SB*SC : :

X(32423) lies on the cubic K466, the curve Q110 and these lines: {2,11694}, {3,2888}, {4,195}, {5,49}, {20,10620}, {26,9920}, {30,511}, {52,32196}, {68,1658}, {69,32306}, {74,550}, {99,15545}, {113,137}, {125,128}, {141,12584}, {143,10112}, {146,382}, {155,18377}, {156,9927}, {182,25328}, {252,19268}, {323,7574}, {343,22109}, {355,2948}, {376,15041}, {381,9143}, {389,6153}, {427,15463}, {495,10066}, {496,10082}, {547,5642}, {548,12041}, {549,9140}, {568,7730}, {576,25329}, {631,15040}, {632,15027}, {895,1353}, {946,11699}, {973,12236}, {974,18914}, {1112,6756}, {1147,10224}, {1216,13470}, {1350,25335}, {1351,11061}, {1352,2930}, {1385,13605}, {1483,7979}, {1484,10778}, {1495,25338}, {1513,5987}, {1539,3853}, {1594,3043}, {1595,15472}, {1656,15081}, {1657,12244}, {1770,11670}, {1885,12292}, {1986,3575}, {2935,14216}, {3028,3327}, {3047,10024}, {3070,12375}, {3071,12376}, {3090,15039}, {3091,20125}, {3530,6699}, {3545,15046}, {3580,7575}, {3581,12380}, {3585,14101}, {3589,20301}, {3627,7728}, {3628,5972}, {3845,5655}, {3850,7687}, {3857,15044}, {3861,6053}, {4857,7343}, {5050,25320}, {5066,23516}, {5073,13432}, {5085,25330}, {5093,25321}, {5102,25331}, {5254,14901}, {5270,6126}, {5318,10657}, {5321,10658}, {5448,18379}, {5449,10125}, {5462,13365}, {5480,19140}, {5498,12038}, {5501,25340}, {5504,6145}, {5654,32395}, {5690,12778}, {5874,6276}, {5875,6277}, {5876,15532}, {5889,13423}, {5901,11720}, {5946,16223}, {6101,11750}, {6102,11562}, {6193,12319}, {6240,6242}, {6243,7731}, {6247,13293}, {6253,6255}, {6284,6286}, {6321,15342}, {6593,18583}, {6644,26869}, {6696,25564}, {6723,16239}, {6776,32251}, {6794,22146}, {7354,7356}, {7487,18947}, {7526,12168}, {7577,9703}, {7579,11935}, {7689,15332}, {7723,12605}, {8550,9976}, {8703,15055}, {8981,10819}, {8995,8998}, {9544,10254}, {9825,9826}, {9833,10117}, {9934,32359}, {9970,21850}, {9985,12501}, {10020,32391}, {10021,16164}, {10095,13163}, {10111,14708}, {10116,11802}, {10126,18016}, {10127,12099}, {10205,30484}, {10226,12901}, {10263,13417}, {10282,18282}, {10299,15042}, {10540,11563}, {10663,32397}, {10664,32398}, {10706,15687}, {10721,16659}, {10820,13966}, {10942,12890}, {10943,12889}, {11064,32235}, {11202,15330}, {11250,12118}, {11412,15100}, {11442,18570}, {11477,25336}, {11536,18428}, {11559,13418}, {11565,32142}, {11577,15738}, {11579,32233}, {11807,13419}, {11818,14853}, {11819,14449}, {12079,15468}, {12084,32337}, {12103,16111}, {12105,32269}, {12107,13289}, {12108,20397}, {12112,18325}, {12133,13488}, {12165,12173}, {12201,12208}, {12219,12225}, {12227,12233}, {12270,12278}, {12273,12281}, {12293,17824}, {12334,12341}, {12358,12362}, {12359,12893}, {12364,32349}, {12428,12888}, {12596,32368}, {12661,32370}, {12790,12797}, {12824,13451}, {12891,32384}, {12892,32385}, {12894,12998}, {12895,12999}, {12897,32137}, {12900,15088}, {12905,13121}, {12906,13122}, {13142,32332}, {13188,18331}, {13198,31804}, {13202,13431}, {13353,27866}, {13383,20773}, {13393,15605}, {13413,23292}, {13979,13986}, {14480,20957}, {14791,15106}, {14869,15020}, {14912,18420}, {14934,16340}, {15036,15057}, {15051,15712}, {15054,15704}, {15068,18396}, {15085,17835}, {15091,18572}, {15093,22265}, {15113,15114}, {15122,15124}, {15123,32355}, {15136,32353}, {15345,27868}, {15465,23411}, {15761,32379}, {16165,25337}, {16266,17847}, {16337,24385}, {18358,32274}, {18381,23315}, {18440,31861}, {18563,22584}, {18567,19479}, {18874,23409}, {18932,32334}, {18933,18945}, {18970,19469}, {19051,19095}, {19052,19096}, {19138,32344}, {19139,23049}, {19195,19205}, {19456,32341}, {19457,19467}, {19478,22586}, {19482,32386}, {19483,32387}, {19484,19498}, {19485,19499}, {19552,24144}, {20030,20414}, {22115,25739}, {32114,32275}

X(32423) = isogonal conjugate of X(14979)


X(32424) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: 4th BROCARD, CIRCUMMEDIAL, AND 5th EULER

Barycentrics    3*(9*R^2-SW)*S^4+(3*SW*SA^2-3*(27*R^2-5*SW)*SB*SC-2*SW^3)*S^2+3*SB*SC*SW^3 : :

X(32424) lies on these lines: {2,10748}, {3,9829}, {4,31824}, {5,9172}, {30,511}, {110,11159}, {111,381}, {113,13994}, {125,11569}, {126,549}, {140,31606}, {143,31763}, {376,6031}, {546,31749}, {547,6719}, {550,31729}, {1296,3534}, {1316,32222}, {1385,31747}, {3543,20099}, {3579,31746}, {3830,10734}, {3845,5512}, {5077,9140}, {5476,28662}, {5694,31823}, {5946,31743}, {5987,9855}, {6101,31736}, {6102,31745}, {6232,9129}, {9940,31818}, {9955,31755}, {9956,31758}, {11591,31753}, {12041,32311}, {12161,31809}, {13643,13644}, {13762,13763}, {14657,18324}, {15303,18907}, {31727,31748}, {31761,32161}, {32219,32225}

X(32424) = isogonal conjugate of X(32425)


X(32425) = ISOGONAL CONJUGATE OF X(32424)

Barycentrics    (SB+SC)*(3*(9*R^2-SW)*S^4+(3*SB^2*SW-3*(27*R^2-5*SW)*SC*SA-2*SW^3)*S^2+3*SA*SC*SW^3)*(3*(9*R^2-SW)*S^4+(3*SC^2*SW-3*(27*R^2-5*SW)*SA*SB-2*SW^3)*S^2+3*SA*SB*SW^3) : :

X(32425) lies on the circumcircle and these lines: {476,11159}, {523,11568}, {524,6236}, {1296,8705}, {1499,6325}

X(32425) = isogonal conjugate of X(32424)
X(32425) = (circumsymmedial)-isogonal conjugate of-X(2780)
X(32425) = X(2696) of circumsymmedial triangle
X(32425) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (74, 3, 352), (111, 3, 11663), (477, 3, 11628), (1296, 3, 17414), (11568, 2, 3)


X(32426) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: EXCENTERS-MIDPOINTS, GARCIA-REFLECTION, AND 2nd SCHIFFLER

Barycentrics    2*a^4-4*(b+c)*a^3-(b^2-20*b*c+c^2)*a^2+2*(b+c)*(2*b^2-7*b*c+2*c^2)*a-(b^2-c^2)^2 : :

X(32426) lies on these lines: {8,1997}, {30,511}, {145,1376}, {497,3621}, {1699,3680}, {2886,12648}, {3338,3633}, {3476,5221}, {3632,15829}, {3813,5790}, {3913,7967}, {4969,16561}, {5506,13606}, {5603,10912}, {6667,6735}, {8256,17728}, {10164,11260}, {10915,11230}, {11219,11256}, {11246,14923}, {12645,26333}, {17784,20014}

X(32426) = isogonal conjugate of X(32427)


X(32427) = ISOGONAL CONJUGATE OF X(32426)

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

X(32427) lies on the circumcircle and these lines: {100,20323}, {30236,31798}

X(32427) = isogonal conjugate of X(32426)
X(32427) = X(110)-of-3rd mixtilinear triangle


X(32428) = POINT AT INFINITY OF THE BROCARD AXIS OF THE CIRCUMORTHIC TRIANGLE

Barycentrics    (S^2+SB*SC)*(S^2-2*SB*SC+SW*(-SW+4*R^2)) : :

X(32428) lies on these lines: {2,10184}, {3,95}, {4,3164}, {5,53}, {20,31388}, {26,157}, {30,511}, {52,6751}, {68,8612}, {110,32439}, {140,6709}, {143,15912}, {155,17849}, {324,418}, {381,14635}, {1209,15780}, {1316,19128}, {1513,12131}, {2052,6638}, {2070,30716}, {2980,17714}, {5872,8175}, {5873,8174}, {6662,10627}, {6663,10095}, {9747,9909}, {10125,13467}, {13371,23333}, {13599,17039}, {17041,31505}, {18377,18380}, {18951,18953}, {19154,19156}, {19210,19212}, {27352,27361}

X(32428) = complementary conjugate of X(129)
X(32428) = isogonal conjugate of X(1298)
X(32428) = point at infinity of Brocard axis of any triangle homothetic to circumorthic triangle


X(32429) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 6th ANTI-BROCARD, ANTI-EULER, AND 1st NEUBERG

Barycentrics    (SA+SW)*S^4+(5*SA^2+2*SB*SC-4*SW^2)*SW*S^2+3*SB*SC*SW^3 : :
X(32429) = 3*X(182)-2*X(24256) = X(1352)-3*X(7709) = 2*X(1352)-3*X(11261) = 3*X(5085)-X(13108) = 4*X(10007)-3*X(11178) = 3*X(11171)-2*X(24206) = 3*X(11179)-X(18906) = 3*X(13331)-2*X(19130)

X(32429) lies on these lines: {6,18501}, {20,185}, {39,3818}, {76,5092}, {182,2782}, {542,1569}, {732,3098}, {1352,7709}, {3095,29012}, {5085,13108}, {5116,12188}, {5476,7739}, {6248,7803}, {7757,11645}, {7765,13331}, {7795,13334}, {8149,14880}, {10007,11178}, {11171,14981}, {11179,18906}

X(32429) = reflection of X(i) in X(j) for these (i,j): (76, 5092), (3818, 39), (11261, 7709), (32430, 14712)
X(32429) = (1st Neuberg)-isogonal conjugate of-X(6194)
X(32429) = (1st Ehrmann)-anticomplement of-X(24256)
X(32429) = X(9821)-of-1st Brocard triangle


X(32430) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: ANTI-EULER, 1st BROCARD-REFLECTED, AND 2nd NEUBERG

Barycentrics    3*(SA+14*SW)*S^6+(30*SA^2-57*SB*SC+19*SW^2)*SW*S^4+(11*SA^2-57*SB*SC-4*SW^2)*SW^3*S^2-3*SB*SC*SW^5 : :

X(32430) lies on these lines: {20,185}, {8150,14881}, {10796,11261}

X(32430) = reflection of X(32429) in X(14712)


X(32431) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: ANTI-ORTHOCENTROIDAL, EXCENTRAL, AND FEUERBACH

Barycentrics    a^5+b*c*a^3+(b^3+c^3)*a^2-(b^2-c^2)^2*a-(b^2-c^2)^2*(b+c) : :
X(32431) = 6*X(381)-X(3019)

X(32431) lies on these lines: {2,17190}, {3,31872}, {4,9}, {5,572}, {6,13}, {7,24224}, {8,24048}, {30,1213}, {37,18480}, {80,2171}, {191,21014}, {219,24045}, {284,6841}, {355,4053}, {391,3839}, {403,1474}, {429,15946}, {430,2328}, {517,21873}, {594,18357}, {604,7741}, {941,5560}, {1030,13743}, {1100,9955}, {1400,3585}, {1568,22133}, {1765,6839}, {1781,21044}, {1999,10478}, {2160,22798}, {2173,7110}, {2178,18761}, {2268,7951}, {2269,3583}, {2285,10826}, {3686,18483}, {3723,28204}, {3845,17330}, {4034,31162}, {4253,6849}, {4909,5712}, {5080,21061}, {5086,21078}, {5257,31673}, {5443,17440}, {5747,6866}, {6894,18865}, {6996,17307}, {7377,17352}, {7384,17300}, {8287,24884}, {9355,13610}, {9665,21785}, {10446,17343}, {10883,19642}, {12699,17275}, {13478,14534}, {15971,26079}, {16777,18525}, {16884,18493}, {17205,28091}, {17258,29069}, {17362,22791}, {17748,27871}, {20546,24267}, {21773,26321}, {24271,27688}

X(32431) = (2nd Fuhrmann)-isotomic conjugate of-X(22791)
X(32431) = intersection of the Brocard axes of these triangles: anti-orthocentroidal, 2nd extouch and Feuerbach
X(32431) = intersection of the Brocard axes of these triangles: anti-orthocentroidal, Feuerbach and 2nd Zaniah
X(32431) = inverse-in-Kiepert-hyperbola of X(3017)
X(32431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 5816, 573), (13, 14, 3017)


X(32432) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES, EULER, AND OUTER-VECTEN

Barycentrics    ((b^2+c^2)*a^2-b^4-c^4)*a^2+(2*(b^2+c^2)*a^2-4*b^4+4*b^2*c^2-4*c^4)*S : :
X(32432) = X(6566)-5*X(31275) = X(6567)+3*X(31173)

X(32432) lies on these lines: {2,2459}, {5,141}, {316,2460}, {371,7773}, {372,7887}, {487,23259}, {641,3070}, {642,13449}, {1691,11314}, {2456,6290}, {3102,7752}, {3103,5025}, {6567,31173}, {7825,9738}, {7862,9739}, {13665,22623}

X(32432) = midpoint of X(316) and X(2460)
X(32432) = reflection of X(32435) in X(625)
X(32432) = complement of X(2459)
X(32432) = (outer-Vecten)-isogonal conjugate of-X(13926)
X(32432) = (1st Brocard)-complement of-X(2459)
X(32432) = inverse of X(639) in the nine-point circle
X(32432) = X(6567)-of-outer-Vecten triangle
X(32432) = intersection of the Brocard axes of these triangles: 3rd anti-tri-squares, medial and outer-Vecten
X(32432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 5031, 32435), (2039, 2040, 639)


X(32433) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES, 4th TRI-SQUARES, AND INNER-VECTEN

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

X(32433) lies on these lines: {30,511}, {371,7851}, {486,489}, {487,23259}, {642,3071}, {2459,12221}, {3103,7921}, {6119,18762}, {6316,12601}

X(32433) = isogonal conjugate of X(32434)


X(32434) = ISOGONAL CONJUGATE OF X(32433)

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

X(32434) lies on the circumcircle and the line {110,32074}

X(32434) = isogonal conjugate of X(32433)


X(32435) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES, EULER, AND INNER-VECTEN

Barycentrics    -2*((b^2+c^2)*a^2-2*b^4+2*b^2*c^2-2*c^4)*S+((b^2+c^2)*a^2-b^4-c^4)*a^2 : :
X(32435) = X(6566)+3*X(31173) = X(6567)-5*X(31275)

X(32435) lies on these lines: {2,2460}, {5,141}, {316,2459}, {371,7887}, {372,7773}, {488,23249}, {641,13449}, {642,3071}, {1691,11313}, {2456,6289}, {3102,5025}, {3103,7752}, {6566,31173}, {7825,9739}, {7862,9738}, {13785,22594}

X(32435) = midpoint of X(316) and X(2459)
X(32435) = reflection of X(32432) in X(625)
X(32435) = (inner-Vecten)-isogonal conjugate of-X(13873)
X(32435) = (1st Brocard)-complement of-X(2460)
X(32435) = complement of X(2460)
X(32435) = inverse of X(640) in the nine-point circle
X(32435) = intersection of the Brocard axes of these triangles: 4th anti-tri-squares, medial and inner-Vecten
X(32435) = X(6567)-of-inner-Vecten triangle
X(32435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 5031, 32432), (2039, 2040, 640)


X(32436) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES, 3rd TRI-SQUARES, AND OUTER-VECTEN

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

X(32436) lies on these lines: {30,511}, {187,13879}, {372,7851}, {485,490}, {488,23249}, {641,3070}, {2460,12222}, {3102,7921}, {6118,18538}, {6312,12602}

X(32436) = isogonal conjugate of X(32437)


X(32437) = ISOGONAL CONJUGATE OF X(32436)

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

X(32437) lies on the circumcircle and the line {110,11199}

X(32437) = isogonal conjugate of X(32436)


X(32438) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: AAOA, AOA, AND 1st HYACINTH

Barycentrics    (SB+SC)*(3*S^4-(6*R^2*(8*R^2+3*SA-4*SW)-5*SA^2+2*SB*SC+3*SW^2)*S^2+(4*R^2-SW)*(6*R^2+SA-2*SW)*SA*SW) : :

X(32438) lies on these lines: {30,511}, {74,1303}, {97,110}, {113,130}, {125,129}, {265,6528}, {1511,22052}, {5504,8612}, {12310,22551}, {17838,22552}, {21649,21661}

X(32438) = isogonal conjugate of X(32439)


X(32439) = ISOGONAL CONJUGATE OF X(32438)

Barycentrics    (3*S^4-(6*R^2*(8*R^2+3*SB-4*SW)-5*SB^2+2*SA*SC+3*SW^2)*S^2+(4*R^2-SW)*(6*R^2+SB-2*SW)*SB*SW)*(3*S^4-(6*R^2*(8*R^2+3*SC-4*SW)-5*SC^2+2*SA*SB+3*SW^2)*S^2+(4*R^2-SW)*(6*R^2+SC-2*SW)*SC*SW) : :

X(32439) lies on the circumcircle and these lines: {30,1303}, {418,476}, {436,1304}, {523,1298}, {2713,12022}, {8613,10420}

X(32439) = isogonal conjugate of X(32438)


X(32440) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: EXCENTERS-MIDPOINTS, GARCIA-REFLECTION AND 2nd SCHIFFLER

Barycentrics    a*(2*(b+c)*a^7-(7*b^2+8*b*c+7*c^2)*a^6+(b+c)*(3*b^2+26*b*c+3*c^2)*a^5+2*(6*b^4+6*c^4-(20*b^2+19*b*c+20*c^2)*b*c)*a^4-4*(b+c)*(b^2-b*c-3*c^2)*(3*b^2+b*c-c^2)*a^3-(3*b^6+3*c^6-(44*b^4+44*c^4-53*(b^2+c^2)*b*c)*b*c)*a^2+(b^2-c^2)*(b-c)*(7*b^4+7*c^4-2*(10*b^2-3*b*c+10*c^2)*b*c)*a-2*(b^2-c^2)^2*(b^2-b*c+c^2)^2) : :

X(32440) lies on these lines: {8,18811}, {30,511}

X(32440) = isogonal conjugate of X(32441)


X(32441) = ISOGONAL CONJUGATE OF X(32440)

Barycentrics    a*(2*a^8-(7*b+4*c)*a^7+(3*b^2+27*b*c+2*c^2)*a^6+(12*b^3+4*c^3-(44*b+19*c)*b*c)*a^5-(12*b^4+8*c^4-(4*b^2+53*b*c-c^2)*b*c)*a^4-(3*b^5-4*c^5-(40*b^3-52*b^2*c-c^3)*b*c)*a^3+(b-c)*(7*b^5-2*c^5-(22*b^3-17*c^3-4*(4*b-9*c)*b*c)*b*c)*a^2-(b^2-c^2)*(b-c)*(2*b^4+4*c^4-(6*b^2-25*b*c+23*c^2)*b*c)*a-(b^2-c^2)^2*(b-c)*(b-2*c)*(2*b-c)*c)*(2*a^8-(4*b+7*c)*a^7+(2*b^2+27*b*c+3*c^2)*a^6+(4*b^3+12*c^3-(19*b+44*c)*b*c)*a^5-(8*b^4+12*c^4+(b^2-53*b*c-4*c^2)*b*c)*a^4+(4*b^5-3*c^5-(b^3+52*b*c^2-40*c^3)*b*c)*a^3+(b-c)*(2*b^5-7*c^5-(17*b^3-22*c^3-4*(9*b-4*c)*b*c)*b*c)*a^2-(b^2-c^2)*(b-c)*(4*b^4+2*c^4-(23*b^2-25*b*c+6*c^2)*b*c)*a+(b^2-c^2)^2*(b-c)*(b-2*c)*(2*b-c)*b) : :

X(32441) lies on the circumcircle and these lines: {}

X(32441) = isogonal conjugate of X(32440)
X(32441) = X(99)-of-3rd mixtilinear triangle


X(32442) = REFLECTION OF X(6786) IN X(27088)

Barycentrics    a^2*(a^4*b^4 - a^2*b^6 - 8*a^4*b^2*c^2 + 4*a^2*b^4*c^2 + b^6*c^2 + a^4*c^4 + 4*a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6) : :
X(32442) = 4 X[187] - X[5167],X[6787] - 3 X[26613]

X(32442) lies on the cubic K1099 and these lines: {30, 6784}, {187, 237}, {376, 511}, {1691, 19136}, {2080, 8717}, {3111, 3849}, {6179, 14135}, {6786, 27088}, {6787, 26613}, {14830, 14915}

X(32442) = reflection of X(6786) in X(27088)


X(32443) = WALSMITH-LEMOINE POINT

Barycentrics    Sqrt[2*a^8 - 3*a^6*b^2 + 2*a^4*b^4 - 3*a^2*b^6 + 2*b^8 - 3*a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 + 2*a^4*c^4 + 2*a^2*b^2*c^4 + 2*b^4*c^4 - 3*a^2*c^6 - 3*b^2*c^6 + 2*c^8 + 2*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)]*((-5*a^4 + 4*a^2*b^2 + b^4 + 4*a^2*c^2 - 2*b^2*c^2 + c^4)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4] + 4*(2*a^2 - b^2 - c^2)*S^2) + (b^2 - c^2)*(13*a^8 - 21*a^6*b^2 + a^4*b^4 + 9*a^2*b^6 - 2*b^8 - 21*a^6*c^2 + 43*a^4*b^2*c^2 - 17*a^2*b^4*c^2 + 3*b^6*c^2 + a^4*c^4 - 17*a^2*b^2*c^4 - 2*b^4*c^4 + 9*a^2*c^6 + 3*b^2*c^6 - 2*c^8 - 8*(2*a^2 - b^2 - c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S^2) : :

See the preamble just before X(32215). The connection with the Lemoine point (X(6), the symmedian point) is that X(32443)-of-Walsmith-Lemoine-triangle = X(6); see the preamble just before X(32217). Contributed by Peter Moses, May 6, 2019.

X(32443) lies on the circumcircle and on no lines X(i)X(j) for 0 < i < j < 32444.


X(32444) = X(2)X(3)∩X(39)X(6000)

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

As a point on the Euler line, X(32444) has Shinagawa coefficients (EF+F2+S2,2E2+EF-F2 -S2).

X(32444) lies on these lines: {2, 3}, {39, 6000}, {217, 9605}, {3095, 13754}, {3331, 3426}, {4550, 5167}, {9155, 16261}, {11171, 14915}, {12294, 30258}, {18440, 20794}

X(32444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 381, 11328}, {3, 12083, 21512}, {376, 14096, 3}, {378, 3148, 3}


X(32445) = X(3)X(1625)∩X(4)X(6)

Barycentrics    a^2*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6) : :
X(32445) = 3 X[154] - 2 X[15270]

X(32445) lies on the cubics K622 and K1100 and also on these lines: {3, 1625}, {4, 6}, {20, 3289}, {32, 1971}, {39, 6000}, {64, 5013}, {112, 1614}, {154, 237}, {159, 3499}, {172, 10535}, {184, 1968}, {185, 232}, {187, 10282}, {206, 1691}, {216, 5907}, {221, 16781}, {230, 16252}, {389, 3199}, {394, 7750}, {512, 3202}, {574, 3357}, {1384, 14530}, {1506, 20299}, {1660, 2056}, {1914, 26888}, {1993, 7823}, {2052, 27359}, {2076, 11674}, {2174, 8761}, {2176, 10537}, {2275, 7355}, {2276, 6285}, {2393, 13330}, {2548, 14216}, {2549, 5878}, {2777, 7756}, {3016, 7746}, {3051, 11206}, {3094, 12502}, {3224, 14601}, {3269, 6241}, {3566, 10685}, {3815, 6247}, {5023, 17821}, {5024, 13093}, {5033, 23042}, {5038, 12202}, {5206, 11202}, {5301, 7113}, {5475, 18381}, {6225, 7738}, {7736, 12324}, {7737, 9833}, {7747, 18400}, {7748, 22802}, {7755, 14862}, {7904, 15066}, {8571, 13406}, {8778, 9412}, {9291, 9308}, {9418, 11325}, {9419, 11257}, {9574, 9899}, {9597, 12940}, {9598, 12950}, {9605, 12315}, {9863, 11441}, {9985, 13236}, {10060, 31448}, {10192, 21001}, {10311, 26883}, {10312, 14157}, {10533, 12963}, {10534, 12968}, {10574, 15355}, {10575, 14961}, {10606, 15815}, {10790, 27374}, {11204, 15515}, {12111, 22240}, {14264, 18573}, {15068, 32151}, {15305, 26216}, {18388, 27371}, {18621, 21788}, {19780, 30403}, {19781, 30402}, {20775, 31382}, {20965, 32064}, {23128, 32139}, {23329, 31455}, {30435, 32063}

X(32445) = isogonal conjugate of the isotomic conjugate of X(3164)
X(32445) = isogonal conjugate of the polar conjugate of X(3168)
X(32445) = polar conjugate of the isotomic conjugate of X(6638)
X(32445) = X(i)-Ceva conjugate of X(j) for these (i,j): {184, 6}, {1968, 3053}, {3164, 6638}
X(32445) = X(3168)-cross conjugate of X(6)
X(32445) = X(75)-isoconjugate of X(1988)
X(32445) = crosspoint of X(3164) and X(3168)
X(32445) = crossdifference of every pair of points on line {520, 6130}
X(32445) = tangential-isotomic conjugate of X(159)
X(32445) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 3168}, {4, 6638}, {5, 26887}, {6, 3164}
X(32445) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {32, 1988}, {3164, 76}, {3168, 264}, {6638, 69}, {26887, 95}
X(32445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 217, 6}, {32, 6759, 1971}, {112, 1614, 14585}, {184, 1968, 1970}, {217, 3331, 4}, {1181, 2207, 6}, {2211, 6776, 6}, {12111, 22240, 22416}, {12964, 12970, 19149}


X(32446) = X(2)X(2124)∩X(10)X(971)

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

See Angel Montesdeoca, Hyacinthos 29006.

X(32446) lies on these lines: {2,2124}, {10,971}, {142,10004}, {279,19605}, {2391,3452}, {6706,20205}

X(32446) = complement of X(2124)
X(32446) = X(i)-complementary conjugate of X(j) for these (i,j): {55, 17113}, {2125, 10}, {8917, 142}


X(32447) = MIDPOINT OF X(262) AND X(7757)

Barycentrics    a^2*(a^4*b^2 - 3*a^2*b^4 + 2*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 + 2*c^6) : :
Trilinears    cos A - 2 cos(A + 2ω) : :
X(32447) = X[3] - 4 X[39],X[3] + 2 X[3095],7 X[3] - 4 X[5188],5 X[3] - 2 X[9821],2 X[5] + X[194],4 X[5] - X[13108],2 X[39] + X[3095],7 X[39] - X[5188],10 X[39] - X[9821],2 X[76] - 5 X[1656],X[76] - 4 X[11272],4 X[140] - X[12251],2 X[194] + X[13108],5 X[262] - 2 X[22681],X[381] + 2 X[7757],5 X[381] - 4 X[22681],X[382] + 2 X[11257],X[382] - 4 X[14881],X[1351] + 2 X[3094],X[1482] + 2 X[12782],2 X[1569] + X[6321],5 X[1656] - 8 X[11272],2 X[1916] + X[13188],7 X[3090] - X[20081],7 X[3095] + 2 X[5188],5 X[3095] + X[9821],7 X[3526] - 10 X[7786],8 X[3628] - 5 X[31276],7 X[3851] - 4 X[6248],8 X[3934] - 11 X[5070],3 X[5054] - 2 X[22712],3 X[5055] - 2 X[7697],11 X[5056] + X[20105],10 X[5188] - 7 X[9821],2 X[7709] + X[22728],5 X[7757] + 2 X[22681],2 X[7838] + X[32152],2 X[7976] + X[12645],4 X[9466] - 7 X[15703],X[9902] - 4 X[9956],2 X[11152] + X[12355],X[11257] + 2 X[14881],3 X[14269] - 4 X[22682],3 X[15688] - 2 X[22676],5 X[15694] - 4 X[15819],4 X[18583] - X[18906].

Let X be a point on the 2nd Brocard circle. As X varies, the locus of X(381) of triangle XPU(1) is a circle with center X(32447). (Randy Hutson, June 7, 2019)

Let (O1) and (O2) be the circles that are the loci of the 1st and 2nd Isogonic Centers, respectively, in a Brocard porism (triangles sharing circumcircle and Brocard inellipse with ABC). The center of (O1) is X(3107). The center of (O2) is X(3106). The insimilicenter of (O1) and (O2) is X(6), and the exsimilicenter is X(32447). (Randy Hutson, June 7, 2019)

X(32447) lies on these lines: {2, 8179}, {3, 6}, {5, 194}, {30, 7709}, {76, 1656}, {99, 10796}, {140, 7806}, {237, 11002}, {262, 381}, {382, 11257}, {517, 3097}, {538, 5055}, {549, 6194}, {597, 31958}, {599, 11261}, {698, 14561}, {726, 5886}, {730, 5790}, {732, 13085}, {736, 9766}, {999, 12837}, {1482, 12782}, {1569, 5475}, {1916, 11170}, {3090, 20081}, {3202, 9704}, {3295, 12836}, {3399, 7754}, {3526, 7786}, {3534, 12156}, {3552, 32134}, {3628, 31276}, {3851, 6248}, {3934, 5070}, {5054, 22712}, {5056, 20105}, {5191, 11422}, {5355, 6036}, {5476, 8724}, {5640, 9155}, {5663, 32444}, {5969, 11165}, {6234, 18872}, {6390, 18583}, {6660, 6800}, {7753, 23698}, {7760, 10104}, {7781, 10358}, {7783, 18501}, {7813, 24206}, {7820, 25555}, {7838, 32152}, {7976, 12645}, {8704, 9178}, {9466, 15703}, {9654, 18982}, {9669, 13077}, {9902, 9956}, {10063, 31479}, {10247, 14839}, {10567, 30209}, {11152, 11317}, {11188, 20794}, {12150, 21166}, {12188, 13860}, {13586, 22521}, {14269, 22682}, {14981, 19130}, {15048, 15980}, {15072, 31952}, {15531, 23635}, {15688, 22676}, {15694, 15819}, {22650, 28204}

X(32447) = midpoint of X(262) and X(7757)
X(32447) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 11171}, {381, 262}, {599, 11261}, {6194, 549}, {31958, 597}
X(32447) = midpoint of centers of circles {{X(1340),X(3557),PU(1)}} and {{X(1341),X(3558),PU(1)}}
X(32447) = harmonic center of circumcircle and circle (X(6), |OK|/2)
X(32447) = Brocard-circle-inverse of X(11842)
X(32447) = 2nd-Brocard-circle-inverse of X(575)
X(32447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 11842}, {3, 1351, 9301}, {5, 194, 13108}, {39, 3094, 5024}, {39, 3095, 3}, {76, 11272, 1656}, {574, 576, 2080}, {574, 2080, 3}, {575, 18860, 26316}, {576, 8586, 1351}, {1351, 5024, 3}, {1670, 1671, 575}, {1689, 1690, 187}, {2021, 13330, 1384}, {3102, 3103, 13330}, {3106, 3107, 6}, {3398, 9737, 3}, {5640, 9155, 11328}, {7772, 9737, 3398}, {9605, 10983, 3}, {9734, 15520, 32}, {9821, 13334, 3}, {11257, 14881, 382}, {11482, 12313, 3311}, {11482, 12314, 3312}, {12054, 30270, 3}, {13343, 13344, 2076}, {14961, 30258, 3}, {18860, 26316, 3}


X(32448) = MIDPOINT OF X(3) AND X(194)

Barycentrics    2*a^6*b^2 - 3*a^4*b^4 + a^2*b^6 + 2*a^6*c^2 - 6*a^4*b^2*c^2 - b^6*c^2 - 3*a^4*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6 : :
X(32448) = 5 X[3] - 3 X[6194],X[3] - 3 X[7709],3 X[3] - X[12251],X[4] - 3 X[32447],3 X[5] - 2 X[6248],3 X[5] - 4 X[11272],3 X[39] - X[6248],3 X[39] - 2 X[11272],X[76] - 3 X[11171],2 X[140] - 3 X[11171],5 X[194] + 3 X[6194],X[194] + 3 X[7709],3 X[194] + X[12251],3 X[262] - 2 X[546],X[355] - 3 X[3097],3 X[549] - 4 X[13334],5 X[631] - X[20081],5 X[632] - 4 X[3934],X[3095] - 3 X[7757],X[3146] - 3 X[22728],7 X[3523] + X[20105],7 X[3526] - 5 X[31276],4 X[3530] - 3 X[22712],4 X[3628] - 3 X[7697],4 X[3628] - 5 X[7786],7 X[3857] - 6 X[22681],3 X[5050] - X[18906],2 X[5188] - 3 X[8703],X[6194] - 5 X[7709],9 X[6194] - 5 X[12251],3 X[7697] - 5 X[7786],9 X[7709] - X[12251],3 X[7757] + X[11257],2 X[9466] - 3 X[11539],X[9902] - 3 X[26446],X[11055] + 2 X[12100],3 X[13331] - 2 X[18583],2 X[14711] - 5 X[15713],7 X[14869] - 6 X[15819],5 X[15712] - 6 X[21163]

X(32448) lies on these lines: {2, 13108}, {3, 194}, {4, 32447}, {5, 39}, {6, 32134}, {30, 3095}, {54, 15093}, {76, 140}, {83, 23235}, {99, 3398}, {182, 698}, {262, 546}, {355, 3097}, {384, 10353}, {397, 3107}, {398, 3106}, {495, 18982}, {496, 13077}, {511, 550}, {538, 549}, {548, 9821}, {574, 10104}, {575, 5026}, {631, 20081}, {632, 3934}, {726, 1385}, {730, 5690}, {952, 12782}, {1483, 14839}, {1503, 32429}, {1595, 12143}, {2080, 7760}, {3094, 3564}, {3146, 22728}, {3523, 20105}, {3526, 31276}, {3530, 22712}, {3552, 11842}, {3627, 14881}, {3628, 7697}, {3857, 22681}, {5050, 18906}, {5171, 7798}, {5188, 8703}, {5844, 7976}, {5965, 7830}, {6287, 14692}, {7755, 14693}, {7772, 10796}, {7827, 8724}, {7828, 15561}, {7839, 11676}, {8370, 11152}, {9466, 11539}, {9737, 14880}, {9902, 26446}, {10079, 15325}, {11055, 12100}, {12836, 15171}, {12837, 18990}, {13331, 18583}, {14711, 15713}, {14869, 15819}, {15712, 21163}, {19522, 31036}

X(32448) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 194}, {3095, 11257}
X(32448) = reflection of X(i) in X(j) for these lines: {i,j}: {5, 39}, {76, 140}, {3627, 14881}, {6248, 11272}, {9821, 548}
X(32448) = complement of X(13108)
X(32448) = inverse-in-circle-{{X(3102),X(3103),PU(1)}} of X(115)
X(32448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 6248, 11272}, {76, 11171, 140}, {194, 7709, 3}, {3102, 3103, 115}, {6248, 11272, 5}, {7697, 7786, 3628}, {7757, 11257, 3095}, {32470, 32471, 6}


X(32449) = MIDPOINT OF X(6) AND X(194)

Barycentrics    (b^2 + c^2)*(2*a^4 + a^2*b^2 + a^2*c^2 - b^2*c^2) : :
X(32449) = 3 X[6] - X[18906],3 X[39] - 2 X[10007],3 X[39] - X[14994],X[76] - 3 X[13331],3 X[141] - 4 X[10007],3 X[141] - 2 X[14994],3 X[194] + X[18906],3 X[597] - 2 X[24256],X[1350] - 3 X[7709],X[1352] - 3 X[32447],X[3094] - 3 X[7757],3 X[3097] - X[3416],2 X[3589] - 3 X[13331],5 X[3618] - X[20081],2 X[5052] - 3 X[8584],3 X[5085] - X[12251],X[13108] - 3 X[14561],4 X[13334] - 3 X[21167]}

X(32449) lies on these lines: {6, 194}, {30, 32429}, {39, 141}, {76, 3589}, {99, 12212}, {182, 7798}, {385, 5116}, {427, 17949}, {511, 550}, {524, 3094}, {538, 597}, {726, 1386}, {736, 15048}, {1078, 12055}, {1100, 17760}, {1350, 7709}, {1352, 32447}, {1503, 3095}, {1569, 5052}, {1691, 7760}, {1916, 12830}, {2076, 7783}, {2782, 5480}, {3051, 4576}, {3097, 3416}, {3106, 23000}, {3107, 23009}, {3231, 31088}, {3329, 24273}, {3618, 20081}, {3867, 12143}, {4074, 19568}, {5017, 31859}, {5031, 7764}, {5039, 7781}, {5085, 12251}, {5092, 7805}, {5103, 5254}, {5207, 13571}, {5305, 8149}, {5306, 5976}, {5846, 12782}, {6309, 7789}, {7754, 8177}, {7766, 10335}, {7792, 9865}, {7838, 29012}, {7976, 9053}, {8024, 11205}, {8267, 20965}, {8891, 10191}, {9605, 31981}, {11257, 29181}, {13108, 14561}, {13334, 21167}, {20583, 22486}, {31406, 32189}

X(32449) = midpoint of X(6) and X(194)
X(32449) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 3589}, {141, 39}, {14994, 10007}, {22486, 20583}
X(32449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 14994, 10007}, {76, 13331, 3589}, {7839, 12215, 6}, {10007, 14994, 141}
X(32449) = X(14617)-Ceva conjugate of X(141)
X(32449) = crossdifference of every pair of points on line {3221, 18105}
X(32449) = barycentric product X(i)*X(j) for these lines: {i,j}: {141, 7766}, {3051, 10010}, {4576, 25423}, {10335, 14617}
X(32449) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {1634, 25424}, {7766, 83}


X(32450) = MIDPOINT OF X(39) AND X(194)

Barycentrics    3*a^2*b^2 + 3*a^2*c^2 - 2*b^2*c^2 : :
X(32450) = 3 X[2] - 5 X[39],9 X[2] - 5 X[76],3 X[2] + 5 X[194],6 X[2] - 5 X[3934],9 X[2] - 10 X[6683],X[2] - 5 X[7757],21 X[2] - 25 X[7786],7 X[2] - 5 X[9466],7 X[2] + 5 X[11055],11 X[2] - 5 X[14711],21 X[2] - 5 X[20081],27 X[2] + 5 X[20105],27 X[2] - 25 X[31239],33 X[2] - 25 X[31276],3 X[39] - X[76],3 X[39] - 2 X[6683],X[39] - 3 X[7757],7 X[39] - 5 X[7786],7 X[39] - 3 X[9466],7 X[39] + 3 X[11055],11 X[39] - 3 X[14711],7 X[39] - X[20081],9 X[39] + X[20105],9 X[39] - 5 X[31239],11 X[39] - 5 X[31276],X[76] + 3 X[194]

X(32450) lies on these lines: {2, 39}, {3, 7798}, {6, 7781}, {30, 7838}, {32, 31859}, {99, 5007}, {148, 7858}, {187, 7760}, {262, 3855}, {316, 13571}, {325, 7765}, {382, 3095}, {384, 5041}, {511, 550}, {524, 7830}, {543, 7745}, {546, 2782}, {574, 7754}, {620, 5305}, {625, 5254}, {626, 15048}, {698, 6329}, {726, 3636}, {730, 3626}, {732, 3631}, {736, 8357}, {1015, 25264}, {1078, 31652}, {1500, 25303}, {1569, 19687}, {1916, 14042}, {1975, 7772}, {2482, 5368}, {2549, 7759}, {2996, 31415}, {3244, 14839}, {3528, 5188}, {3529, 11257}, {3530, 13334}, {3552, 5008}, {3632, 12782}, {3734, 9605}, {3849, 7756}, {3851, 6248}, {3933, 4045}, {5013, 7751}, {5024, 7815}, {5079, 13108}, {5206, 14614}, {5319, 6337}, {5346, 16925}, {5355, 7807}, {5969, 20583}, {6179, 15513}, {6390, 6680}, {6459, 26340}, {6460, 26339}, {6655, 7845}, {6656, 7813}, {7738, 7758}, {7748, 7774}, {7750, 7890}, {7766, 7782}, {7773, 11648}, {7776, 7872}, {7778, 7902}, {7779, 7847}, {7784, 7916}, {7788, 7935}, {7789, 7829}, {7790, 7821}, {7791, 7848}, {7792, 7863}, {7793, 8589}, {7796, 7853}, {7802, 7837}, {7825, 9766}, {7826, 8356}, {7833, 7877}, {7835, 7920}, {7840, 7911}, {7841, 7903}, {7851, 7888}, {7856, 7891}, {7866, 7908}, {7871, 7933}, {7881, 7913}, {7896, 11287}, {7897, 7918}, {7898, 7949}, {7909, 7923}, {7910, 7946}, {7917, 7924}, {7919, 7947}, {7921, 14537}, {7941, 31173}, {7976, 20050}, {8716, 30435}, {9821, 15688}, {10299, 12251}, {11171, 15720}, {11174, 17130}, {11285, 17131}, {12263, 15808}, {14482, 18841}, {14881, 15687}, {15482, 22332}, {22330, 32134}

X(32450) = midpoint of X(i) and X(j) for these lines: {i,j}: {39, 194}, {7750, 7890}, {7756, 7762}, {9466, 11055}
X(32450) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 6683}, {3934, 39}
X(32450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7798, 7805}, {6, 7781, 7816}, {39, 76, 6683}, {39, 9466, 7786}, {76, 6683, 3934}, {99, 7839, 5007}, {194, 7757, 39}, {194, 20081, 11055}, {325, 7765, 7861}, {574, 7754, 7780}, {1975, 7772, 7804}, {2549, 7759, 7842}, {3552, 7894, 5008}, {3788, 5286, 7817}, {3926, 7739, 7834}, {3926, 7834, 7880}, {3933, 4045, 7849}, {3933, 9607, 4045}, {5013, 22253, 7751}, {5254, 7764, 625}, {5309, 7763, 7886}, {6655, 7905, 7845}, {6656, 7813, 7895}, {7738, 7758, 7761}, {7748, 7774, 7843}, {7758, 7761, 7882}, {7760, 7783, 187}, {7779, 7847, 7873}, {7781, 7816, 15301}, {7786, 11055, 20081}, {7786, 20081, 9466}, {7790, 7906, 7821}, {7791, 7855, 7848}, {7796, 7864, 7853}, {7797, 7799, 7874}, {7801, 7803, 7915}, {7827, 7836, 7852}, {7829, 14148, 7789}


X(32451) = MIDPOINT OF X(193) AND X(194)

Barycentrics    2*a^4*b^2 + 2*a^4*c^2 + a^2*b^2*c^2 - b^4*c^2 - b^2*c^4 : :
X(32451) = 3X[6] - 2 X[24256],3 X[76] - 4 X[24256],4 X[141] - 5 X[7786],2 X[141] - 3 X[13331],4 X[182] - 3 X[22712],3 X[262] - 2 X[1352],3 X[599] - 4 X[10007],3 X[1992] - 2 X[5052],3 X[1992] - X[18906],2 X[3094] - 3 X[7757],5 X[3618] - 4 X[3934],7 X[3619] - 8 X[6683],4 X[5052] - 3 X[22486],3 X[5093] - X[13108],3 X[5182] - 2 X[5976],2 X[5188] - 3 X[25406],2 X[6248] - 3 X[14853],3 X[7697] - 4 X[18583],3 X[7757] - 4 X[32449],5 X[7786] - 6 X[13331],3 X[10519] - 4 X[13334],X[11008] + 4 X[32450],X[11055] + 2 X[15534],3 X[11257] - 4 X[32429],X[11898] - 3 X[32447],X[12251] - 3 X[14912],2 X[12263] - 3 X[16475],2 X[13354] - 3 X[14912],2 X[18906] - 3 X[22486]

X(32451) lies on these lines: {2, 11175}, {6, 76}, {20, 185}, {32, 6309}, {39, 69}, {99, 5017}, {141, 7786}, {182, 385}, {262, 1352}, {287, 1993}, {305, 3051}, {384, 5039}, {518, 7976}, {524, 3094}, {538, 1992}, {542, 1916}, {599, 10007}, {698, 3629}, {730, 3751}, {736, 5028}, {1350, 31859}, {1351, 2782}, {1503, 7762}, {1569, 14645}, {1691, 6179}, {1692, 7805}, {2023, 9766}, {2024, 7763}, {2025, 3767}, {2076, 7782}, {3056, 25264}, {3060, 8267}, {3095, 3564}, {3098, 7783}, {3104, 23000}, {3105, 23009}, {3231, 11059}, {3266, 9463}, {3589, 7856}, {3618, 3934}, {3619, 6683}, {3763, 7909}, {3818, 7785}, {3926, 13357}, {3972, 4048}, {5031, 7814}, {5034, 7751}, {5038, 8177}, {5092, 7793}, {5093, 13108}, {5116, 7771}, {5182, 5976}, {5188, 25406}, {5207, 7759}, {5476, 19570}, {5847, 12782}, {5969, 8593}, {6248, 6392}, {7697, 18583}, {7766, 9865}, {7777, 24206}, {7823, 29012}, {7839, 9983}, {7926, 11646}, {7998, 31088}, {8878, 11550}, {9917, 19459}, {10519, 13334}, {11008, 32450}, {11898, 32447}, {12143, 12167}, {12251, 13354}, {12263, 16475}, {13877, 19103}, {13930, 19104}, {14467, 30739}, {14881, 18440}

X(32451) = midpoint of X(193) and X(194)
X(32451) = reflection of X(i) in X(j) for these lines: {i,j}: {69, 39}, {76, 6}, {3094, 32449}, {12251, 13354}, {13330, 3629}, {18440, 14881}, {18906, 5052}, {22486, 1992}
X(32451) = anticomplement of X(14994)
X(32451) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {263, 21289}, {2186, 1369}, {3402, 2896}
X(32451) = crosssum of X(1084) and X(3288)
X(32451) = crossdifference of every pair of points on line {688, 2451}
X(32451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 13331, 7786}, {1992, 18906, 5052}, {3094, 32449, 7757}, {4048, 12212, 3972}, {5052, 18906, 22486}, {6272, 19090, 76}, {6273, 19089, 76}, {12251, 14912, 13354}


X(32452) = MIDPOINT OF X(194) and X(315)

Barycentrics   a^2*(b^6 - a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 + c^6) : :
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 : :
Trilinears    2 sin(A + 2ω) (sin(A - 2ω) sin A + sin(B - 2ω) sin B + sin(C - 2ω) sin C) + (sin 2A + sin 2B + sin 2C) cos A : :
X(32452) = 4 X[3934] - 5 X[7867],4 X[6680] - 5 X[7786]

X(32452) lies on these lines: {2, 18806}, {3, 6}, {69, 31981}, {76, 115}, {99, 10350}, {183, 32189}, {194, 315}, {262, 1506}, {298, 6294}, {299, 6581}, {325, 8149}, {538, 7788}, {698, 3933}, {730, 4769}, {732, 7855}, {754, 7757}, {760, 12782}, {1015, 12836}, {1500, 12837}, {1569, 2794}, {1571, 3097}, {2023, 7746}, {2782, 7748}, {2979, 8623}, {3117, 20859}, {3202, 9696}, {3229, 3981}, {3735, 3865}, {3767, 12251}, {3788, 5976}, {3934, 7867}, {5149, 10349}, {5475, 14881}, {5969, 7801}, {6309, 7813}, {6680, 7786}, {7749, 22712}, {7768, 9983}, {7782, 10351}, {7795, 18906}, {7796, 9865}, {7810, 13085}, {7822, 24256}, {7836, 8782}, {7906, 10335}, {9466, 11318}, {9651, 18982}, {9664, 13077}, {9753, 31401}, {10000, 10333}, {11272, 31455}

X(32452) = midpoint of X(194) and X(315)
X(32452) = reflection of X(i) in X(j) for these lines: {i,j}: {32, 39}, {76, 626}
X(32452) = reflection of X(32) in line PU(1)
X(32452) = anticomplement of X(18806)
X(32452) = 2nd-Brocard-Circle-inverse of X(1691)
X(32452) = X(30254)-Ceva conjugate of X(512)
X(32452) = circle-{{X(3102),X(3103),PU(1)}}-inverse of X(182)
X(32452) = X(163)-isoconjugate of X(30492)
X(32452) = barycentric quotient X(523)/X(30492)
X(32452) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 30270, 5162}, {39, 5041, 13331}, {39, 5188, 2021}, {1569, 7756, 11257}, {1670, 1671, 1691}, {1689, 1690, 3398}, {2021, 5188, 5206}, {2458, 5028, 6}, {2562, 2563, 11171}, {3094, 3095, 39}, {3102, 3103, 182}, {5013, 32447, 39}, {5028, 30270, 32}, {13325, 13326, 3094}


X(32453) = MIDPOINT OF X(192) and X(194)

Barycentrics   a^3*b^3 + a^3*b^2*c + a^3*b*c^2 + a^3*c^3 - b^3*c^3 : :
X(32453) = X[3644] + 4 X[32450],4 X[3739] - 5 X[7786],4 X[3934] - 5 X[4687],5 X[4704] - X[20081],7 X[4751] - 8 X[6683],7 X[27268] - 5 X[31276]

X(32453) lies on these lines: {1, 87}, {2, 21443}, {37, 76}, {39, 75}, {42, 17486}, {511, 30273}, {518, 7976}, {536, 7757}, {538, 4664}, {561, 21814}, {579, 17034}, {700, 24696}, {716, 3774}, {730, 984}, {740, 12782}, {742, 3094}, {1045, 19566}, {1278, 26801}, {1575, 10009}, {1655, 9902}, {1921, 27091}, {2350, 17027}, {2782, 20430}, {3095, 29010}, {3097, 17759}, {3210, 17026}, {3550, 30661}, {3644, 32450}, {3739, 7786}, {3875, 24727}, {3934, 4687}, {3995, 17032}, {4660, 17493}, {4704, 20081}, {4751, 6683}, {6376, 21830}, {6382, 21877}, {8620, 30964}, {9055, 32449}, {16468, 30667}, {17028, 17495}, {17033, 17489}, {17262, 21788}, {24621, 27478}, {27268, 31276}, {27481, 31036}

X(32453) = midpoint of X(192) and X(194)
X(32453) = reflection of X(i) in X(j) for these lines: {i,j}: {75, 39}, {76, 37}
X(32453) = anticomplement of X(21443)
X(32453) = {X(192),X(19565)}-harmonic conjugate of X(1)


X(32454) = MIDPOINT OF X(149) and X(194)

Barycentrics    a*(a*b^2 - b^3 - a*b*c + a*c^2)*(a*b^2 - a*b*c + a*c^2 - c^3) : :
X(32454) = 2 X[119] - 3 X[262],4 X[3035] - 5 X[7786],3 X[3097] - X[5541],4 X[3934] - 5 X[31272],4 X[6713] - 3 X[22712],3 X[7709] - X[13199],2 X[12263] - 3 X[16173],X[12331] - 3 X[32447]

X(32454) lies on these lines: {3, 12199}, {6, 13194}, {11, 76}, {39, 100}, {80, 730}, {104, 511}, {106, 24516}, {119, 262}, {149, 194}, {528, 7757}, {538, 10707}, {726, 21630}, {952, 3095}, {1317, 12837}, {1320, 14839}, {1916, 2787}, {2530, 31129}, {2782, 10738}, {2802, 12782}, {3035, 7786}, {3045, 3202}, {3094, 9024}, {3097, 5541}, {3934, 31272}, {5533, 10079}, {5840, 11257}, {6713, 22712}, {7709, 13199}, {8068, 10063}, {9263, 23646}, {10742, 14881}, {12263, 16173}, {12331, 32447}, {13077, 13274}, {13273, 18982}

X(32454) = midpoint of X(149) and X(194)
X(32454) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 11}, {100, 39}, {10742, 14881}
X(32454) = {X(12836),X(12923)}-harmonic conjugate of X(76)


X(32455) = MIDPOINT OF X(6) and X(3629)

Barycentrics    -6*a^2 + b^2 + c^2 : :
X(32455) = 3 X[2] - 7 X[6],15 X[2] - 7 X[69],9 X[2] - 7 X[141],9 X[2] + 7 X[193],5 X[2] - 7 X[597],11 X[2] - 7 X[599],X[2] + 7 X[1992],6 X[2] - 7 X[3589],27 X[2] - 35 X[3618],57 X[2] - 49 X[3619],51 X[2] - 35 X[3620],3 X[2] + 7 X[3629],12 X[2] - 7 X[3631],39 X[2] - 35 X[3763],5 X[2] - 21 X[5032],3 X[2] + X[6144],9 X[2] - 14 X[6329],X[2] - 7 X[8584],33 X[2] + 7 X[11008],23 X[2] - 7 X[11160],19 X[2] - 7 X[15533],5 X[2] + 7 X[15534],39 X[2] - 7 X[20080],8 X[2] - 7 X[20582],2 X[2] - 7 X[20583],29 X[2] - 21 X[21356],25 X[2] - 21 X[21358],13 X[2] - 7 X[22165],X[5] - 3 X[15520],5 X[6] - X[69],3 X[6] - X[141],3 X[6] + X[193],5 X[6] - 3 X[597],11 X[6] - 3 X[599],X[6] + 3 X[1992],9 X[6] - 5 X[3618],19 X[6] - 7 X[3619],17 X[6] - 5 X[3620],7 X[6] - X[3630],4 X[6] - X[3631],13 X[6] - 5 X[3763],5 X[6] - 9 X[5032],7 X[6] + X[6144],3 X[6] - 2 X[6329],X[6] - 3 X[8584],11 X[6] + X[11008],23 X[6] - 3 X[11160],19 X[6] - 3 X[15533],5 X[6] + 3 X[15534],13 X[6] - X[20080],8 X[6] - 3 X[20582],2 X[6] - 3 X[20583],29 X[6] - 9 X[21356],25 X[6] - 9 X[21358],13 X[6] - 3 X[22165],X[66] - 3 X[23326],3 X[69] - 5 X[141],3 X[69] + 5 X[193],X[69] - 3 X[597],11 X[69] - 15 X[599],X[69] + 15 X[1992],2 X[69] - 5 X[3589],9 X[69] - 25 X[3618],19 X[69] - 35 X[3619],17 X[69] - 25 X[3620],X[69] + 5 X[3629],7 X[69] - 5 X[3630],4 X[69] - 5 X[3631],13 X[69] - 25 X[3763],X[69] - 9 X[5032],7 X[69] + 5 X[6144],3 X[69] - 10 X[6329],X[69] - 15 X[8584],11 X[69] + 5 X[11008],23 X[69] - 15 X[11160],19 X[69] - 15 X[15533],X[69] + 3 X[15534],13 X[69] - 5 X[20080],8 X[69] - 15 X[20582],2 X[69] - 15 X[20583],29 X[69] - 45 X[21356],5 X[69] - 9 X[21358],13 X[69] - 15 X[22165],5 X[141] - 9 X[597],11 X[141] - 9 X[599],X[141] + 9 X[1992],2 X[141] - 3 X[3589],3 X[141] - 5 X[3618],19 X[141] - 21 X[3619],17 X[141] - 15 X[3620],X[141] + 3 X[3629],7 X[141] - 3 X[3630],4 X[141] - 3 X[3631],13 X[141] - 15 X[3763],5 X[141] - 27 X[5032],7 X[141] + 3 X[6144],X[141] - 9 X[8584],11 X[141] + 3 X[11008],23 X[141] - 9 X[11160],19 X[141] - 9 X[15533],5 X[141] + 9 X[15534],13 X[141] - 3 X[20080],8 X[141] - 9 X[20582],2 X[141] - 9 X[20583],29 X[141] - 27 X[21356]

X(32455) lies on these lines: {2, 6}, {5, 15520}, {39, 3793}, {44, 17390}, {66, 23326}, {140, 15516}, {182, 15712}, {239, 7277}, {487, 6432}, {488, 6431}, {511, 548}, {518, 3635}, {536, 4856}, {542, 14893}, {545, 4852}, {575, 12108}, {576, 1353}, {594, 17120}, {625, 5305}, {648, 6748}, {698, 5052}, {742, 4726}, {894, 4399}, {895, 25329}, {1086, 17121}, {1100, 17332}, {1285, 8716}, {1350, 21735}, {1351, 1657}, {1352, 5072}, {1449, 4364}, {1743, 17243}, {1974, 15471}, {1990, 27377}, {2321, 28337}, {2325, 4889}, {2393, 21847}, {2854, 9969}, {3124, 10552}, {3564, 3850}, {3625, 4663}, {3633, 3751}, {3663, 28333}, {3686, 4472}, {3707, 28639}, {3729, 28309}, {3739, 4700}, {3758, 7227}, {3759, 4395}, {3818, 23046}, {3843, 5093}, {3875, 28297}, {3879, 4422}, {3912, 16671}, {3946, 4715}, {4357, 16668}, {4361, 7222}, {4363, 4371}, {4370, 17315}, {4393, 17334}, {4402, 4644}, {4405, 17118}, {4416, 16666}, {4478, 17363}, {4643, 16667}, {4665, 5839}, {4667, 17348}, {4691, 5847}, {4718, 9055}, {4725, 17355}, {4755, 4909}, {4851, 16670}, {4946, 9024}, {4966, 16477}, {4971, 17351}, {4991, 17771}, {5007, 7789}, {5008, 6390}, {5041, 7767}, {5092, 14891}, {5102, 6776}, {5111, 19695}, {5368, 8361}, {5596, 17813}, {5965, 12812}, {6467, 8705}, {6593, 32114}, {6664, 31506}, {6749, 9308}, {7238, 17364}, {7745, 7760}, {7762, 7790}, {7798, 18907}, {7801, 14075}, {7819, 7890}, {7839, 14712}, {7877, 7937}, {7882, 8364}, {7949, 8363}, {8787, 14928}, {9019, 32366}, {9027, 9822}, {9607, 20065}, {9973, 15531}, {10022, 28634}, {10115, 32284}, {10168, 14890}, {10192, 21970}, {11179, 15689}, {11216, 15583}, {11422, 32269}, {11477, 14912}, {12017, 15706}, {12161, 16252}, {12212, 13196}, {13330, 32449}, {14032, 18906}, {14892, 18358}, {15492, 29574}, {15585, 32218}, {15684, 31670}, {15826, 32220}, {16176, 25320}, {17014, 17255}, {17246, 20072}, {17340, 17377}, {17347, 17395}, {17350, 17388}, {21639, 26926}, {25331, 32255}, {25488, 32127}

X(32455) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 3629}, {141, 193}, {576, 1353}, {597, 15534}, {895, 25329}, {1351, 8550}, {1992, 8584}, {3630, 6144}, {7798, 18907}, {13330, 32449}, {15826, 32220}
X(32455) = reflection of X(i) in X(j) for these lines: {i,j}: {140, 15516}, {141, 6329}, {3589, 6}, {3631, 3589}, {18583, 22330}, {20583, 8584}
X(32455) = complement of X(3630)
X(32455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6144, 3630}, {6, 69, 597}, {6, 141, 6329}, {6, 193, 141}, {6, 1992, 3629}, {6, 6144, 2}, {6, 15534, 69}, {69, 5032, 6}, {141, 3629, 193}, {141, 6329, 3589}, {597, 8584, 5032}, {894, 4969, 4399}, {1992, 5032, 15534}, {3589, 3631, 20582}, {3589, 20583, 6}, {3629, 8584, 6}, {3629, 20583, 3631}, {3758, 17362, 7227}, {3759, 17365, 4395}, {3763, 20080, 22165}, {3879, 16669, 4422}, {4416, 16666, 17045}, {5032, 15534, 597}, {7585, 26340, 591}, {7586, 26339, 1991}, {17330, 17379, 6707}, {17363, 17369, 4478}, {17364, 17366, 7238}
X(32455) = crosssum of X(6) and X(15513)
X(32455) = crossdifference of every pair of points on line {512, 15514}


X(32456) = MIDPOINT OF X(99) and X(187)

Barycentrics    4*a^4 - 3*a^2*b^2 - 3*a^2*c^2 + 2*b^2*c^2 : :
X(32456) = 3 X[99] + X[385],X[99] + 3 X[13586],3 X[187] - X[385],X[187] - 3 X[13586],2 X[187] + X[15301],X[230] - 3 X[27088],X[325] - 3 X[2482],X[325] + 3 X[8598],X[385] - 9 X[13586],2 X[385] + 3 X[15301],X[671] - 3 X[5215],3 X[1692] - X[10754],3 X[2482] + X[6781],5 X[5026] - 3 X[13196],X[5107] - 3 X[5182],X[6781] - 3 X[8598],3 X[7799] - X[7845],3 X[7799] + X[14712],5 X[7925] + 3 X[9855],5 X[7925] - 3 X[31173],X[8352] - 3 X[9167],X[8591] + 3 X[26613],3 X[10150] - 4 X[22247],X[11676] + 3 X[21166],X[13449] - 3 X[15561],6 X[13586] + X[15301],3 X[14041] - 5 X[31275],3 X[14568] + X[20094],X[18860] - 3 X[21166],3 X[21445] + X[23235]

X(32456) lies on these lines: {2, 8589}, {3, 3734}, {20, 3788}, {30, 620}, {32, 31859}, {39, 3552}, {76, 15513}, {83, 31652}, {99, 187}, {126, 7426}, {141, 8703}, {183, 8588}, {230, 543}, {232, 4235}, {325, 2482}, {376, 7761}, {382, 7862}, {384, 6683}, {439, 3767}, {511, 5026}, {524, 14148}, {548, 7789}, {550, 626}, {574, 1003}, {671, 5215}, {754, 6390}, {1153, 11164}, {1384, 7798}, {1495, 5108}, {1506, 19687}, {1657, 7825}, {1692, 10754}, {1975, 5206}, {2030, 5969}, {2549, 7817}, {3053, 7781}, {3363, 7619}, {3522, 7795}, {3528, 7800}, {3534, 7778}, {3926, 7882}, {4027, 10631}, {4045, 8369}, {4048, 14810}, {4226, 11052}, {5007, 7783}, {5008, 7757}, {5023, 7751}, {5031, 29323}, {5107, 5182}, {5118, 9418}, {5148, 15452}, {5149, 11676}, {6337, 7759}, {6636, 15822}, {6655, 7874}, {6658, 7769}, {6704, 19697}, {7492, 30749}, {7603, 11361}, {7618, 7736}, {7622, 11159}, {7748, 7886}, {7750, 7863}, {7756, 7807}, {7763, 7843}, {7770, 15515}, {7771, 9466}, {7777, 14537}, {7784, 15696}, {7791, 7915}, {7799, 7845}, {7801, 7848}, {7802, 7821}, {7808, 15815}, {7820, 8356}, {7833, 7835}, {7836, 7873}, {7844, 11288}, {7847, 7852}, {7865, 15688}, {7870, 7898}, {7897, 11057}, {7910, 7945}, {7925, 9855}, {8176, 11147}, {8182, 15589}, {8352, 9167}, {8591, 26613}, {8667, 15655}, {9341, 25264}, {10150, 22247}, {11286, 15482}, {13349, 22689}, {13350, 22687}, {13449, 15561}, {14035, 31455}, {14041, 31275}, {14568, 20094}, {14762, 15491}, {14767, 18570}, {14928, 15993}, {15031, 16923}, {15300, 22329}, {15810, 16986}, {16589, 17693}, {21445, 23235}, {21937, 24275}, {26276, 31128}

X(32456) = midpoint of X(i) and X(j) for these lines: {i,j}: {99, 187}, {325, 6781}, {2482, 8598}, {7845, 14712}, {9855, 31173}, {11676, 18860}, {14928, 15993}, {15300, 22329}
X(32456) = reflection of X(i) in X(j) for these lines: {i,j}: {625, 620}, {15301, 99}
X(32456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7816, 3934}, {20, 3788, 7842}, {99, 13586, 187}, {325, 8598, 6781}, {548, 7789, 7830}, {574, 1003, 7804}, {1384, 8716, 7798}, {1975, 5206, 7780}, {2482, 6781, 325}, {3053, 7781, 7805}, {3552, 7782, 39}, {7748, 16925, 7886}, {7750, 7863, 7895}, {7756, 7807, 7861}, {7789, 7830, 7849}, {7799, 14712, 7845}, {7801, 14907, 7848}, {7802, 7891, 7821}, {7833, 7835, 7853}, {11676, 21166, 18860}


X(32457) = MIDPOINT OF X(148) and X(187)

Barycentrics   a^2*b^2 + 2*b^4 + a^2*c^2 - 6*b^2*c^2 + 2*c^4 : :
X(32457) = 3 X[115] - X[325],5 X[115] - X[7813],X[148] + 3 X[14568],X[187] - 3 X[14568],5 X[230] - 3 X[27088],X[316] + 3 X[19570],2 X[325] - 3 X[625],5 X[325] - 3 X[7813],X[385] + 3 X[671],5 X[385] + 3 X[8597],5 X[625] - 2 X[7813],5 X[671] - X[8597],3 X[5215] - X[8591],4 X[5461] - 3 X[10150],3 X[5461] - X[14148],X[6781] - 3 X[22329],X[7779] + 3 X[11054],X[7779] - 3 X[31173],3 X[7799] - 5 X[31275],X[7845] - 3 X[14041],5 X[7925] - 9 X[9166],X[8596] + 3 X[26613],9 X[10150] - 4 X[14148],3 X[14651] - X[18860]}

X(32457) lies on these lines: {4, 7805}, {5, 32450}, {6, 18546}, {39, 16921}, {76, 7849}, {115, 325}, {148, 187}, {183, 11648}, {230, 543}, {316, 19570}, {381, 7798}, {385, 671}, {546, 7838}, {620, 15301}, {754, 15480}, {1975, 7886}, {2996, 3767}, {3314, 14711}, {3629, 3845}, {3734, 7817}, {3934, 4045}, {5008, 11361}, {5025, 7895}, {5041, 16044}, {5215, 8591}, {5304, 7620}, {5309, 7804}, {5346, 14035}, {5355, 8370}, {5461, 10150}, {6390, 6722}, {6392, 7759}, {6683, 7765}, {6781, 22329}, {7603, 7757}, {7615, 7736}, {7617, 31489}, {7748, 7780}, {7751, 7842}, {7754, 7843}, {7761, 15589}, {7766, 14537}, {7774, 18424}, {7775, 22253}, {7779, 11054}, {7781, 13881}, {7790, 9466}, {7799, 31275}, {7814, 20105}, {7821, 20081}, {7825, 7882}, {7839, 15031}, {7841, 7848}, {7844, 7880}, {7845, 14041}, {7851, 7915}, {7852, 17128}, {7855, 14063}, {7864, 31239}, {7873, 17129}, {7877, 14062}, {7908, 11318}, {7917, 14045}, {7925, 9166}, {8589, 17004}, {8596, 26613}, {11174, 14762}, {14651, 18860}, {15048, 15491}

X(32457) = midpoint of X(i) and X(j) for these lines: {i,j}: {148, 187}, {11054, 31173}
X(32457) = reflection of X(i) in X(j) for these lines: {i,j}: {625, 115}, {6390, 6722}, {15301, 620}
X(32457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 7861, 7849}, {148, 14568, 187}, {5309, 11185, 7804}, {7841, 17131, 7848}, {7851, 17130, 7915}


X(32458) = MIDPOINT OF X(99) and X(315)

Barycentrics   (a^2*b^2 - b^4 + a^2*c^2 - c^4)^2 : :
X(32458) = X[5989] + 3 X[7788],4 X[6680] - 5 X[31274],4 X[6722] - 5 X[7867]

X(32458) lies on these lines: {2, 2987}, {20, 99}, {32, 620}, {69, 98}, {76, 115}, {114, 325}, {132, 877}, {141, 2023}, {183, 6036}, {305, 1972}, {439, 20065}, {524, 12829}, {542, 5989}, {543, 7818}, {670, 15526}, {736, 1569}, {754, 2482}, {1007, 9753}, {1506, 18806}, {1975, 23698}, {2458, 4027}, {2782, 3933}, {2967, 23098}, {3266, 23965}, {3329, 6680}, {3425, 9723}, {4558, 11610}, {5017, 9766}, {5026, 12830}, {5149, 7759}, {5152, 7768}, {5181, 23342}, {5503, 21356}, {5984, 10513}, {6033, 7776}, {6337, 21166}, {6722, 7867}, {7767, 12042}, {7836, 10350}, {7896, 8178}, {7897, 8782}, {8024, 23962}, {9146, 30789}, {10722, 32006}

X(32458) = midpoint of X(99) and X(315)
X(32458) = reflection of X(i) in X(j) for these lines: {i,j}: {32, 620}, {115, 626}
X(32458) = isotomic conjugate of isogonal conjugate of X(36790)
X(32458) = complement of X(36849)
X(32458) = X(i)-isoconjugate of X(j) for these (i,j): {1821, 14601}, {1910, 1976}
X(32458) = crosspoint of X(2396) and X(4590)
X(32458) = crosssum of X(i) and X(j) for these (i,j): {1501, 14601}, {2422, 3124}
X(32458) = crossdifference of every pair of points on line {2422, 14601}
X(32458) = barycentric product X(i)*X(j)for these lines: {i,j}: {297, 6393}, {305, 2967}, {325, 325}, {561, 23996}, {850, 15631}, {877, 6333}, {1502, 11672}, {2396, 2799}, {16725, 27801}, {18024, 23098}
X(32458) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {237, 14601}, {297, 6531}, {325, 98}, {511, 1976}, {684, 878}, {877, 685}, {1355, 1397}, {1959, 1910}, {2396, 2966}, {2421, 2715}, {2799, 2395}, {2967, 25}, {3289, 14600}, {3569, 2422}, {6333, 879}, {6393, 287}, {7062, 2175}, {9419, 1501}, {11672, 32}, {15631, 110}, {16725, 1333}, {18829, 18858}, {23098, 237}, {23611, 9418}, {23996, 31}
X(32458) = X(325),X(5976)}-harmonic conjugate of X(114),is on K778,X(i)-Ceva conjugate of X(j) for these (i,j): {670, 6333}, {4590, 2396}


X(32459) = MIDPOINT OF X(99) and X(230)

Barycentrics   (2*a^2 - b^2 - c^2)*(3*a^2 - b^2 - c^2) : :
X(32459) = 5 X[99] + 3 X[14568],X[187] + 3 X[2482],3 X[187] - X[3793],3 X[187] + X[7813],X[187] - 3 X[27088],5 X[230] - 3 X[14568],X[316] + 3 X[8598],X[316] - 3 X[22110],X[325] + 3 X[13586],3 X[325] + X[14712],3 X[620] - X[625],X[1513] + 3 X[21166],9 X[2482] + X[3793],3 X[2482] - X[6390],9 X[2482] - X[7813],X[3793] + 3 X[6390],X[3793] - 9 X[27088],3 X[5215] + X[15300],3 X[6390] - X[7813],X[6390] + 3 X[27088],X[7813] + 9 X[27088],9 X[9167] - 5 X[31275],3 X[10256] - X[15980],9 X[13586] - X[14712]

X(32459) lies on these lines: {2, 11147}, {3, 66}, {5, 9734}, {30, 620}, {39, 6329}, {69, 5210}, {99, 230}, {126, 468}, {140, 7816}, {187, 524}, {193, 439}, {316, 8598}, {325, 13586}, {376, 7778}, {548, 626}, {549, 3734}, {550, 3788}, {574, 3589}, {597, 5024}, {599, 5585}, {698, 2021}, {1003, 3815}, {1213, 21937}, {1384, 3629}, {1513, 21166}, {1975, 17008}, {2080, 13196}, {2549, 11288}, {3054, 11185}, {3055, 8370}, {3522, 7784}, {3524, 15271}, {3530, 3934}, {3552, 7745}, {3566, 3798}, {3580, 5866}, {3618, 5013}, {3627, 7862}, {3630, 15655}, {3631, 7801}, {3712, 7267}, {3926, 5023}, {3933, 5206}, {3972, 9300}, {4045, 8368}, {4760, 7181}, {5215, 15300}, {5241, 21511}, {5254, 16925}, {5306, 31859}, {5467, 15471}, {5743, 16436}, {6683, 19697}, {7472, 16320}, {7664, 24855}, {7735, 8716}, {7750, 7891}, {7756, 8361}, {7761, 8703}, {7767, 7863}, {7769, 19687}, {7782, 7790}, {7815, 15712}, {7820, 8359}, {7825, 15704}, {7835, 7937}, {7842, 12103}, {7853, 8354}, {7874, 8357}, {7899, 19695}, {7908, 14929}, {7934, 8353}, {8182, 22165}, {8355, 22247}, {8362, 15515}, {8584, 11165}, {9167, 31275}, {9737, 21850}, {9771, 11159}, {10011, 23698}, {10256, 15980}, {11149, 11151}, {11286, 15491}, {13468, 21843}, {14001, 15815}, {14033, 31489}, {17005, 19686}, {18860, 29181}, {19661, 20583}, {21163, 24256}

X(32459) = midpoint of X(i) and X(j) for these lines: {i,j}: {99, 230}, {187, 6390}, {2482, 27088}, {3793, 7813}, {7472, 16320}, {8598, 22110}
X(32459) = reflection of X(8355) in X(22247)
X(32459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {187, 2482, 6390}, {187, 7813, 3793}, {439, 6337, 3053}, {574, 8369, 3589}, {3793, 6390, 7813}, {6390, 27088, 187}, {7820, 8589, 8359}, {7863, 15513, 7767}
X(32459) = X(468)-Ceva conjugate of X(524)
X(32459) = X(i)-isoconjugate of X(j) for these (i,j): {111, 8769}, {897, 8770}, {923, 2996}, {3565, 23894}
X(32459) = crossdifference of every pair of points on line {2485, 8770}
X(32459) = barycentric product X(i)*X(j)for these lines: {i,j}: {193, 524}, {468, 6337}, {896, 18156}, {1707, 14210}, {3053, 3266}, {3566, 5468}, {3712, 17081}, {4028, 6629}, {6353, 6390}, {16741, 21874}
X(32459) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {187, 8770}, {193, 671}, {524, 2996}, {896, 8769}, {1707, 897}, {3053, 111}, {3167, 895}, {3292, 6391}, {3566, 5466}, {5095, 5203}, {5467, 3565}, {6091, 15398}, {6337, 30786}, {6353, 17983}, {6390, 6340}, {8651, 9178}, {19118, 8753}


X(32460) = EULER LINE INTERCEPT OF TRILINEAR POLAR OF X(14)

Barycentrics    -2*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*sqrt(3)*S+3*(a^2+b^2-c^2)*(2*a^2-b^2-c^2)*(a^2+c^2-b^2) : :
Barycentrics    9*(4*R^2-SW)*S^2+3*SB*SC*SW+S*sqrt(3)*(S^2-3*SB*SC) : :

As a point on the Euler line, X(32460) has Shinagawa coefficients (-3*F+sqrt(3)*S/3, E+F-sqrt(3)*S).

See Konstantin Knop, Vladimir Dubrovsky and César Lozada, Hyacinthos 29009.

X(32460) lies on these lines: {2, 3}, {13, 11657}, {14, 3166}, {15, 16319}, {110, 11092}, {396, 523}, {398, 8015}, {476, 8838}, {530, 32225}, {531, 5642}, {533, 3292}, {627, 15794}, {635, 15785}, {1525, 2777}, {2453, 16644}, {3163, 23713}, {3284, 23715}, {3642, 5651}, {5318, 30468}, {6105, 6107}, {8836, 20253}, {14704, 22510}, {18487, 23712}

X(32460) = midpoint of X(i) and X(j) for these lines: {i,j}: {110, 11092}, {16179, 16181}
X(32460) = reflection of X(32461) in X(468)
X(32460) = isogonal conjugate of the antigonal conjugate of X(2993)
X(32460) = circumcircle-inverse-of X(3130)
X(32460) = inner-Napoleon circle-inverse-of X(4)
X(32460) = orthoptic circle of Steiner inellipse-inverse-of X(383)
X(32460) = polar circle-inverse-of X(471)
X(32460) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1316, 32461), (3, 4, 23722), (1113, 1114, 3130)

X(32461) = EULER LINE INTERCEPT OF TRILINEAR POLAR OF X(13)

Barycentrics    2*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*sqrt(3)*S+3*(a^2+b^2-c^2)*(2*a^2-b^2-c^2)*(a^2+c^2-b^2) : :
Barycentrics    9*(4*R^2-SW)*S^2+3*SB*SC*SW-S*sqrt(3)*(S^2-3*SB*SC) : :

As a point on the Euler line, X(32461) has Shinagawa coefficients (-3*F-sqrt(3)*S/3, E+F+sqrt(3)*S).

See Konstantin Knop, Vladimir Dubrovsky and César Lozada, Hyacinthos 29009.

X(32461) lies on these lines: {2, 3}, {13, 3165}, {14, 11657}, {16, 16319}, {62, 8919}, {110, 11078}, {395, 523}, {397, 8014}, {476, 8836}, {530, 5642}, {531, 32225}, {532, 3292}, {628, 15793}, {636, 15784}, {1524, 2777}, {2453, 16645}, {3163, 23712}, {3284, 23714}, {3643, 5651}, {5321, 30465}, {6104, 6106}, {8838, 20252}, {14705, 22511}, {18487, 23713}

X(32461) = midpoint of X(i) and X(j) for these lines: {i,j}: {110, 11078}, {16180, 16182}
X(32461) = reflection of X(32460) in X(468)
X(32461) = isogonal conjugate of the antigonal conjugate of X(2992)
X(32461) = circumcircle-inverse-of X(3129)
X(32461) = outer-Napoleon circle-inverse-of X(4)
X(32461) = orthoptic circle of Steiner inellipse-inverse-of X(1080)
X(32461) = polar circle-inverse-of X(470)
X(32461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1316, 32460), (3, 4, 23721), (1113, 1114, 3129)

leftri

Points associated with the inscribed triply bilogic triangle: X(32462)-X(32480)

rightri

Centers X(32462)-X(32480) were contributed by Peter Moses, May 11, 2019.

The appearance of (i,j) in the following list means that X(j) = ITB-isogonal conjugate of X(i), where the ITB triangle (inscribed triply bilogic triangle) is described at K003 and K1098.

(1,32462), (2,32463), (5,32464), (15,32465, (16,32466), (25,32514), (30,32515), (39,32467), (40,32468), (110,32592), (140,32516), (186,32517), (187,32469), (237,32518), (371,32470), (372,32471), (381,32519), (382,32520), (399,32595), (550,32521), (616,32596), (617,32597), (631,32522), (632,32523), (729,32472), (755,32473), (1350,32474), (2370,32475), (3398,32476), (5171,32477), (5966,32478), (8600,32479), (11842,32480)


X(32462) = X(1)X(85)∩X(3)X(238)

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

X(32462) lies on these lines: {1, 85}, {3, 238}, {10, 26068}, {43, 170}, {78, 32117}, {497, 20731}, {954, 4335}, {1045, 1047}, {1053, 2082}, {2808, 12782}, {3010, 3212}, {15726, 24696}, {19545, 20368}, {21778, 21882}

X(32462) = excentral-isogonal conjugate of X(1759)
X(32462) = excentral-isotomic conjugate of X(1766)
X(32462) = X(41)-Ceva conjugate of X(1)
X(32462) = X(21882)-cross conjugate of X(21218)
X(32462) = crosspoint of X(21218) and X(31604)
X(32462) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 21218}, {9, 31604}, {75, 21778}, {86, 21882}, {92, 23078}
X(32462) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {21218, 75}, {21778, 1}, {21882, 10}, {23078, 63}, {31604, 85}


X(32463) = X(3)X(3231)∩X(30)X(1351)

Barycentrics    a^2*(a^6*b^2 - 4*a^4*b^4 + 3*a^2*b^6 + a^6*c^2 + 5*a^4*b^2*c^2 - 9*a^2*b^4*c^2 - 3*b^6*c^2 - 4*a^4*c^4 - 9*a^2*b^2*c^4 + 10*b^4*c^4 + 3*a^2*c^6 - 3*b^2*c^6) : :
X(32463) = 2 X[11472] - 3 X[32444]

X(32463) lies on these lines: {3, 3231}, {30, 1351}, {182, 30229}, {2080, 8717}, {3095, 14915}, {3426, 10983}, {6321, 7706}, {11472, 32444}


X(32464) = X(576)X(3146)∩X(1176)X(30496)

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

X(32464) lies on these lines: {576, 3146}, {1176, 30496}, {5206, 6030}, {7802, 23061}


X(32465) = REFLECTION OF X(13) IN X(3107)

Barycentrics    3*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6 + 3*a^6*c^2 - 11*a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 - 5*a^4*c^4 + a^2*b^2*c^4 + 4*b^4*c^4 + 2*a^2*c^6 - 2*b^2*c^6 - 2*Sqrt[3]*a^2*(a^2*b^2 + a^2*c^2 + b^2*c^2)*S : :
X(32465) = 3 X[5469] - 4 X[22692],3 X[16530] - 2 X[22702]

X(32465) lies on these lines: {6, 1569}, {13, 2782}, {14, 32447}, {16, 7709}, {17, 13108}, {18, 39}, {61, 194}, {62, 32448}, {262, 11602}, {511, 5473}, {538, 16962}, {3095, 16964}, {3105, 11257}, {3106, 5463}, {5238, 12251}, {5469, 9762}, {6194, 10645}, {6777, 22695}, {7697, 16966}, {8594, 9114}, {9112, 22701}, {11171, 16242}, {19107, 22728}

X(32465) = reflection of X(13) in X(3107)
X(32465) = reflection of X(32466) in X(1569)


X(32466) = REFLECTION OF X(14) IN X(3106)

Barycentrics    3*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6 + 3*a^6*c^2 - 11*a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 - 5*a^4*c^4 + a^2*b^2*c^4 + 4*b^4*c^4 + 2*a^2*c^6 - 2*b^2*c^6 + 2*Sqrt[3]*a^2*(a^2*b^2 + a^2*c^2 + b^2*c^2)*S : :
X(32466) = 3 X[5470] - 4 X[22691],3 X[16529] - 2 X[22701]

X(32466) lies on these lines: {6, 1569}, {13, 32447}, {14, 2782}, {15, 7709}, {17, 39}, {18, 13108}, {61, 32448}, {62, 194}, {262, 11603}, {511, 5474}, {538, 16963}, {3095, 16965}, {3104, 11257}, {3107, 5464}, {5237, 12251}, {5470, 9760}, {6194, 10646}, {6778, 22696}, {7697, 16967}, {8595, 9116}, {9113, 22702}, {11171, 16241}, {19106, 22728}

X(32466) = reflection of X(14) in X(3106)
X(32466) = reflection of X(32465) in X(1569)


X(32467) = REFLECTION OF X(3399) IN X(39)

Barycentrics    a^8 + a^6*b^2 - 3*a^4*b^4 + a^2*b^6 + a^6*c^2 - 9*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 - 3*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6 : :
X(32467) = 2 X[4] - 3 X[14492],14 X[3526] - 9 X[10302],4 X[7839] + X[12122],3 X[9302] - 4 X[11623],3 X[9751] - 4 X[12054]

X(32467) lies on these lines: {3, 6179}, {4, 7739}, {5, 6054}, {6, 11257}, {20, 576}, {30, 12156}, {32, 7709}, {39, 98}, {54, 826}, {83, 2782}, {99, 3398}, {114, 7797}, {140, 7799}, {182, 194}, {262, 9605}, {384, 575}, {385, 13334}, {401, 13366}, {511, 7839}, {572, 12197}, {631, 7622}, {1078, 11171}, {1353, 7750}, {1506, 14651}, {1569, 12176}, {1656, 7884}, {1975, 5050}, {2896, 5965}, {3095, 12203}, {3329, 6248}, {3413, 14630}, {3414, 14631}, {3526, 7607}, {3734, 10359}, {5007, 11676}, {5013, 9755}, {5028, 7738}, {5111, 12007}, {5171, 7766}, {5254, 14639}, {5286, 9744}, {6776, 9873}, {7608, 9302}, {7754, 22712}, {7783, 13335}, {7798, 12251}, {7805, 21163}, {7817, 23234}, {7829, 14981}, {7858, 15980}, {8550, 9607}, {8721, 9993}, {9751, 12054}, {10722, 15048}, {11272, 12188}, {14880, 32447}, {15819, 17129}

X(32467) = reflection of X(3399) in X(39)
X(32467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11257, 12110}, {3398, 32448, 99}, {7783, 13335, 21166}


X(32468) = X(31)-CEVA CONJUGATE OF X(9)

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

X(32468) lies on these lines: {6, 979}, {8, 23640}, {9, 341}, {40, 740}, {55, 2053}, {200, 4531}, {1018, 7031}, {1043, 4050}, {2136, 24578}, {3503, 3875}, {3729, 24579}, {3880, 17448}, {5710, 17754}, {14829, 17144}, {17752, 19591}

X(32468) = X(31)-Ceva conjugate of X(9)
X(32468) = barycentric product X(318)*X(23159)
X(32468) = barycentric quotient X(23159)/X(77)
X(32468) = {X(2319),X(3208)}-harmonic conjugate of X(2329)


X(32469) = REFLECTION OF X(98) IN X(7709)

Barycentrics    3*a^10*b^2 - 11*a^8*b^4 + 13*a^6*b^6 - 7*a^4*b^8 + 2*a^2*b^10 + 3*a^10*c^2 - 23*a^8*b^2*c^2 + 23*a^6*b^4*c^2 - 11*a^4*b^6*c^2 + 4*a^2*b^8*c^2 - 2*b^10*c^2 - 11*a^8*c^4 + 23*a^6*b^2*c^4 + 3*a^4*b^4*c^4 - 6*a^2*b^6*c^4 + 9*b^8*c^4 + 13*a^6*c^6 - 11*a^4*b^2*c^6 - 6*a^2*b^4*c^6 - 14*b^6*c^6 - 7*a^4*c^8 + 4*a^2*b^2*c^8 + 9*b^4*c^8 + 2*a^2*c^10 - 2*b^2*c^10 : :
X(32469) = X[98] - 4 X[1569],2 X[194] + X[23235],4 X[262] - 3 X[14639],3 X[5182] - 2 X[31958],2 X[6194] - 3 X[21166],4 X[11152] - X[12117]

X(32469) lies on these lines: {39, 7608}, {98, 574}, {99, 2080}, {194, 576}, {262, 381}, {511, 8593}, {538, 19911}, {5182, 31958}, {6194, 21166}, {7617, 23234}, {7697, 8179}, {8586, 10753}, {8724, 11054}, {9166, 14159}, {10723, 22728}, {12191, 15520}

X(32469) = reflection of X(i) in X(j) for these lines: {i,j}: {98, 7709}, {671, 32447}, {7709, 1569}, {10723, 22728}


X(32470) = X(6)X(32134)∩X(39)X(486)

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

X(32470) lies on these lines: {6, 32134}, {39, 486}, {76, 5418}, {194, 371}, {372, 7709}, {485, 2782}, {511, 12124}, {590, 13108}, {698, 19145}, {1504, 1569}, {3071, 32447}, {3095, 6561}, {3102, 7757}, {3103, 6560}, {5420, 11171}, {6200, 12251}, {9540, 20081}, {9683, 9917}, {11152, 13669}, {14881, 22615}

X(32470) = {X(6),X(32448)}-harmonic conjugate of X(32471)
X(32470) = {X(3103),X(11257)}-harmonic conjugate of X(6560)


X(32471) = X(6)X(32134)∩X(39)X(485)

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

X(32471) lies on these lines: {6, 32134}, {39, 485}, {76, 5420}, {194, 372}, {371, 7709}, {486, 2782}, {511, 12123}, {615, 13108}, {698, 19146}, {1505, 1569}, {3070, 32447}, {3095, 6560}, {3102, 6561}, {3103, 7757}, {5418, 11171}, {11152, 13789}, {13935, 20081}, {14881, 22644}

X(32471) = {X(6),X(32448)}-harmonic conjugate of X(32470)
X(32471) = {X(3103),X(11257)}-harmonic conjugate of X(6561)


X(32472) = X(2)X(8644)∩X(3)X(9489)

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

X(32472) lies on these lines: {2, 8644}, {3, 9489}, {4, 2489}, {30, 511}, {98, 5970}, {114, 9152}, {182, 9426}, {351, 31176}, {381, 9175}, {647, 5996}, {669, 9148}, {850, 3804}, {887, 11616}, {2485, 11620}, {3818, 11182}, {3830, 9178}, {3835, 8653}, {4108, 31174}, {4140, 4761}, {4170, 7212}, {5466, 14458}, {5926, 16235}, {8430, 10722}, {8651, 11176}, {9123, 13306}, {9137, 10989}, {9185, 13307}, {24782, 26148}, {25084, 25299}

X(32472) = Thomson-isogonal conjugate of X(729)
X(32472) = Lucas-isogonal conjugate of X(729)
X(32472) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {850, 31299, 3804}, {5996, 9147, 647}


X(32473) = X(3)X(18105)∩X(30)X(511)

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

X(32473) lies on these lines: {3, 18105}, {30, 511}, {1637, 5996}, {1649, 11633}, {3005, 14420}, {3098, 14318}, {3804, 6563}, {4108, 14417}, {5466, 14492}, {9123, 13308}, {9125, 15724}, {9134, 31176}, {9180, 9302}, {9185, 13309}, {11616, 21006}, {21732, 32467}

X(32473) = Lucas-isogonal conjugate of X(755)
X(32473) = Thomson-isogonal conjugate of X(755)


X(32474) = REFLECTION OF X(4) IN X(9764)

Barycentrics    3*a^6*b^2 - 8*a^4*b^4 - 3*a^2*b^6 + 3*a^6*c^2 - 7*a^4*b^2*c^2 - a^2*b^4*c^2 + 3*b^6*c^2 - 8*a^4*c^4 - a^2*b^2*c^4 + 10*b^4*c^4 - 3*a^2*c^6 + 3*b^2*c^6 : :
X(32474) = 3 X[5485] - 4 X[9466],3 X[7709] - 4 X[8716],2 X[7757] - 3 X[9741]

X(32474) lies on these lines: {4, 9764}, {39, 18841}, {194, 1003}, {376, 538}, {511, 15428}, {698, 5085}, {2782, 3424}, {5485, 9466}, {7757, 9741}, {8782, 11148}

X(32474) = reflection of X(4) in X(9764)


X(32475) = X(3)X(1459)∩X(4)X(20293)

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

X(32475) lies on these lines: {3, 1459}, {4, 20293}, {5, 20316}, {30, 511}, {40, 21173}, {573, 6586}, {1293, 15403}, {3261, 10446}, {4791, 15488}

X(32475) = isogonal conjugate of X(32704)
X(32475) = Lucas-isogonal conjugate of X(2370)
X(32475) = Thomson-isogonal conjugate of X(2370)
X(32475) = crossdifference of every pair of points on line {6, 8756}


X(32476) = MIDPOINT OF X(194) AND X(2896)

Barycentrics    2*a^4*b^4 + a^2*b^6 + 3*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 - b^4*c^4 + a^2*c^6 : :
X(32476) = 3 X[262] - 2 X[6249],3 X[3097] - X[9903],4 X[3934] - 5 X[31268],4 X[6704] - 5 X[7786],3 X[7709] - X[12252],3 X[7833] - X[9990],3 X[9751] - 4 X[13334],X[13111] - 3 X[32447]

X(194) and X(2896) are the centers of the 1st and 2nd Neuberg radical circles, resp.

X(32476) lies on these lines: {5, 9772}, {6, 10131}, {20, 3095}, {39, 83}, {69, 194}, {76, 4045}, {115, 32190}, {262, 6249}, {385, 6308}, {511, 7839}, {538, 31168}, {574, 8150}, {730, 12783}, {736, 7847}, {754, 7757}, {1975, 24273}, {2549, 31982}, {2782, 3399}, {3097, 9903}, {3314, 6309}, {3663, 17760}, {3934, 7923}, {4048, 10345}, {5254, 9478}, {5976, 7797}, {6296, 6775}, {6297, 6772}, {6337, 16898}, {6655, 9866}, {6656, 9865}, {6683, 16896}, {6704, 7786}, {7750, 32449}, {7766, 9821}, {7787, 13331}, {7790, 8149}, {7827, 18806}, {7977, 14839}, {9751, 13334}, {9765, 14041}, {9855, 12156}, {9873, 32429}, {10329, 16985}, {10333, 12215}, {10350, 12216}, {11257, 29012}, {12836, 13078}, {12837, 18983}, {12944, 18982}, {12954, 13077}, {13111, 32447}, {13357, 13586}

X(32476) = midpoint of X(194) and X(2896)
X(32476) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 6292}, {83, 39}
X(32476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {194, 7791, 9983}, {7864, 10335, 76}


X(32477) = REFLECTION OF X(76) IN X(6337)

Barycentrics    6*a^6*b^2 - 8*a^4*b^4 + 2*a^2*b^6 + 6*a^6*c^2 - 15*a^4*b^2*c^2 + 4*a^2*b^4*c^2 - 3*b^6*c^2 - 8*a^4*c^4 + 4*a^2*b^2*c^4 + 10*b^4*c^4 + 2*a^2*c^6 - 3*b^2*c^6 : :
X(32477) = 3 X[7612] - 4 X[13334],5 X[7786] - 4 X[13881]

X(32477) lies on these lines: {39, 2996}, {76, 631}, {99, 3053}, {194, 5052}, {1975, 5050}, {2782, 8781}, {3564, 7750}, {5033, 10131}, {5395, 32450}, {7757, 8370}, {7786, 13881}, {11152, 14645}

X(32477) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 6337}, {2996, 39}


X(32478) = X(2)X(18308)∩X(3)X(18336)

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

X(32478) lies on these lines: {2, 18308}, {3, 18336}, {4, 18335}, {30, 511}, {381, 1116}, {669, 14417}, {879, 16835}, {1637, 31176}, {2519, 7651}, {2525, 8664}, {3569, 22889}, {3830, 15475}, {3845, 15543}, {4807, 18004}, {5027, 13315}, {5466, 33698}, {5652, 6030}, {8718, 8723}, {9135, 22888}, {9208, 13318}, {9218, 15342}, {9494, 14824}, {9979, 12075}, {10097, 15321}, {11550, 14582}, {12077, 13412}, {18310, 18313}

X(32478) = Lucas-isogonal conjugate of X(5966)
X(32478) = Thomson-isogonal conjugate of X(5966)
X(32478) = crossdifference of every pair of points on line {6, 11451}


X(32479) = X(2)X(8589)∩X(3)X(1153)

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

X(32479) lies on these lines: {2, 8589}, {3, 1153}, {4, 7618}, {5, 7619}, {20, 7620}, {21, 7621}, {30, 511}, {39, 598}, {99, 8597}, {115, 8598}, {187, 671}, {316, 8591}, {325, 15300}, {376, 5569}, {381, 7622}, {382, 7775}, {549, 20112}, {550, 16509}, {574, 11317}, {625, 2482}, {1657, 7780}, {2080, 12355}, {3146, 7843}, {3529, 5485}, {3534, 7610}, {3734, 5077}, {3830, 11184}, {3845, 9771}, {3934, 7833}, {5007, 19696}, {5008, 33687}, {5032, 7737}, {5073, 7781}, {5092, 7606}, {5107, 8593}, {5140, 12132}, {5148, 12354}, {5184, 9875}, {5194, 18969}, {5215, 9166}, {5254, 19661}, {5309, 33193}, {5461, 27088}, {5999, 9877}, {6658, 7827}, {6683, 7756}, {6781, 22329}, {7746, 33208}, {7748, 7817}, {7751, 17800}, {7758, 11541}, {7759, 33703}, {7761, 21356}, {7801, 7842}, {7804, 11159}, {7810, 32819}, {7812, 32450}, {7816, 7841}, {7845, 20094}, {7848, 32815}, {7849, 19695}, {7854, 33271}, {7861, 8369}, {7870, 33019}, {7872, 33237}, {7873, 19691}, {7880, 33017}, {7883, 33256}, {7886, 32985}, {7915, 33190}, {8355, 22247}, {8586, 10488}, {8588, 8860}, {8596, 11054}, {8667, 15685}, {8703, 15597}, {8716, 15684}, {8724, 13449}, {9167, 10150}, {9466, 33264}, {9770, 15682}, {10302, 17128}, {11055, 19569}, {11057, 14711}, {11147, 32984}, {12040, 15687}, {12117, 18860}, {13330, 33683}, {13468, 19710}, {14042, 31652}, {26613, 33265}, {31709, 33476}, {31710, 33477}

X(32479) = Lucas-isogonal conjugate of X(8600)
X(32479) = Thomson-isogonal conjugate of X(8600)
X(32479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7617, 1153}, {4, 7618, 8176}, {20, 7620, 8182}, {99, 8597, 31173}, {376, 7615, 5569}, {671, 9855, 187}, {2482, 8352, 625}, {8596, 14712, 11054}, {9166, 13586, 5215}


X(32480) = REFLECTION OF X(76) IN X(15810)

Barycentrics    4*a^4 - 7*a^2*b^2 - 2*b^4 - 7*a^2*c^2 + 5*b^2*c^2 - 2*c^4 : :
X(32480) = 5 X[194] + 4 X[7750],X[194] + 2 X[7833],7 X[194] + 2 X[7893],2 X[194] + X[9939],2 X[7750] - 5 X[7833],14 X[7750] - 5 X[7893],8 X[7750] - 5 X[9939],2 X[7756] + X[7812],5 X[7786] - 4 X[14762],4 X[7810] - X[20081],8 X[7830] + X[20105],7 X[7833] - X[7893],4 X[7833] - X[9939],X[7837] + 2 X[8353],2 X[7837] + X[14976],4 X[7893] - 7 X[9939],4 X[8353] - X[14976],8 X[8359] - 5 X[31276],X[9878] + 2 X[11152]

X(32480) lies on these lines: {2, 99}, {3, 8859}, {4, 10484}, {6, 9855}, {20, 576}, {30, 7709}, {39, 598}, {76, 15810}, {182, 12117}, {194, 524}, {376, 2080}, {384, 11164}, {1975, 21358}, {1992, 8586}, {2896, 11148}, {3091, 7608}, {3094, 9830}, {3329, 11159}, {3543, 9744}, {3552, 7827}, {3849, 7757}, {5024, 11317}, {5038, 7738}, {5077, 7840}, {5116, 7606}, {5309, 26613}, {5569, 14568}, {7748, 8176}, {7756, 7812}, {7777, 8352}, {7781, 7883}, {7782, 7817}, {7783, 7841}, {7785, 23334}, {7786, 14762}, {7791, 21356}, {7793, 8182}, {7801, 7847}, {7806, 27088}, {7810, 20081}, {7830, 20105}, {7837, 8353}, {7864, 8369}, {7870, 7933}, {7891, 8360}, {7923, 8366}, {7924, 8716}, {7937, 15301}, {8359, 31276}, {8597, 11163}, {8598, 15048}, {9606, 14066}, {10168, 10992}, {11147, 16925}, {11178, 23235}, {11184, 14041}, {11257, 11645}, {14042, 22332}

X(32480) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 15810}, {598, 39}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8596, 11185}, {194, 7833, 9939}, {574, 671, 2}, {2482, 7790, 2}, {5077, 7840, 7898}, {5077, 31859, 7840}, {7622, 9166, 2}, {7622, 11648, 9166}, {7837, 8353, 14976}


X(32481) = X(3)X(76)∩X(114)X(2567)

Barycentrics    a^6*b^2 - a^4*b^4 + a^6*c^2 - 2*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6 - a^2*(a^2 - b^2 - c^2)*Sqrt[(a^2*b^2 + a^2*c^2 + b^2*c^2)*(a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4)] : :
X(32481) = (Sqrt[Csc[w]^2 - 4] Sin[w] - 1) X[3] + X[76]

X(32481) lies on the the 2nd Brocard circle, the cubics K019 and K1103, and on these lines: {3, 76}, {114, 2567}, {115, 2566}, {1663, 12215}, {1664, 6776}, {1665, 18906}, {1670, 3414}, {1671, 3413}, {2564, 3023}, {2565, 3027}, {2572, 9860}, {2573, 13174}

X(32481) = reflection of X(32482) in X(3)
X(32481) = antipode in 2nd Brocard circle of X(32482)
X(32481) = {X(76),X(99)}-harmonic conjugate of X(32482)
X(32481) = {X(98),X(11257)}-harmonic conjugate of X(32482)
X(32481) = X(1663)-of-6th-Brocard-triangle
X(32481) = X(1665)-of-1st-anti-Brocard-triangle


X(32482) = X(3)X(76)∩X(114)X(2566)

Barycentrics    a^6*b^2 - a^4*b^4 + a^6*c^2 - 2*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6 + a^2*(a^2 - b^2 - c^2)*Sqrt[(a^2*b^2 + a^2*c^2 + b^2*c^2)*(a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4)] : :
X(32482) = (Sqrt[Csc[w]^2 - 4] Sin[w] + 1) X[3] - X[76]

X(32482) lies on the the 2nd Brocard circle, the cubics K019 and K1103, and on these lines: {3, 76}, {114, 2566}, {115, 2567}, {1662, 12215}, {1664, 18906}, {1665, 6776}, {1670, 3413}, {1671, 3414}, {2564, 3027}, {2565, 3023}, {2572, 13174}, {2573, 9860}

X(32482) = reflection of X(32481) in X(3)
X(32482) = antipode in 2nd Brocard circle of X(32481)
X(32482) = {X(76),X(99)}-harmonic conjugate of X(32481)
X(32482) = {X(98),X(11257)}-harmonic conjugate of X(32481)
X(32482) = X(1662)-of-6th-Brocard-triangle
X(32482) = X(1664)-of-1st-anti-Brocard-triangle


X(32483) = X(98)X(385)∩X(880)X(2782)

Barycentrics    a^14*b^6 - a^12*b^8 + a^10*b^10 - a^8*b^12 - a^16*b^2*c^2 + 3*a^14*b^4*c^2 - 8*a^12*b^6*c^2 + 9*a^10*b^8*c^2 - 8*a^8*b^10*c^2 + 4*a^6*b^12*c^2 - a^4*b^14*c^2 + 3*a^14*b^2*c^4 - 7*a^12*b^4*c^4 + 10*a^10*b^6*c^4 - a^8*b^8*c^4 + a^6*b^10*c^4 + 3*a^4*b^12*c^4 + a^2*b^14*c^4 + a^14*c^6 - 8*a^12*b^2*c^6 + 10*a^10*b^4*c^6 - 15*a^8*b^6*c^6 + 3*a^6*b^8*c^6 - 8*a^4*b^10*c^6 - 3*a^2*b^12*c^6 - a^12*c^8 + 9*a^10*b^2*c^8 - a^8*b^4*c^8 + 3*a^6*b^6*c^8 + 9*a^4*b^8*c^8 + 2*a^2*b^10*c^8 - b^12*c^8 + a^10*c^10 - 8*a^8*b^2*c^10 + a^6*b^4*c^10 - 8*a^4*b^6*c^10 + 2*a^2*b^8*c^10 + 2*b^10*c^10 - a^8*c^12 + 4*a^6*b^2*c^12 + 3*a^4*b^4*c^12 - 3*a^2*b^6*c^12 - b^8*c^12 - a^4*b^2*c^14 + a^2*b^4*c^14 : :

X(32483) lies on the cubic K1103 and these lines: {98, 385}, {880, 2782}


X(32484) = X(39)X(512)∩X(99)X(511)

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

X(32484) lies on the cubic K1103 and these lines: {39, 512}, {99, 511}, {1916, 14509}, {2023, 6071}, {2679, 2782}, {8870, 13137}

X(32484) = midpoint of X(1916) and X(14509)
X(32484) = reflection of X(i) in X(j) for these lines: {i,j}: {6071, 2023}, {16068, 39}
X(32484) = reflection of X(16068) in the Brocard axis
X(32484) = orthogonal projection of X(99) on line PU(1)


X(32485) = (name pending)

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

X(32485) lies on this line: {3,6}


X(32486) = MIDPOINT OF X(1) AND X(5400)

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

See Angel Montesdeoca, Hyacinthos 29011 and HG130519

X(32486) lies on these lines: {1,5}, {3,23404}, {40,1054}, {43,16200}, {56,1777}, {57,1361}, {102,105}, {104,106}, {117,614}, {244,2800}, {386,10595}, {392,25939}, {484,23153}, {515,1149}, {517,1739}, {551,1064}, {581,3622}, {759,953}, {899,28234}, {912,4694}, {946,1201}, {962,28370}, {978,7982}, {995,4000}, {999,6180}, {1086,1537}, {1125,26095}, {1193,13464}, {1318,14511}, {1331,13279}, {1482,3216}, {1616,3149}, {1647,10265}, {1724,10680}, {1742,3576}, {1772,12758}, {2718,28219}, {3073,5563}, {3293,10222}, {3953,5887}, {3976,5693}, {3987,23340}, {4202,19861}, {4657,17044}, {5844,31855}, {6261,28011}, {6684,28352}, {6788,12247}, {8583,25882}, {8686,28233}, {10090,23703}, {11362,27627}, {12245,17749}, {12608,23675}, {12616,28018}, {14217,24715}, {15558,24028}, {16483,22753}, {17154,30196}

X(32486) = midpoint of X(i) and X(j), for these lines: {i, j}: {1, 5400}, {17154, 30196}


X(32487) = X(2292)X(3754)∩X(4535)X(18697)

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

See Angel Montesdeoca, Hyacinthos 29011 and HG130519

X(32487) lies on these lines: {2292,3754}, {4535,18697}

leftri

2nd and 3rd Vecten triangles: X(32488)-X(32513)

rightri

This preamble and centers X(32488)-X(32513) were contributed by César Eliud Lozada, May 14, 2019.

Given a triangle ABC, build the square σ'a = AA'bA'aA'c, with the same orientation as ABC, and such that B and C lie on the lines A'aA'b and A'aA'c, respectively. Define σ'b and σ'c cyclically.

Build now the square σ"a = AA"bA"aA"c, with opposite orientation of ABC, and such that B and C lie on the lines A"aA"b and A"aA"c, respectively, and construct σ"b and σ"c cyclically.

A'a and A"a have barycentric coordinates:

   A'a = 1/SA : 1/(SB-S) : 1/(SC-S).

   A"a = 1/SA : 1/(SB+S) : 1/(SC+S).

The lines AA'a, BB`b and CC'a concur at X(486) and similarly the lines AA"a, BB"b and CC"a concur at X(485). Moreover, the triangle bounded by the lines A'bA'c, B'aB'c and C'aC'b is the inner-Vecten triangle of ABC and the triangle enclosed by the lines A"bA"c, B"aB"c and C"aC"b is the outer-Vecten triangle of ABC. For the latter reasons, the triangle A'aB'bC'c are here named here the 2nd inner-Vecten triangle of ABC and the triangle A"aB"bC"c are here named the 2nd outer-Vecten triangle of ABC.

Let A', A" be the centers of σ'a and σ"a, respectively, and define (B', B"), (C', C") cyclically. The triangles A'B'C' and A"B"C" are here named the 3rd inner-Vecten triangle of ABC and 3rd outer-Vecten triangle of ABC, respectively. The have first vertices barycentrics coordinates:

   A' = (3*S^2+SB*SC-2*S*SW)/SA : SC-S : SB-S

   A" = (3*S^2+SB*SC+2*S*SW)/SA : SC+S : SB+S

Perspective triangles and perspectors:

   2nd inner-Vecten triangle: (ABC, 486), (anticomplementary, 32488), (outer-squares, 486), (inner-Vecten, 486), (3rd inner-Vecten, 486).
   2nd outer-Vecten triangle: (ABC, 485), (anticomplementary, 32489), (inner-squares, 485), (outer-Vecten, 485), (3rd outer-Vecten, 485).
   3rd inner-Vecten triangle: (ABC, 486), (medial, 32490), (outer-squares, 486), (inner-Vecten, 486), (2nd inner-Vecten, 486).
   3rd outer-Vecten triangle: (ABC, 485), (medial, 32491), (inner-squares, 485), (outer-Vecten, 485), (2nd outer-Vecten, 485).

Orthologic triangles and orthologic centers:

   2nd inner-Vecten triangle: (3rd anti-tri-squares, 486, 32492), (Lucas(-1) reflection, 3071, 32493), (4th tri-squares, 486, 32494), (inner-Vecten, 486, 3071).
   2nd outer-Vecten triangle: (4th anti-tri-squares, 485, 32495), (Lucas reflection, 3070, 32496), (3rd tri-squares, 485, 32497), (outer-Vecten, 485, 3070).
   3rd inner-Vecten triangle: (3rd anti-tri-squares, 486, 32498), (4th tri-squares, 486, 13933), (inner-Vecten, 486, 642).
   3rd outer-Vecten triangle: (4th anti-tri-squares, 485, 32499), (3rd tri-squares, 485, 13879), (outer-Vecten, 485, 641).

The following pairs of triangles are directly similar: {3rd inner-Vecten, Lucas(-1) central}, {3rd outer-Vecten, Lucas(+1) central}


X(32488) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-VECTEN AND ANTICOMPLEMENTARY

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

As a point on the Euler line, X(32488) has Shinagawa coefficients (E+F-S, -2*S).

X(32488) lies on these lines: {2,3}, {193,9975}, {486,638}, {487,23259}, {489,23261}, {490,615}, {491,3071}, {637,640}, {1132,1271}, {1587,7797}, {1588,7785}, {3069,12323}, {3070,7851}, {5591,12322}, {6776,26469}, {13758,13881}

X(32488) = anticomplement of the anticomplement of X(32490)
X(32488) = inverse of X(11293) in the orthocentroidal circle
X(32488) = X(12963)-of-3rd anti-tri-squares triangle, when ABC is obtuse
X(32488) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11293), (4, 5025, 32489), (4, 11292, 14035)


X(32489) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-VECTEN AND ANTICOMPLEMENTARY

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

As a point on the Euler line, X(32489) has Shinagawa coefficients (E+F+S, 2*S).

X(32489) lies on these lines: {2,3}, {69,31412}, {193,9974}, {485,637}, {488,23249}, {489,590}, {490,23251}, {492,3070}, {638,639}, {1131,1270}, {1587,7785}, {1588,7797}, {3068,12322}, {3071,7851}, {3594,13757}, {5590,12323}, {5860,31414}, {6118,6200}, {6250,11825}, {6425,13663}, {6776,26468}, {7581,7921}, {7582,7920}, {7585,12221}, {7745,13758}, {8376,13941}, {8960,32419}, {13638,13881}

X(32489) = anticomplement of the anticomplement of X(32491)
X(32489) = inverse of X(11294) in the orthocentroidal circle
X(32489) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11294), (4, 5025, 32488), (4, 11291, 14035)


X(32490) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-VECTEN AND MEDIAL

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

As a point on the Euler line, X(32490) has Shinagawa coefficients (2*E+2*F-3*S, -S).

X(32490) lies on these lines: {2,3}, {69,13951}, {115,32494}, {141,10577}, {372,23312}, {487,13785}, {491,7584}, {590,1506}, {597,8960}, {615,640}, {637,18762}, {638,13966}, {639,7867}, {642,3071}, {1270,3317}, {1271,13939}, {1588,26362}, {3589,10576}, {3595,7582}, {3618,8976}, {6318,22725}, {6395,12222}, {6398,12323}, {10195,13663}, {31455,32497}

X(32490) = complement of the complement of X(32488)
X(32490) = inverse of X(11316) in the orthocentroidal circle
X(32490) = X(371)-of-inner-Vecten triangle, when ABC is obtuse
X(32490) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11316), (5, 8361, 32491), (3090, 6811, 5)


X(32491) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-VECTEN AND MEDIAL

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

As a point on the Euler line, X(32491) has Shinagawa coefficients (2*E+2*F+3*S, S).

X(32491) lies on these lines: {2,3}, {69,8976}, {115,32497}, {141,10576}, {371,23311}, {488,13665}, {492,7583}, {524,8960}, {590,639}, {615,1506}, {637,8981}, {638,18538}, {640,7867}, {641,3070}, {1270,13886}, {1271,3316}, {1587,26361}, {3589,10577}, {3593,7581}, {3618,13951}, {6199,12221}, {6221,12322}, {6314,22724}, {10194,13783}, {26288,31414}, {31454,32419}, {31455,32494}

X(32491) = complement of the complement of X(32489)
X(32491) = inverse of X(11315) in the orthocentroidal circle
X(32491) = X(371)-of-outer-Vecten triangle
X(32491) = X(6213)-of-3rd outer-Vecten triangle
X(32491) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11315), (5, 8361, 32490), (3090, 6813, 5)


X(32492) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES TO 2nd INNER-VECTEN

Barycentrics    a^6-7*(b^2+c^2)*a^4+(5*b^4-6*b^2*c^2+5*c^4)*a^2+2*(5*a^4-3*(b^2-c^2)^2)*S+(b^4-c^4)*(b^2-c^2) : :
X(32492) = 3*X(486)-2*X(32494) = 3*X(3071)-X(32494)

The reciprocal orthologic center of these triangles is X(486).

X(32492) lies on these lines: {3,486}, {30,12969}, {315,32419}, {371,6251}, {487,23259}, {489,642}, {616,22601}, {617,22603}, {1322,13036}, {1503,9975}, {1588,12296}, {2782,22501}, {6290,23261}, {12221,20081}, {12509,23275}, {20423,32495}, {22484,22591}, {32506,32508}

X(32492) = reflection of X(i) in X(j) for these (i,j): (486, 3071), (489, 642), (32506, 32508)
X(32492) = (3rd anti-tri-squares)-isogonal conjugate of-X(486)
X(32492) = X(372)-of-3rd anti-tri-squares triangle, when ABC is obtuse
X(32492) = X(8982)-of-inner-Vecten triangle, when ABC is obtuse
X(32492) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6561, 22617, 486), (13785, 13934, 486)


X(32493) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) REFLECTION TO 2nd INNER-VECTEN

Barycentrics    S^4+(4*R^2*SA+SA^2-3*SB*SC-2*SW^2)*S^2+(4*R^2-SW)*SB*SC*SW+S*((4*R^2-3*SA+3*SW)*S^2-(SB+SC)*(2*R^2*(4*SA+SW)-SA^2+SB*SC-SW^2)) : :

The reciprocal orthologic center of these triangles is X(3071).

X(32493) lies on these lines: {32,6402}, {184,3071}

X(32493) = X(1)-of-Lucas(-1) reflection triangle
X(32493) = (Lucas(-1) reflection)-isogonal conjugate of-X(32493)


X(32494) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES TO 2nd INNER-VECTEN

Barycentrics    (a^2-3*b^2-3*c^2)*a^2+2*(a^2+b^2+c^2)*S : :
X(32494) = 3*X(486)-X(32492) = 3*X(3071)-2*X(32492)

The reciprocal orthologic center of these triangles is X(486).

X(32494) lies on these lines: {2,1975}, {3,486}, {4,19493}, {6,487}, {32,32419}, {37,31535}, {39,590}, {69,6463}, {115,32490}, {372,3564}, {489,3053}, {494,11091}, {524,12969}, {574,6119}, {591,3785}, {597,12962}, {1152,1503}, {1322,13020}, {1352,15884}, {1384,13770}, {1588,12509}, {2548,9767}, {2549,11314}, {2782,13926}, {3070,6290}, {3767,11316}, {3815,7389}, {3926,5491}, {5023,13798}, {5024,13711}, {5206,32209}, {5210,13941}, {6414,8420}, {6776,8406}, {7375,31400}, {7745,11293}, {8252,11292}, {8253,22332}, {8576,13046}, {8855,8964}, {9605,19105}, {9906,13973}, {10991,13989}, {11313,31401}, {12169,19005}, {12296,23261}, {12963,13972}, {13036,13429}, {13880,13968}, {18937,19411}, {19104,30435}, {31455,32491}

X(32494) = midpoint of X(489) and X(12221)
X(32494) = reflection of X(3071) in X(486)
X(32494) = (4th tri-squares)-isogonal conjugate of-X(486)
X(32494) = X(371)-of-4th tri-squares triangle, when ABC is acute
X(32494) = X(372)-of-4th tri-squares triangle, when ABC is obtuse
X(32494) = X(489)-of-4th tri-squares-central triangle
X(32494) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5013, 32497), (5254, 7789, 32497), (6337, 13881, 32497)


X(32495) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES TO 2nd OUTER-VECTEN

Barycentrics    a^6-7*(b^2+c^2)*a^4+(5*b^4-6*b^2*c^2+5*c^4)*a^2-2*(5*a^4-3*(b^2-c^2)^2)*S+(b^4-c^4)*(b^2-c^2) : :
X(32495) = 3*X(485)-2*X(32497) = 3*X(3070)-X(32497)

The reciprocal orthologic center of these triangles is X(485).

X(32495) lies on these lines: {3,485}, {30,12962}, {315,32421}, {372,6250}, {488,23249}, {490,641}, {616,22630}, {617,22632}, {1321,13035}, {1503,9974}, {1587,12297}, {2782,22502}, {5254,19102}, {6118,6396}, {6200,13879}, {6228,7389}, {6289,23251}, {6561,19103}, {8352,12159}, {8376,13834}, {12222,20081}, {12510,23269}, {20423,32492}, {22485,22592}, {32507,32509}

X(32495) = reflection of X(i) in X(j) for these (i,j): (485, 3070), (490, 641), (32507, 32509)
X(32495) = (4th anti-tri-squares)-isogonal conjugate of-X(485)
X(32495) = X(8982)-of-outer-Vecten triangle
X(32495) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6560, 22646, 485), (13665, 13882, 485)


X(32496) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS REFLECTION TO 2nd OUTER-VECTEN

Barycentrics    S^4+(4*R^2*SA+SA^2-3*SB*SC-2*SW^2)*S^2+(4*R^2-SW)*SB*SC*SW-S*((4*R^2-3*SA+3*SW)*S^2-(SB+SC)*(2*R^2*(4*SA+SW)-SA^2+SB*SC-SW^2)) : :

The reciprocal orthologic center of these triangles is X(3070).

X(32496) lies on these lines: {32,6401}, {184,3070}

X(32496) = (Lucas reflection)-isogonal conjugate of-X(32496)
X(32496) = X(1)-of-Lucas reflection triangle


X(32497) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES TO 2nd OUTER-VECTEN

Barycentrics    (a^2-3*b^2-3*c^2)*a^2-2*(a^2+b^2+c^2)*S : :
X(32497) = 3*X(485)-X(32495) = 3*X(3070)-2*X(32495)

The reciprocal orthologic center of these triangles is X(485).

X(32497) lies on these lines: {2,1975}, {3,485}, {4,19492}, {6,488}, {32,32421}, {39,615}, {69,6462}, {115,32491}, {187,13879}, {371,3564}, {490,3053}, {493,11090}, {524,12962}, {574,6118}, {597,12969}, {1144,6529}, {1151,1503}, {1321,13019}, {1352,15883}, {1384,13651}, {1587,12510}, {1991,3785}, {2548,9768}, {2549,11313}, {2782,13873}, {3071,6289}, {3767,11315}, {3815,7388}, {3926,5490}, {5023,13678}, {5024,13834}, {5206,13924}, {5210,8972}, {6413,8408}, {6776,8414}, {7376,31400}, {7745,11294}, {8252,22332}, {8253,11291}, {8577,13047}, {8997,10991}, {9605,19102}, {9907,13911}, {11314,31401}, {12170,19006}, {12297,23251}, {12968,13910}, {13035,13440}, {13908,13921}, {18938,19410}, {19103,30435}, {31455,32490}

X(32497) = midpoint of X(490) and X(12222)
X(32497) = reflection of X(3070) in X(485)
X(32497) = (3rd tri-squares)-isogonal conjugate of-X(485)
X(32497) = X(372)-of-3rd tri-squares triangle
X(32497) = X(490)-of-3rd tri-squares-central triangle
X(32497) = X(31559)-of-3rd outer-Vecten triangle
X(32497) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5013, 32494), (5254, 7789, 32494), (6337, 13881, 32494)


X(32498) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES TO 3rd INNER-VECTEN

Barycentrics    -(3*a^4+2*(b^2+c^2)*a^2-3*(b^2-c^2)^2)*S+2*(b^2+c^2)*a^4-(b^4-4*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2) : :
X(32498) = 3*X(486)-2*X(13933) = 3*X(1328)-X(22617)

The reciprocal orthologic center of these triangles is X(486).

X(32498) lies on these lines: {4,372}, {6,22596}, {30,13934}, {487,23259}, {642,6561}, {1161,12601}, {1328,5491}, {3071,6290}, {3564,9975}, {6119,11291}, {6229,12322}, {6564,19105}, {7000,13926}, {7900,12221}, {8184,11293}, {12296,23263}, {12306,23261}, {13881,22625}, {19130,32499}

X(32498) = (3rd anti-tri-squares)-isogonal conjugate of-X(22617)
X(32498) = (3rd anti-tri-squares)-complement of-X(22617)
X(32498) = X(3)-of-3rd anti-tri-squares triangle


X(32499) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES TO 3rd OUTER-VECTEN

Barycentrics    (3*a^4+2*(b^2+c^2)*a^2-3*(b^2-c^2)^2)*S+2*(b^2+c^2)*a^4-(b^4-4*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2) : :
X(32499) = 3*X(485)-2*X(13879) = 3*X(1327)-X(22646)

The reciprocal orthologic center of these triangles is X(485).

X(32499) lies on these lines: {4,371}, {6,22625}, {30,13882}, {488,23249}, {641,6560}, {1160,12602}, {1327,5490}, {3070,6289}, {3564,9974}, {6118,11292}, {6228,12323}, {6565,19102}, {7374,13873}, {7900,12222}, {8180,11294}, {12297,23253}, {12305,23251}, {13881,22596}, {19130,32498}

X(32499) = (4th anti-tri-squares)-isogonal conjugate of-X(22646)
X(32499) = (4th anti-tri-squares)-complement of-X(22646)
X(32499) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (488, 23249, 32495), (12257, 31412, 485)


X(32500) = EULEROLOGIC CENTER OF THESE TRIANGLES: INNER-VECTEN TO 3rd INNER-VECTEN

Barycentrics    3*S^4-3*(SA^2+SB*SC)*S^2-SB*SC*SW^2-S*(2*(12*R^2-SA)*S^2-(SA^2+4*SB*SC+SW^2)*SW) : :

There is not reciprocal eulerologic center for these triangles

X(32500) lies on these lines: {2,7599}, {136,641}, {369,20799}

X(32500) = complement of X(13520)
X(32500) = X(125)-of-inner-Vecten triangle
X(32500) = orthoptic-circle-of-Steiner-inellipse-inverse of X(33340)


X(32501) = EULEROLOGIC CENTER OF THESE TRIANGLES: OUTER-VECTEN TO 3rd INNER-VECTEN

Barycentrics    3*S^4-3*(SA^2+SB*SC)*S^2-SB*SC*SW^2+S*(2*(12*R^2-SA)*S^2-(SA^2+4*SB*SC+SW^2)*SW) : :

There is not reciprocal eulerologic center for these triangles

X(32501) lies on these lines: {2,7598}, {136,642}

X(32501) = complement of X(13521)
X(32501) = X(100)-of-3rd outer-Vecten triangle
X(32501) = X(125)-of-outer-Vecten triangle
X(32501) = orthoptic-circle-of-Steiner-inellipse-inverse of X(33341)


X(32502) = CENTROID OF THE 2nd INNER-VECTEN TRIANGLE

Barycentrics    28*S^4+4*(11*SA^2-29*SB*SC-12*SW^2)*S^2-20*SB*SC*SW^2-S*(8*(2*R^2+5*SA-17*SW)*S^2-4*(19*SA-3*SW)*(SA-SW)*SW) : :
X(32502) = X(486)+2*X(32508) = X(642)-4*X(32512) = 2*X(3071)+X(32506) = X(3071)+2*X(32510) = X(32506)-4*X(32510)

X(32502) lies on these lines: {2,32433}, {486,32508}, {642,32512}, {3071,32506}

X(32502) = reflection of X(2) in X(32504)
X(32502) = {X(3071), X(32510)}-harmonic conjugate of X(32506)
X(32502) = X(3060)-of-inner-Vecten triangle


X(32503) = CENTROID OF THE 2nd OUTER-VECTEN TRIANGLE

Barycentrics    28*S^4+4*(11*SA^2-29*SB*SC-12*SW^2)*S^2-20*SB*SC*SW^2+S*(8*(2*R^2+5*SA-17*SW)*S^2-4*(19*SA-3*SW)*(SA-SW)*SW) : :
X(32503) = X(485)+2*X(32509) = X(641)-4*X(32513) = 2*X(3070)+X(32507) = X(3070)+2*X(32511) = X(32507)-4*X(32511)

X(32503) lies on these lines: {2,32436}, {485,32509}, {641,32513}, {3070,32507}

X(32503) = reflection of X(2) in X(32505)
X(32503) = X(1699)-of-3rd outer-Vecten triangle
X(32503) = X(3060)-of-outer-Vecten triangle
X(32503) = {X(3070), X(32511)}-harmonic conjugate of X(32507)


X(32504) = CENTROID OF THE 3rd INNER-VECTEN TRIANGLE

Barycentrics    3*S^4-(11*SA^2-29*SB*SC-22*SW^2)*S^2+5*SB*SC*SW^2+S*(2*(4*R^2+5*SA-15*SW)*S^2+(3*SA^2-22*SB*SC-5*SW^2)*SW) : :

X(32504) lies on these lines: {2,32433}, {6119,32508}

X(32504) = midpoint of X(2) and X(32502)
X(32504) = X(51)-of-inner-Vecten triangle
X(32504) = {X(6119), X(32512)}-harmonic conjugate of X(32508)


X(32505) = CENTROID OF THE 3rd OUTER-VECTEN TRIANGLE

Barycentrics    3*S^4-(11*SA^2-29*SB*SC-22*SW^2)*S^2+5*SB*SC*SW^2-S*(2*(4*R^2+5*SA-15*SW)*S^2+(3*SA^2-22*SB*SC-5*SW^2)*SW) : :
X(32505) = 2*X(6118)+X(32509)

X(32505) lies on these lines: {2,32436}, {6118,32509}

X(32505) = midpoint of X(2) and X(32503)
X(32505) = X(51)-of-outer-Vecten triangle
X(32505) = {X(6118), X(32513)}-harmonic conjugate of X(32509)


X(32506) = ORTHOCENTER OF THE 2nd INNER-VECTEN TRIANGLE

Barycentrics    2*(2*R^2+5*SW)*S^4+(8*(SA-SW)*SA*R^2+(SA^2-5*SA*SW+5*SW^2)*SW)*S^2+SB*SC*SW^3-S*(S^4-(SA*(4*R^2+3*SA)-SB*SC-13*SW^2)*S^2+(4*SA-SW)*(SA-SW)*SW^2) : :
X(32506) = 2*X(3071)-3*X(32502)

X(32506) lies on these lines: {486,489}, {3071,32502}, {32492,32508}

X(32506) = reflection of X(i) in X(j) for these (i,j): (3071, 32510), (32492, 32508)
X(32506) = {X(3071), X(32510)}-harmonic conjugate of X(32502)


X(32507) = ORTHOCENTER OF THE 2nd OUTER-VECTEN TRIANGLE

Barycentrics    2*(2*R^2+5*SW)*S^4+(8*(SA-SW)*SA*R^2+(SA^2-5*SA*SW+5*SW^2)*SW)*S^2+SB*SC*SW^3+S*(S^4-(SA*(4*R^2+3*SA)-SB*SC-13*SW^2)*S^2+(4*SA-SW)*(SA-SW)*SW^2) : :
X(32507) = 2*X(3070)-3*X(32503)

X(32507) lies on these lines: {485,490}, {3070,32503}, {32495,32509}

X(32507) = reflection of X(i) in X(j) for these (i,j): (3070, 32511), (32495, 32509)
X(32507) = {X(3070), X(32511)}-harmonic conjugate of X(32503)


X(32508) = ORTHOCENTER OF THE 3rd INNER-VECTEN TRIANGLE

Barycentrics    (4*R^2+15*SA-67*SW)*S^4-(SA-SW)*(2*R^2*SA+SW*(47*SA-12*SW))*S^2-4*SB*SC*SW^3-S*(20*S^4+(2*(SA+SW)*R^2+23*SA^2-54*SB*SC-49*SW^2)*S^2-2*(12*SA-SW)*(SA-SW)*SW^2) : :

X(32508) lies on these lines: {486,32502}, {642,3071}, {6119,32504}, {32492,32506}

X(32508) = midpoint of X(32492) and X(32506)
X(32508) = reflection of X(6119) in X(32512)
X(32508) = X(52)-of-inner-Vecten triangle
X(32508) = {X(6119), X(32512)}-harmonic conjugate of X(32504)


X(32509) = ORTHOCENTER OF THE 3rd OUTER-VECTEN TRIANGLE

Barycentrics    (4*R^2+15*SA-67*SW)*S^4-(SA-SW)*(2*R^2*SA+SW*(47*SA-12*SW))*S^2-4*SB*SC*SW^3+S*(20*S^4+(2*(SA+SW)*R^2+23*SA^2-54*SB*SC-49*SW^2)*S^2-2*(12*SA-SW)*(SA-SW)*SW^2) : :

X(32509) lies on these lines: {485,32503}, {641,3070}, {6118,32505}, {32495,32507}

X(32509) = midpoint of X(32495) and X(32507)
X(32509) = reflection of X(6118) in X(32513)
X(32509) = X(52)-of-outer-Vecten triangle
X(32509) = {X(6118), X(32513)}-harmonic conjugate of X(32505)


X(32510) = X(5)-OF-2nd INNER-VECTEN TRIANGLE

Barycentrics    (5*SA-33*SW)*S^4-(4*(SA-SW)*SA*R^2+(19*SA^2-28*SA*SW+10*SW^2)*SW)*S^2-3*SB*SC*SW^3-S*(8*S^4+2*((SA+SW)*R^2+6*SA^2-10*SB*SC-16*SW^2)*S^2-2*(7*SA-SW)*(SA-SW)*SW^2) : :

X(32510) lies on these lines: {3071,32502}, {6119,18762}

X(32510) = midpoint of X(3071) and X(32506)
X(32510) = {X(32502), X(32506)}-harmonic conjugate of X(3071)


X(32511) = X(5)-OF-2nd OUTER-VECTEN TRIANGLE

Barycentrics    (5*SA-33*SW)*S^4-(4*(SA-SW)*SA*R^2+(19*SA^2-28*SA*SW+10*SW^2)*SW)*S^2-3*SB*SC*SW^3+S*(8*S^4+2*((SA+SW)*R^2+6*SA^2-10*SB*SC-16*SW^2)*S^2-2*(7*SA-SW)*(SA-SW)*SW^2) : :

X(32511) lies on these lines: {3070,32503}, {6118,18538}

X(32511) = midpoint of X(3070) and X(32507)
X(32511) = {X(32503), X(32507)}-harmonic conjugate of X(3070)


X(32512) = X(5)-OF-3rd INNER-VECTEN TRIANGLE

Barycentrics
(20*R^2+35*SA-203*SW)*S^4-(2*(SA-SW)*SA*R^2+(103*SA^2-44*(3*SA-SW)*SW)*SW)*S^2-9*SB*SC*SW^3-S*(24*S^4+(2*(SA+5*SW)*R^2+55*SA^2-122*SB*SC-97*SW^2)*S^2+(5*SA^2-58*SB*SC-7*SW^2)*SW^2) : :
X(32512) = X(642)+3*X(32502)

X(32512) lies on these lines: {642,32502}, {6119,32504}

X(32512) = midpoint of X(6119) and X(32508)
X(32512) = X(143)-of-inner-Vecten triangle
X(32512) = {X(32504), X(32508)}-harmonic conjugate of X(6119)


X(32513) = X(5)-OF-3rd OUTER-VECTEN TRIANGLE

Barycentrics
(20*R^2+35*SA-203*SW)*S^4-(2*(SA-SW)*SA*R^2+(103*SA^2-44*(3*SA-SW)*SW)*SW)*S^2-9*SB*SC*SW^3+S*(24*S^4+(2*(SA+5*SW)*R^2+55*SA^2-122*SB*SC-97*SW^2)*S^2+(5*SA^2-58*SB*SC-7*SW^2)*SW^2) : :
X(32513) = X(641)+3*X(32503)

X(32513) lies on these lines: {641,32503}, {6118,32505}

X(32513) = midpoint of X(6118) and X(32509)
X(32513) = X(143)-of-outer-Vecten triangle
X(32513) = {X(32505), X(32509)}-harmonic conjugate of X(6118)


X(32514) = X(3)X(194)∩X(699)X(1384)

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

X(32514) = X(25)-of-inscribed-triply-bilogic-triangle; see the preamble just before X(32562)

X(32514) lies on these lines: {3, 194}, {699, 1384}, {2076, 32442}, {3552, 19597}, {5017, 9431}


X(32515) = X(3)X(194)∩X(5)X(76)

Barycentrics    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(32515) lies on these lines: {2, 8179}, {3, 194}, {4, 7779}, {5, 76}, {6, 22525}, {15, 32465}, {16, 32466}, {20, 20105}, {26, 9917}, {30, 511}, {39, 140}, {98, 10290}, {99, 2080}, {114, 7813}, {141, 11261}, {182, 7798}, {187, 1569}, {298, 20426}, {299, 20425}, {316, 6321}, {323, 1316}, {355, 9902}, {381, 7840}, {384, 22521}, {395, 3106}, {396, 3107}, {397, 3105}, {398, 3104}, {495, 10063}, {496, 10079}, {546, 6248}, {547, 9466}, {548, 5188}, {549, 7757}, {550, 9821}, {576, 3734}, {620, 14693}, {632, 7786}, {1151, 32470}, {1152, 32471}, {1351, 18906}, {1353, 32451}, {1483, 7976}, {1484, 32454}, {1513, 9772}, {1656, 7881}, {1916, 15980}, {3094, 15048}, {3097, 26446}, {3102, 7584}, {3103, 7583}, {3186, 22152}, {3398, 7760}, {3530, 13334}, {3580, 11007}, {3589, 32149}, {3628, 3934}, {3926, 9752}, {4385, 15973}, {5054, 8859}, {5066, 14711}, {5093, 11286}, {5097, 7804}, {5149, 13196}, {5171, 7781}, {5254, 32452}, {5690, 12782}, {5874, 6272}, {5875, 6273}, {5901, 12263}, {5976, 6390}, {5999, 12188}, {6234, 18829}, {6683, 16239}, {6756, 12143}, {6781, 10992}, {6795, 32599}, {7467, 8267}, {7617, 14159}, {7694, 7758}, {7751, 9737}, {7763, 9754}, {7766, 11842}, {7789, 18806}, {7799, 15561}, {7805, 13335}, {7809, 14639}, {7826, 32152}, {7845, 13449}, {8597, 12355}, {8598, 11152}, {8703, 11055}, {8782, 9301}, {8992, 13925}, {9743, 9764}, {9748, 32830}, {9751, 12054}, {9753, 32833}, {9756, 31981}, {9983, 22678}, {10263, 16983}, {10358, 17130}, {10942, 12933}, {10943, 12923}, {11054, 11632}, {12042, 18860}, {12100, 21163}, {12338, 22556}, {12474, 22668}, {12475, 22672}, {12794, 22698}, {12992, 22709}, {12993, 22710}, {13077, 15171}, {13109, 22731}, {13110, 22732}, {13172, 14712}, {13330, 18907}, {13983, 13993}, {14651, 19570}, {14853, 32836}, {14880, 30270}, {15122, 16315}, {16266, 23128}, {16316, 16619}, {16320, 25338}, {18583, 24256}, {18971, 18982}, {19063, 19089}, {19064, 19090}, {22680, 22779}, {22735, 33873}

X(32515) = Lucas-isogonal conjugate of X(25424)
X(32515) = Thomson-isogonal conjugate of X(25424)
X(32515) = X(30)-of-inscribed-triply-bilogic-triangle

X(32515) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 194, 32448}, {4, 20081, 13108}, {76, 262, 7697}, {76, 3095, 5}, {194, 6194, 7709}, {194, 12251, 3}, {262, 7697, 5}, {576, 3734, 10796}, {3095, 7697, 262}, {3934, 11272, 3628}, {6194, 7709, 3}, {6248, 14881, 546}, {6248, 22682, 22681}, {7709, 12251, 6194}, {7751, 9737, 10104}, {7757, 22712, 11171}, {9301, 13188, 11676}, {9821, 11257, 550}, {10063, 12837, 495}, {10063, 22729, 22705}, {10079, 12836, 496}, {10079, 22730, 22706}, {11152, 22564, 8598}, {11171, 22712, 549}, {12836, 22706, 22730}, {12837, 22705, 22729}, {14881, 22681, 22682}, {22681, 22682, 546}, {22705, 22729, 495}, {22706, 22730, 496}


X(32516) = X(3)X(194)∩X(30)X(39)

Barycentrics    4*a^6*b^2 - 5*a^4*b^4 + a^2*b^6 + 4*a^6*c^2 - 8*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 - 5*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(32516) = 3 X[3] + X[194],7 X[3] - 3 X[6194],X[3] + 3 X[7709],5 X[3] - X[12251],3 X[5] - 5 X[7786],X[5] - 3 X[11171],X[20] + 3 X[32447],3 X[39] - X[14881],X[76] - 3 X[549],3 X[140] - 2 X[3934],7 X[194] + 9 X[6194],X[194] - 9 X[7709],5 X[194] + 3 X[12251],X[194] - 3 X[32448],3 X[262] - X[3627],3 X[547] - 4 X[6683],5 X[631] - X[13108],5 X[632] - 3 X[7697],3 X[3097] + X[18481],9 X[3524] - X[20081],X[3529] + 3 X[22728],2 X[3530] - 3 X[21163],X[3934] - 3 X[13334],9 X[5054] - 5 X[31276],X[6194] + 7 X[7709],15 X[6194] - 7 X[12251],3 X[6194] + 7 X[32448],9 X[7618] - X[18768],15 X[7709] + X[12251],3 X[7709] - X[32448],3 X[7757] + X[9821],5 X[7786] - 9 X[11171],5 X[7786] + 3 X[11257],3 X[8356] - X[32151],3 X[8703] - X[9821],3 X[8716] + X[31981],6 X[10124] - 5 X[31239],7 X[10541] - 3 X[31958],X[11055] + 5 X[15711],3 X[11171] + X[11257],5 X[12017] - X[18906],2 X[12102] - 3 X[22682],4 X[12108] - 3 X[15819],X[12251] + 5 X[32448],4 X[12811] - 3 X[22681],3 X[13331] - X[21850],15 X[15692] + X[20105],5 X[15712] - 3 X[22712]

X(32516) lies on these lines: {3, 194}, {5, 7786}, {20, 32447}, {30, 39}, {76, 549}, {99, 12054}, {140, 620}, {141, 32429}, {262, 3627}, {511, 548}, {538, 12100}, {546, 11272}, {547, 6683}, {550, 3095}, {574, 14880}, {631, 13108}, {632, 7697}, {698, 5092}, {726, 13624}, {1151, 32471}, {1152, 32470}, {1569, 12042}, {2021, 5305}, {2080, 32467}, {3097, 18481}, {3098, 32449}, {3524, 20081}, {3529, 22728}, {3530, 21163}, {3628, 6248}, {5054, 31276}, {5237, 32465}, {5238, 32466}, {6033, 7847}, {7467, 31088}, {7618, 18768}, {7757, 8703}, {7782, 26316}, {7824, 12188}, {7832, 8724}, {7839, 9301}, {8356, 32151}, {8716, 31981}, {9466, 11812}, {10007, 18358}, {10124, 31239}, {10541, 31958}, {11055, 15711}, {11676, 32134}, {12017, 18906}, {12102, 22682}, {12108, 15819}, {12811, 22681}, {13077, 15325}, {13331, 21850}, {15692, 20105}, {15712, 22712}, {18806, 32459}

X(32516) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32448}, {5, 11257}, {141, 32429}, {550, 3095}, {1569, 12042}, {3098, 32449}, {7757, 8703}
X(32516) = reflection of X(i) in X(j) for these lines: {i,j}: {140, 13334}, {546, 11272}, {6248, 3628}, {9466, 11812}, {18358, 10007}
X(32516) = X(140)-of-inscribed-triply-bilogic-triangle
X(32516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7709, 32448}, {11171, 11257, 5}


X(32517) = X(3)X(194)∩X(187)X(699)

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

X(32517) lies on these lines: {3, 194}, {187, 699}, {9491, 13586}

X(32517) = circumcircle-inverse of X(194)
X(32517) = X(186)-of-inscribed-triply-bilogic-triangle


X(32518) = X(3)X(194)∩X(32)X(9490)

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

X(32518) lies on these lines: {3, 194}, {32, 9490}, {187, 237}, {805, 2080}, {865, 5913}, {1613, 23221}, {3053, 3224}, {3360, 5023}, {3511, 13586}, {7771, 14096}, {11332, 11580}, {16514, 22386}

X(32518) = {X(187),X(21444)}-harmonic conjugate of X(237)
X(32518) = X(237)-of-inscribed-triply-bilogic-triangle


X(32519) = X(3)X(194)∩X(6)X(15690)

Barycentrics    3*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6 + 3*a^6*c^2 - 11*a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 - 5*a^4*c^4 + a^2*b^2*c^4 + 4*b^4*c^4 + 2*a^2*c^6 - 2*b^2*c^6 : :
X(32519) = X[3] + 2 X[194],3 X[3] - 2 X[6194],5 X[3] - 2 X[12251],X[3] - 4 X[32448],8 X[39] - 5 X[1656],4 X[39] - X[13108],4 X[76] - 7 X[3526],4 X[140] - X[20081],3 X[194] + X[6194],5 X[194] + X[12251],X[194] + 2 X[32448],4 X[262] - 3 X[381],X[262] - 3 X[7757],3 X[262] - 2 X[22681],2 X[262] - 3 X[32447],X[381] - 4 X[7757],9 X[381] - 8 X[22681],X[382] - 4 X[3095],X[382] - 16 X[32450],5 X[631] + X[20105],X[1351] - 4 X[32449],4 X[1569] - X[13188]

X(32519) lies on these lines: {3, 194}, {6, 1569}, {39, 1656}, {76, 3526}, {99, 11842}, {140, 20081}, {262, 381}, {382, 3095}, {511, 3534}, {538, 1153}, {631, 20105}, {698, 5050}, {726, 10246}, {732, 22677}, {1351, 32449}, {1499, 32463}, {1657, 11257}, {2070, 22655}, {2080, 7798}, {3094, 11898}, {3097, 5790}, {3311, 32470}, {3312, 32471}, {3398, 7781}, {3818, 14692}, {3906, 8723}, {5072, 6248}, {5076, 14881}, {5079, 11272}, {5309, 15561}, {7748, 10242}, {7839, 22521}, {9466, 15723}, {9756, 12188}, {9917, 13564}, {10256, 18768}, {10796, 23235}, {11055, 15693}, {11152, 11159}, {12645, 12782}, {13077, 22730}, {15696, 22676}, {15700, 21163}, {18525, 22650}, {18982, 22729}

X(32519) = midpoint of X(i) and X(j) for these lines: {i,j}: {194, 7709}, {11055, 22712}
X(32519) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 7709}, {381, 32447}, {382, 22728}, {5790, 3097}, {7697, 39}, {7709, 32448}, {13108, 7697}, {18525, 22650}, {22728, 3095}, {32447, 7757}
X(32519) = X(381)-of-inscribed-triply-bilogic-triangle
X(32519) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 13108, 1656}, {194, 32448, 3}, {32465, 32466, 6}


X(32520) = X(3)X(194)∩X(4)X(20105)

Barycentrics    a^6*b^2 - 3*a^4*b^4 + 2*a^2*b^6 + a^6*c^2 - 9*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 + 4*b^4*c^4 + 2*a^2*c^6 - 2*b^2*c^6 : :
X(32520) = 7 X[3] - 6 X[6194],5 X[3] - 6 X[7709],3 X[3] - 2 X[12251],3 X[3] - 4 X[32448],8 X[39] - 7 X[3526],4 X[76] - 5 X[1656],3 X[76] - 4 X[11272],2 X[76] - 3 X[32447],7 X[194] - 3 X[6194],5 X[194] - 3 X[7709],3 X[194] - X[12251],3 X[194] - 2 X[32448],12 X[262] - 11 X[5072],3 X[381] - 4 X[3095],9 X[381] - 8 X[6248],3 X[381] - 2 X[13108],15 X[1656] - 16 X[11272],5 X[1656] - 6 X[32447],3 X[3095] - 2 X[6248],X[3534] - 4 X[11055],3 X[3534] - 4 X[11257]

X(32520) lies on these lines: {3, 194}, {4, 20105}, {5, 7906}, {39, 3526}, {76, 1656}, {262, 5072}, {381, 538}, {382, 2782}, {511, 1657}, {576, 18501}, {698, 1351}, {726, 1482}, {730, 12645}, {732, 11898}, {1569, 3053}, {2080, 7781}, {2937, 9917}, {3102, 18510}, {3103, 18512}, {3398, 7798}, {3534, 11055}, {5050, 32449}, {5054, 7757}, {5070, 31276}, {5076, 22728}, {5079, 7697}, {5093, 18906}, {5188, 15688}, {5790, 9902}, {6221, 32470}, {6321, 7759}, {6398, 32471}, {7760, 11842}, {7890, 23698}, {9821, 15696}, {10983, 31981}, {11171, 15720}, {13334, 15693}, {15069, 18503}, {22236, 32465}, {22238, 32466}

X(32520) = midpoint of X(4) and X(20105)
X(32520) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 194}, {12251, 32448}, {13108, 3095}, {20081, 5}
X(32520) = X(382)-of-inscribed-triply-bilogic-triangle
X(32520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 32447, 1656}, {194, 12251, 32448}, {3095, 13108, 381}, {12251, 32448, 3}


X(32521) = X(3)X(194)∩X(5)X(141)

Barycentrics    2*a^6*b^2 - a^4*b^4 - a^2*b^6 + 2*a^6*c^2 + 2*a^4*b^2*c^2 - 4*a^2*b^4*c^2 + b^6*c^2 - a^4*c^4 - 4*a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6 : :
X(32521) = 3 X[3] - X[194],X[3] - 3 X[6194],5 X[3] - 3 X[7709],3 X[5] - 4 X[3934],3 X[5] - 2 X[14881],2 X[39] - 3 X[549],6 X[140] - 5 X[7786],2 X[140] - 3 X[22712],X[194] - 9 X[6194],5 X[194] - 9 X[7709],X[194] + 3 X[12251],2 X[194] - 3 X[32448],3 X[262] - 4 X[3628],3 X[376] + X[20081],3 X[381] - 5 X[31276],2 X[546] - 3 X[7697],5 X[631] - 3 X[32447],5 X[632] - 4 X[11272],5 X[632] - 6 X[15819],5 X[3091] - 3 X[22728],3 X[3095] - 5 X[7786],X[3095] - 3 X[22712]

X(32521) lies on these lines: {3, 194}, {4, 7929}, {5, 141}, {20, 13108}, {30, 76}, {39, 549}, {140, 3095}, {230, 32452}, {262, 3628}, {343, 21536}, {376, 20081}, {381, 7879}, {384, 9301}, {395, 3104}, {396, 3105}, {524, 8149}, {538, 8703}, {546, 7697}, {548, 11257}, {550, 2782}, {631, 32447}, {632, 11272}, {698, 3098}, {726, 3579}, {1353, 13354}, {1569, 15513}, {2979, 21531}, {3091, 22728}, {3094, 5305}, {3102, 13966}, {3103, 8981}, {3106, 16773}, {3107, 16772}, {3530, 11171}, {3627, 6248}, {3845, 9466}, {3857, 22682}, {3933, 5976}, {5092, 7805}, {5351, 32466}, {5352, 32465}, {6033, 7768}, {6179, 26316}, {6409, 32470}, {6410, 32471}, {6644, 9917}, {6683, 11539}, {7470, 8782}, {7757, 12100}, {7760, 12054}, {7780, 12042}, {7797, 10357}, {7842, 22515}, {7854, 9996}, {8367, 22486}, {8370, 22564}, {8667, 31981}, {9902, 18481}, {10063, 18990}, {10079, 15171}, {10104, 30270}, {10304, 20105}, {11055, 15759}, {11477, 31958}, {12103, 22676}, {12263, 22791}, {12836, 15325}, {13334, 15712}, {13468, 32189}, {14711, 19710}, {15699, 31239}, {17504, 32450}

X(32521) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 12251}, {20, 13108}, {76, 9821}, {8782, 12188}, {9902, 18481}
X(32521) = reflection of X(i) in X(j) for these lines: {i,j}: {550, 5188}, {1353, 13354}, {3095, 140}, {3627, 6248}, {3845, 9466}, {7757, 12100}, {11257, 548}, {14881, 3934}, {21850, 24256}, {22791, 12263}, {32151, 7767}, {32448, 3}, {32449, 5092}
X(32521) = X(550)-of-inscribed-triply-bilogic-triangle
X(32521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3095, 22712, 140}, {3098, 7751, 14880}, {3934, 14881, 5}, {6194, 12251, 3}, {7470, 17129, 12188}, {11272, 15819, 632}


X(32522) = X(3)X(194)∩X(20)X(39)

Barycentrics    5*a^6*b^2 - 6*a^4*b^4 + a^2*b^6 + 5*a^6*c^2 - 9*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - b^6*c^2 - 6*a^4*c^4 - 3*a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6 : :
X(32522) = 9 X[2] - 4 X[6248],3 X[2] + 2 X[11257],3 X[2] - 8 X[13334],4 X[3] + X[194],8 X[3] - 3 X[6194],2 X[3] + 3 X[7709],6 X[3] - X[12251],3 X[3] + 2 X[32448],X[4] - 6 X[11171],3 X[4] - 8 X[11272],X[20] + 4 X[39],2 X[76] - 7 X[3523],X[76] - 6 X[21163],2 X[194] + 3 X[6194],X[194] - 6 X[7709],3 X[194] + 2 X[12251],3 X[194] - 8 X[32448]

X(32522) lies on these lines: {2, 6248}, {3, 194}, {4, 11171}, {20, 39}, {76, 3523}, {114, 7933}, {147, 7791}, {182, 3552}, {262, 3146}, {376, 3095}, {511, 3522}, {538, 15692}, {549, 13108}, {550, 32447}, {574, 12203}, {631, 2782}, {726, 7987}, {1513, 7864}, {1569, 15515}, {2021, 5286}, {3091, 7786}, {3094, 25406}, {3096, 14981}, {3097, 4297}, {3102, 9541}, {3525, 7697}, {3528, 9821}, {3529, 14881}, {3564, 7904}, {3934, 10303}, {5013, 5999}, {5056, 6683}, {5085, 18906}, {5171, 7766}, {5188, 7757}, {5218, 18982}, {5351, 32465}, {5352, 32466}, {5731, 12782}, {6200, 32471}, {6396, 32470}, {6655, 9744}, {7288, 13077}, {7760, 8722}, {7787, 11676}, {7815, 15483}, {8356, 9863}, {8782, 21166}, {9466, 15708}, {9902, 10164}, {15704, 22728}, {15717, 20081}, {20190, 31958}, {31884, 32449}

X(32522) = reflection of X(i) in X(j) for these lines: {i,j}: {3091, 7786}, {31276, 631}
X(32522) = X(631)-of-inscribed-triply-bilogic-triangle
X(32522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 194, 6194}, {3, 7709, 194}, {3, 32448, 12251}, {76, 21163, 3523}, {5171, 32467, 7766}, {7709, 12251, 32448}, {11257, 13334, 2}, {12251, 32448, 194}, {15717, 20081, 22712}


X(32523) = X(3)X(194)∩X(39)X(3627)

Barycentrics    10*a^6*b^2 - 13*a^4*b^4 + 3*a^2*b^6 + 10*a^6*c^2 - 22*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 3*b^6*c^2 - 13*a^4*c^4 - 4*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 3*b^2*c^6 : :
X(32523) = 7 X[3] + 3 X[194],19 X[3] - 9 X[6194],X[3] + 9 X[7709],13 X[3] - 3 X[12251],2 X[3] + 3 X[32448],6 X[39] - X[3627],3 X[76] - 8 X[12108],19 X[194] + 21 X[6194],X[194] - 21 X[7709],13 X[194] + 7 X[12251],2 X[194] - 7 X[32448]

X(32523) lies on these lines: {3, 194}, {39, 3627}, {76, 12108}, {262, 12102}, {538, 15712}, {546, 11257}, {548, 7757}, {549, 14711}, {632, 2782}, {726, 31666}, {3095, 12103}, {3529, 32447}, {3628, 11171}, {3857, 11272}, {6425, 32471}, {6426, 32470}, {7786, 12812}, {10303, 13108}, {11055, 14891}, {13334, 14869}

X(32523) = X(632)-of-inscribed-triply-bilogic-triangle


X(32524) = X(3)X(194)∩X(39)X(3224)

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

X(32524) lies on these s {3, 194}, {39, 3224}, {99, 11328}, {574, 3229}, {1975, 14937}, {3225, 7757}, {3360, 5013}, {3511, 8716}, {8841, 9737}, {9490, 9605}

X(32524) = Thomson-isogonal conjugate of X(6194)


X(32525) = MIDPOINT OF X(2) AND X(9169)

Barycentrics    a^4*b^2 + 3*a^2*b^4 - b^6 + a^4*c^2 - 10*a^2*b^2*c^2 + 2*b^4*c^2 + 3*a^2*c^4 + 2*b^2*c^4 - c^6 : :
X(32525) = 3 X[2] + X[6792],5 X[2] - X[14916],7 X[3090] - X[15098],9 X[5055] - X[18346],X[5108] + 3 X[9169],5 X[5108] - 3 X[14916],X[5971] + 3 X[11647],X[6792] - 3 X[9169],5 X[6792] + 3 X[14916],5 X[9169] + X[14916]

X(32525) lies on the cubic K249 and these s {2, 6}, {5, 1499}, {126, 5969}, {373, 2679}, {542, 6719}, {3090, 15098}, {4045, 11007}, {5026, 10418}, {5055, 18346}, {6034, 30786}, {6082, 14658}, {7603, 9151}, {7804, 22104}, {9152, 31654}, {9172, 9830}, {10160, 10168}, {10278, 22260}, {20382, 23297}

X(32525) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 9169}, {126, 6791}, {5108, 6792}
X(32525) = complement of X(5108)
X(32525) = nine-point-circle-inverse of X(23301)
X(32525) = orthoptic-circle-of-Steiner-inellipe-inverse of X(385)
X(32525) = circumcircle-of-inner-Napoleon-triangle-inverse of X(3180)
X(32525) = circumcircle-of-outer-Napoleon-triangle inverse of X(3181)
X(32525) = complement of the isogonal conjugate of X(14948)
X(32525) = psi-transform of X(148)
X(32525) = X(14948)-complementary conjugate of X(10)
X(32525) = crossdifference of every pair of points lies on these lines: {512, 9225}
X(32525) = orthogonal projection of X(5) on line X(2)X(6)
X(32525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 11053}, {2, 1648, 141}, {2, 6792, 5108}, {5108, 9169, 6792}


X(32526) = X(2)X(39)∩X(23)X(5106)

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

X(32526) lies on the Parry circle, the cubic K794, and on these lines: {2, 39}, {23, 5106}, {110, 1691}, {187, 9999}, {237, 9157}, {353, 5092}, {511, 9998}, {647, 5996}, {694, 20977}, {698, 13518}, {1084, 7840}, {3292, 9463}, {3796, 21001}, {7711, 11580}, {7931, 8265}, {8620, 9978}, {9138, 9210}, {9156, 17414}, {9208, 9212}, {14684, 20481}

X(32526) = reflection of X(9998) in the Lemoine axis
X(32526) = orthoptic-circle-of-Steiner-inellipse-inverse of X(39)
X(32526) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(194)
X(32526) = psi-transform of X(3094)
X(32526) = crossdifference of every pair of points lies on these lines: {669, 11182}
X(32526) = X(5970)-of-2nd-Parry-triangle


X(32527) = X(4)X(147)∩X(25)X(5152)

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

X(32527) lies on these lines: {4, 147}, {25, 5152}, {804, 2489}

X(32527) = polar circle inverse of X(194)
X(32527) = {X(5186),X(12131)}-harmonic conjugate of X(12143)


X(32528) = X(2)X(4159)∩X(4)X(147)

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

X(32528) lies on these lines: {2, 4159}, {4, 147}, {83, 115}, {99, 626}, {315, 8782}, {316, 9865}, {542, 19570}, {543, 7809}, {620, 7944}, {671, 7753}, {804, 2514}, {2794, 14712}, {2896, 5976}, {3926, 20094}, {5025, 5989}, {5103, 12215}, {5939, 7932}, {5987, 19577}, {6034, 9830}, {6656, 8290}, {7752, 8178}, {7790, 10334}, {7791, 7945}, {7793, 9862}, {7803, 10353}, {7839, 12830}, {7889, 14061}, {9880, 14492}, {11646, 24256}, {12177, 14639}

X(32528) = anticomplement of X(5152)
X(32528) = polar circle inverse of X(12143)
X(32528) = circumcircle-of-anticomplementary-triangle-inverse of X(194)
X(32528) = X(30530)-anticomplementary conjugate of X(17217)
X(32528) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 4027, 7797}, {147, 148, 194}, {148, 7785, 1916}, {1916, 6033, 7785}, {6033, 6321, 14881}, {11606, 16044, 115}


X(32529) = X(20)X(185)∩X(22)X(1613)

Barycentrics    a^2*(a^6*b^4 - a^2*b^8 - a^6*b^2*c^2 - a^4*b^4*c^2 + 2*a^2*b^6*c^2 + a^6*c^4 - a^4*b^2*c^4 + a^2*b^4*c^4 - b^6*c^4 + 2*a^2*b^2*c^6 - b^4*c^6 - a^2*c^8) : :
X(32529) = 4 X[2076] - 3 X[11673]

X(32529) lies on these lines: {20, 185}, {22, 1613}, {401, 19585}, {512, 16084}, {805, 1297}, {858, 5103}, {1691, 19121}, {1843, 6658}, {2456, 2698}, {2882, 12215}, {5104, 32464}, {5111, 11416}, {11634, 14965}

X(32529) = crosssum of X(3229) and X(6467)
X(32529) = de Longchamps-circle-inverse of X(194)
X(32529) = anticomplement of the isogonal conjugate of X(8858)
X(32529) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {699, 21216}, {3225, 5905}, {8858, 8}


X(32530) = X(2)X(39)∩X(8651)X(11176)

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

X(32530) lies on these lines: {2, 39}, {8651, 11176}

X(32530) = orthoptic-circle-of-Steiner-inellipse-inverse of X(194)
X(32530) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(20105)


X(32531) = X(2)X(669)∩X(3)X(194)

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

X(32531) lies on these lines: {2, 669}, {3, 194}, {182, 805}, {353, 3231}, {574, 5970}, {3407, 14870}, {5092, 15920}, {5108, 7496}, {8289, 21444}

X(32531) = circumcircle-inverse of X(385)
X(32531) = Brocard-circle-inverse of X(805)
X(32531) = orthoptic-circle-of-Steiner-inellipse-inverse of X(23301)
X(32531) = 2nd-Brocard-circle-inverse of X(194)
X(32531) = psi-transform of X(5027)


X(32532) = ISOGONAL CONJUGATE OF X(15655)

Barycentrics    (7*a^2-11*b^2+7*c^2)*(7*a^2+7*b^2-11*c^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32532) lies on the Kiepert hyperbola and these lines: {4, 8584}, {98, 15682}, {115, 10153}, {376, 7607}, {631, 10185}, {1992, 17503}, {2996, 8352}, {3424, 3830}, {3545, 7608}, {3845, 14484}, {5254, 18843}, {5286, 18844}, {5395, 11317}, {5485, 15533}, {7612, 11001}, {11668, 15719}

X(32532) = reflection of X(10153) in X(115)
X(32532) = isogonal conjugate of X(15655)
X(32532) = antigonal conjugate of X(10153)
X(32532) = antitomic conjugate of X(10153)
X(32532) = isotomic conjugate of the anticomplement of X(15534)
X(32532) = antipode of X(10153) in the Kiepert hyperbola


X(32533) = X(5)X(14528)∩X(6)X(546)

Barycentrics    (-a^2+b^2+c^2)*(3*a^4-2*(3*b^2-2*c^2)*a^2+3*(b^2-c^2)^2)*(3*a^4+2*(2*b^2-3*c^2)*a^2+3*(b^2-c^2)^2) : :
Barycentrics    SA*(S^2-5*SB^2)*(S^2-5*SC^2) : :
Barycentrics    (Cos[A] Sin[A])/(2+3 Cos[2 A]) : :
X(32533) = 7*X(3090)-3*X(25712)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32533) lies on the Jerabek hyperbola and these lines: {5, 14528}, {6, 546}, {30, 3532}, {54, 3091}, {64, 3627}, {66, 18383}, {67, 18569}, {68, 13851}, {69, 9927}, {70, 18394}, {74, 3146}, {895, 15083}, {1352, 13622}, {1899, 3521}, {3090, 3431}, {3426, 5076}, {3519, 18404}, {3529, 11270}, {3839, 10116}, {5486, 18553}, {10113, 11744}, {10293, 31725}, {10297, 15316}, {10594, 18532}, {12102, 22334}, {13754, 15077}, {14542, 18390}, {15740, 18918}, {16625, 18376}, {17538, 20421}, {21400, 25738}

X(32533) = isogonal conjugate of X(32534)
X(32533) = anticomplement of X(33556)


X(32534) = ISOGONAL CONJUGATE OF X(32533)

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(3*a^4-6*(b^2+c^2)*a^2+3*b^4+4*b^2*c^2+3*c^4) : :
Barycentrics    SB*SC*(SB+SC)*(S^2-5*SA^2) : :
Barycentrics    (2+3 Cos[2 A]) Tan[A] : :
Trilinears    6 cos A - sec A : :

As a point on the Euler line, X(32534) has Shinagawa coefficients (-6*F, E+6*F).

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32534) lies on these lines: {2, 3}, {54, 9786}, {64, 11468}, {74, 1498}, {110, 12163}, {112, 5023}, {154, 6241}, {155, 11449}, {184, 13382}, {185, 9707}, {187, 8743}, {232, 5206}, {340, 9723}, {1151, 10881}, {1152, 10880}, {1181, 11464}, {1192, 5890}, {1199, 3431}, {1204, 10282}, {1350, 19128}, {1495, 3357}, {1511, 13148}, {1614, 1620}, {1829, 17502}, {1843, 17508}, {1870, 5204}, {1968, 15513}, {1974, 14810}, {1986, 11412}, {1990, 8553}, {1993, 12038}, {2207, 5210}, {2351, 5963}, {2904, 16879}, {2931, 9938}, {3043, 15040}, {3092, 6411}, {3093, 6412}, {3567, 11425}, {3580, 12118}, {3581, 16266}, {5013, 10312}, {5085, 6403}, {5217, 6198}, {5237, 8740}, {5238, 8739}, {5410, 6450}, {5411, 6449}, {5621, 15581}, {5702, 8573}, {6030, 15086}, {6759, 21663}, {7592, 11438}, {7689, 11441}, {8541, 20190}, {8744, 8778}, {8907, 12893}, {8960, 9682}, {10193, 13419}, {10606, 12290}, {10619, 23358}, {10632, 11481}, {10633, 11480}, {10990, 13289}, {11204, 11381}, {11270, 12315}, {11363, 31663}, {11440, 18451}, {11550, 25563}, {12112, 13093}, {12278, 14852}, {12279, 12292}, {12383, 12429}, {13481, 19189}, {13558, 16080}, {15036, 15472}, {15578, 20987}, {16655, 23328}, {17845, 25739}, {18396, 26917}, {18445, 32171}, {18474, 20191}, {19467, 26879}, {20427, 32111}

X(32534) = reflection of X(3) in X(23323)
X(32534) = isogonal conjugate of X(32533)
X(32534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,4,35477), (3, 7387, 2071), (4, 3515, 24), (14865, 23040, 11410)


X(32535) = X(3)X(1487)∩X(4)X(1493)

Barycentrics    (7*R^2-3*SC-SW)*(7*R^2-3*SB-SW)*(S^2+SB*SC) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32535) lies on these lines: {3, 1487}, {4, 1493}, {20, 3459}, {3853, 15619}, {17507, 20424}


X(32536) = X(4)X(137)∩X(5)X(27684)

Barycentrics    3*S^4-(R^2*(12*R^2+5*SA-12*SW)-2*SA^2+13*SB*SC+3*SW^2)*S^2-(R^2*(28*R^2-17*SW)+SW^2)*SB*SC : :
X(32536) = 3*X(381)-X(30484)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32536) lies on these lines: {4, 137}, {5, 27684}, {30, 13856}, {128, 24573}, {381, 30484}, {539, 23337}, {546, 20413}, {3853, 5893}, {8146, 28341}, {15307, 31376}, {15619, 17507}, {18807, 28237}, {20120, 25150}

X(32536) = reflection of X(i) in X(j) for these (i,j): (13856, 31879), (18016, 23338)


X(32537) = X(5)X(519)∩X(7)X(8)

Barycentrics    2*a^4-3*(b+c)*a^3+10*a^2*b*c+(b+c)*(3*b^2-8*b*c+3*c^2)*a-2*(b^2-c^2)^2 : :
X(32537) = X(3621)+3*X(25568), 3*X(3679)-X(12513), 5*X(4668)-X(6762), 3*X(4669)-X(24391), 3*X(4677)+X(11523), 7*X(4678)-3*X(24477), 3*X(5587)-X(10912), X(7982)-3*X(11236)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32537) lies on these lines: {1, 5123}, {5, 519}, {7, 8}, {10, 6691}, {145, 11376}, {355, 3880}, {474, 3679}, {517, 32159}, {528, 12640}, {529, 11362}, {946, 5854}, {952, 10915}, {960, 12647}, {1012, 3913}, {1210, 3036}, {1317, 27385}, {1319, 17566}, {1387, 3244}, {1482, 22835}, {1837, 12648}, {2098, 5087}, {2802, 18480}, {3057, 5046}, {3241, 6931}, {3337, 4668}, {3621, 25568}, {3625, 5855}, {3632, 10827}, {3633, 23708}, {3742, 5554}, {3811, 12645}, {3838, 9578}, {3893, 5086}, {4134, 15862}, {4297, 32157}, {4669, 24391}, {4677, 11523}, {4678, 24477}, {4861, 7504}, {5048, 11681}, {5258, 19525}, {5587, 10912}, {5795, 15254}, {5837, 15481}, {5844, 21077}, {6735, 10944}, {6738, 15570}, {6871, 31145}, {7483, 10039}, {7982, 11236}, {7991, 28534}, {8256, 10106}, {8715, 28204}, {9037, 31785}, {9956, 22837}, {11567, 22836}, {12641, 13271}, {12672, 12751}, {13463, 19925}, {15888, 25962}, {20323, 25005}, {21627, 32426}

X(32537) = midpoint of X(i) and X(j) for these lines: {i,j}: {8, 32049}, {3632, 12635}, {3811, 12645}, {3913, 5881}, {12641, 13271}
X(32537) = reflection of X(i) in X(j) for these (i,j): (4297, 32157), (11260, 10), (13463, 19925), (22837, 9956)
X(32537) = {X(8), X(5252)}-harmonic conjugate of X(5836)


X(32538) = X(381)X(7620)∩X(3734)X(16509)

Barycentrics    126*S^4+3*(3*SA+SW)*(15*SA-14*SW)*S^2-4*(3*SA+SW)*(3*SA-2*SW)*SW^2 : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32538) lies on these lines: {381, 7620}, {3734, 16509}, {5485, 18907}


X(32539) = X(4)X(52)∩X(125)X(1147)

Barycentrics    SA*((16*R^2-2*SA-2*SW)*S^2+(SB+SC)*(10*R^4-(7*SA+11*SW)*R^2+2*SA^2-2*SB*SC+2*SW^2)) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32539) lies on these lines: {4, 52}, {5, 32166}, {125, 1147}, {155, 10255}, {539, 18281}, {1899, 12038}, {3357, 17702}, {3448, 12118}, {3564, 10224}, {5449, 9306}, {5504, 23294}, {6696, 11250}, {12163, 18565}, {13383, 32145}, {15316, 19477}

X(32539) = reflection of X(32145) in X(13383)
X(32539) = {X(68), X(11442)}-harmonic conjugate of X(9927)


X(32540) = X(3)X(76)∩X(6)X(14251)

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

X(32540) lies on the cubic K1104 and these on lines {3, 76}, {6, 14251}, {32, 512}, {39, 15630}, {248, 30496}, {446, 1503}, {1634, 19120}, {1910, 2053}, {3095, 13137}, {3224, 14601}, {5025, 10342}, {17932, 19597}

X(32540) = X(i)-isoconjugate of X(j) for these (i,j): {240, 8858}, {1959, 3225}
X(32540) = crosssum of X(i) and X(j) for these (i,j): {511, 5976}, {2679, 2799}
X(32540) = crossdifference of every pair of points on line {325, 2491}
X(32540) = barycentric product X(i)*X(j) for these lines: {i,j}: {98, 3229}, {698, 1976}, {1910, 2227}
X(32540) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {248, 8858}, {1976, 3225}, {3229, 325}, {9429, 3569}, {14601, 699}
X(32540) = {X(98),X(8870)}-harmonic conjugate of X(14382)


X(32541) = X(3)X(3224)∩X(3360)X(18829)

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

X(32541) lies on the cubic K1104 and these lines: {3, 3224}, {3360, 18829}, {8789, 10131}

X(32541) = barycentric product X(9468)*X(9493)
X(32541) = barycentric quotient X(9493) / X(14603)


X(32542) = X(3)X(1625)∩X(24)X(2698)

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

X(32542) lies on the cubics K389 and K1104, and on these lines: {3, 1625}, {24, 2698}, {3148, 14251}, {3406, 8743}

X(32542) = isogonal conjugate of the anticomplement of X(14382)
X(32542) = X(i)-isoconjugate of X(j) for these (i,j): {401, 1581}, {1916, 1955}, {1934, 1971}
X(32542) = barycentric product X(i)*X(j) for these lines: {i,j}: {385, 1987}, {419, 14941}, {1580, 1956}, {1691, 1972}
X(32542) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {419, 16089}, {1691, 401}, {1933, 1955}, {1956, 1934}, {1972, 18896}, {1987, 1916}, {5027, 6130}, {14602, 1971}


X(32543) = (name pending)

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

X(32543) lies on the cubic K1104 and this line: {3360, 32514}

X(32543) = isogonal conjugate of X(32548)


X(32544) = X(32)X(99)∩X(880)X(1691)

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

X(32544) lies on the cubics K444 and K1013, and on these lines: {32, 99}, {880, 1691}, {14602, 17941}

X(32544) = X(1691)-cross conjugate of X(699)
X(32544) = X(i)-isoconjugate of X(j) for these (i,j): {694, 2227}, {698, 1967}, {1581, 3229}
X(32544) = cevapoint of X(1691) and X(4027)
X(32544) = barycentric product X(i)*X(j) for these lines: {i,j}: {385, 3225}, {419, 8858}, {699, 3978}
X(32544) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {385, 698}, {699, 694}, {1580, 2227}, {1691, 3229}, {3225, 1916}


X(32545) = X(3)X(2966)∩X(4)X(32)

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

X(32545) lies on the cubics K444, K629, K790, and on these lines: {3, 2966}, {4, 32}, {20, 9218}, {54, 826}, {194, 17974}, {1316, 14265}, {1975, 17932}, {2065, 9307}, {2715, 11257}, {3398, 14382}, {14251, 18858}

X(32545) = X(i)-isoconjugate of X(j) for these (i,j): {240, 14941}, {511, 1956}, {1755, 1972}, {1959, 1987}
X(32545) = trilinear pole of line {1971, 6130}
X(32545) = barycentric product X(i)*X(j) for these lines: {i,j}: {98, 401}, {248, 16089}, {290, 1971}, {1821, 1955}, {2966, 6130}
X(32545) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {98, 1972}, {248, 14941}, {401, 325}, {1910, 1956}, {1955, 1959}, {1971, 511}, {1976, 1987}, {6130, 2799}


X(32546) = (name pending)

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

X(32546) lies on the cubic K444 and on no line X(i)X(j) for 0 < i < j < 32546.


X(32547) = X(2)X(9292)∩X(69)X(32529)

Barycentrics    a^2*(a^4*b^4 - a^2*b^6 - 2*a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 - b^4*c^4 - a^2*c^6 + b^2*c^6) : :
X(32547) = 3 X[2979] - 4 X[7750],3 X[3060] - 2 X[7823],2 X[4173] - 3 X[7833],9 X[5640] - 8 X[7745],10 X[7904] - 9 X[7998],3 X[11459] - 4 X[32151]

X(32547) lies on these lines: {2, 9292}, {69, 32529}, {76, 512}, {110, 32445}, {699, 3224}, {1297, 11440}, {1503, 12272}, {1968, 2001}, {2387, 7802}, {2698, 10104}, {2979, 7750}, {3060, 7823}, {3111, 7940}, {3491, 3552}, {3852, 12220}, {4173, 7833}, {5167, 7793}, {5640, 7745}, {6787, 7746}, {7860, 14962}, {7904, 7998}, {9863, 12111}, {11459, 32151}, {15270, 26881}, {19597, 32464}

X(32547) = reflection of X(12111) in X(9863)
X(32547) = crosspoint of X(3224) and X(30496)
X(32547) = crosssum of X(194) and X(3552)


X(32548) = X(2)X(3224)∩X(69)X(698)

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

X(32548) lies on these lines: {2, 3224}, {69, 698}, {76, 9493}, {315, 1899}, {5207, 32529}, {6337, 22089}, {6374, 9492}, {7785, 13518}, {10453, 17137}, {17138, 21281}

X(32548) = isogonal conjugate of X(32543)
X(32548) = anticomplement of X(3224)
X(32548) = X(6374)-Ceva conjugate of X(2)
X(32548) = isotomic conjugate of cyclocevian conjugate of X(38262)
X(32548) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 20081}, {2, 21299}, {6, 21223}, {31, 2998}, {81, 17157}, {88, 23633}, {100, 20979}, {162, 2451}, {190, 20983}, {194, 8}, {651, 23655}, {660, 23656}, {662, 669}, {673, 20863}, {799, 3221}, {897, 20977}, {1424, 145}, {1613, 192}, {1740, 2}, {3186, 5905}, {3221, 21220}, {4598, 23464}, {6374, 6327}, {7075, 144}, {11325, 21216}, {17082, 7}, {17149, 69}, {18837, 315}, {20332, 20464}, {20794, 6360}, {20910, 3448}, {21080, 2895}, {21191, 149}, {21877, 1654}, {22028, 1330}, {23301, 21221}, {23503, 25054}, {23572, 9263}, {23807, 150}, {27644, 3223}


X(32549) = X(5)X(2883)∩X(546)X(14374)

Barycentrics    SA*(a*b*c*(8*S^2+(SB+SC)*(6*R^2-7*SA-3*SW))+2*(SB+SC)*(10*R^2-SA-SW)*OH*S) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29027.

X(32549) lies on these lines: {5, 2883}, {546, 14374}, {1113, 32110}, {1312, 13754}, {1313, 14915}, {1346, 9730}, {1347, 16194}, {1531, 10751}, {2575, 6699}


X(32550) = X(5)X(2883)∩X(546)X(14375)

Barycentrics    SA*(a*b*c*(8*S^2+(SB+SC)*(6*R^2-7*SA-3*SW))-2*(SB+SC)*(10*R^2-SA-SW)*OH*S) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29027.

X(32550) lies on these lines: {5, 2883}, {546, 14375}, {1114, 32110}, {1312, 14915}, {1313, 13754}, {1346, 16194}, {1347, 9730}, {1531, 10750}, {2574, 6699}


X(32551) = COMPLEMENT OF X(15345)

Barycentrics    (4*S^2+R^2*(R^2-5*SA-SW)+2*SA^2-2*SB*SC)*(S^2+SB*SC) : :
X(32551) = 3*X(2)+X(25043)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29027.

X(32551) lies on these lines: {2, 3459}, {5, 51}, {140, 6592}, {252, 6150}, {1493, 19553}, {1510, 20327}, {3628, 13856}, {5501, 20414}, {8254, 24385}, {10285, 14143}, {14051, 24306}, {14142, 18400}, {15957, 31879}, {18282, 32428}

X(32551) = midpoint of X(i) and X(j) for these lines: {i,j}: {10285, 14143}, {15345, 25043}
X(32551) = reflection of X(i) in X(j) for these (i,j): (13856, 3628), (18016, 140), (20414, 5501), (31879, 15957)
X(32551) = complement of X(15345)
X(32551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 25043, 15345), (5, 21230, 16336)


X(32552) = COMPLEMENT OF X(6777)

Barycentrics    (2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2))*sqrt(3)+2*S*(2*a^4-2*(b^2+c^2)*a^2+b^4+c^4) : :
Barycentrics    2*sqrt(3)*(3*SB*SC*SW+(3*SA-2*SW)*S^2)-2*S*(4*S^2-SA^2-2*SB*SC-SW^2) : :
X(32552) = 3*X(13)-X(148), 3*X(14)-5*X(14061), X(99)-3*X(5464), 5*X(99)-3*X(9116), 2*X(115)-3*X(5459), 5*X(115)-3*X(31696), X(148)+3*X(617), 3*X(618)-4*X(620), 3*X(619)-2*X(620), 5*X(5459)-2*X(31696), 3*X(5460)-4*X(6722), 3*X(5464)+X(6778), 5*X(5464)-X(9116), 3*X(5478)-2*X(22515), 3*X(5613)-X(6033), 6*X(6669)-5*X(14061), X(6773)-3*X(21156), 5*X(6778)+3*X(9116), 3*X(9114)-X(20094), 3*X(15561)-X(22507)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29029.

X(32552) lies onthese lines: {2, 6777}, {3, 22509}, {6, 6299}, {13, 148}, {14, 6669}, {69, 6582}, {98, 635}, {99, 299}, {114, 630}, {115, 396}, {140, 25560}, {141, 542}, {385, 533}, {532, 7813}, {621, 25236}, {623, 6771}, {624, 5613}, {633, 5982}, {2782, 25559}, {3412, 20394}, {3642, 12188}, {3643, 9862}, {5460, 6722}, {5478, 22515}, {5859, 22570}, {5981, 6115}, {6114, 7792}, {6295, 11646}, {6672, 6782}, {6770, 22687}, {6773, 21156}, {6780, 31710}, {8594, 8597}, {9113, 9760}, {9114, 20094}, {10645, 14904}, {11602, 20377}, {14136, 16529}, {15561, 22507}

X(32552) = reflection of X(i) in X(j) for these (i,j): (14, 6669), (618, 619), (6782, 6672), (11602, 20377), (25560, 140)
X(32552) = complement of X(6777)
X(32552) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5464, 6778, 99), (5613, 22689, 624)


X(32553) = COMPLEMENT OF X(6778)

Barycentrics    (2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2))*sqrt(3)-2*S*(2*a^4-2*(b^2+c^2)*a^2+b^4+c^4) : :
Barycentrics    2*sqrt(3)*(3*SB*SC*SW+(3*SA-2*SW)*S^2)+2*S*(4*S^2-SA^2-2*SB*SC-SW^2) : :
X(32553) = 3*X(13)-X(148), 3*X(14)-5*X(14061), X(99)-3*X(5464), 5*X(99)-3*X(9116), 2*X(115)-3*X(5459), 5*X(115)-3*X(31696), X(148)+3*X(617), 3*X(618)-4*X(620), 3*X(619)-2*X(620), 5*X(5459)-2*X(31696), 3*X(5460)-4*X(6722), 3*X(5464)+X(6778), 5*X(5464)-X(9116), 3*X(5478)-2*X(22515), 3*X(5613)-X(6033), 6*X(6669)-5*X(14061), X(6773)-3*X(21156), 5*X(6778)+3*X(9116), 3*X(9114)-X(20094), 3*X(15561)-X(22507)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29029.

X(32553) lies these lines: {2, 6778}, {3, 22507}, {6, 6298}, {13, 6670}, {14, 148}, {69, 6295}, {98, 636}, {99, 298}, {114, 629}, {115, 395}, {140, 25559}, {141, 542}, {385, 532}, {533, 7813}, {622, 25235}, {623, 5617}, {624, 6774}, {634, 5983}, {2782, 25560}, {3411, 20395}, {3642, 9862}, {3643, 12188}, {5459, 6722}, {5479, 22515}, {5858, 22568}, {5980, 6114}, {6115, 7792}, {6582, 11646}, {6671, 6783}, {6770, 21157}, {6773, 22689}, {6779, 31709}, {8595, 8597}, {9112, 9762}, {9116, 20094}, {10646, 14905}, {11603, 20378}, {14137, 16530}, {15561, 22509}

X(32553) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22507}, {14, 616}, {99, 6777}, {622, 25235}, {5858, 22568}, {5979, 22998}
X(32553) = reflection of X(i) in X(j) for these (i,j): (13, 6670), (619, 618), (6783, 6671), (11603, 20378), (25559, 140)
X(32553) = complement of X(6778)
X(32553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5463, 6777, 99), (5617, 22687, 623)


X(32554) = MIDPOINT OF X(104) AND X(3436)

Barycentrics    (b-c)^2*a^8-2*(b+c)*(b^2+c^2)*a^7-2*(b^4+c^4-7*(b^2+c^2)*b*c)*a^6+2*(b+c)*(b^2+b*c+c^2)*(3*b^2-8*b*c+3*c^2)*a^5-4*(5*b^4+5*c^4-4*(b^2+b*c+c^2)*b*c)*b*c*a^4-2*(b^2-c^2)*(b-c)*(3*b^4+3*c^4-4*(b+c)^2*b*c)*a^3+2*(b^2-c^2)^2*(b-c)^2*(b^2+5*b*c+c^2)*a^2+2*(b^2-c^2)^3*(b-c)*(b^2-3*b*c+c^2)*a-(b^2-c^2)^4*(b-c)^2 : :
X(32554) = 2*X(7681)-3*X(23513)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29029.

X(32554) lies these lines: {3, 119}, {11, 517}, {12, 21154}, {46, 8068}, {56, 6713}, {78, 952}, {100, 6827}, {104, 3436}, {153, 6926}, {1385, 10956}, {1537, 4187}, {2478, 12775}, {2800, 21616}, {3826, 6980}, {4413, 6923}, {5533, 30323}, {5690, 18802}, {5840, 6928}, {5854, 19914}, {6174, 28459}, {6667, 7680}, {6842, 11231}, {6863, 31246}, {6948, 10728}, {6961, 11681}, {6963, 10698}, {6971, 7681}, {6978, 31272}, {7491, 24466}, {8256, 26470}, {10265, 24391}, {10955, 26287}, {10958, 26285}, {12611, 31788}, {12616, 18254}, {15017, 30503}, {15528, 21077}, {22799, 31775}

X(32554) = midpoint of X(i) and X(j) for these lines: {i,j}: {104, 3436}, {10310, 12764}
X(32554) = reflection of X(i) in X(j) for these (i,j): (56, 6713), (119, 1329), (18802, 5690)


X(32555) = X(1)X(372)∩X(3)X(9)

Barycentrics    a*( a*(-a^2+b^2+c^2)+(-a+b+c)*S) : :
Trilinears    1 + (sec A - tan A) - (sec B - tan B) - (sec C - tan C) : :

See Vu Thanh Tung and César Lozada, Hyacinthos 29031.

In the configuration at X(6212), the lines IAJA, IBJB, ICJC concur in X(32555), which is also the perspector of A'B'C' and the excentral triangle. (Randy Hutson, June 7, 2019)

X(32555) lies on the cubic K414 and these lines: {1, 372}, {2, 31540}, {3, 9}, {7, 31541}, {20, 30412}, {37, 1152}, {40, 30556}, {41, 30400}, {43, 1685}, {44, 1151}, {45, 6410}, {48, 19067}, {57, 16432}, {63, 16440}, {101, 31564}, {165, 6212}, {169, 31563}, {223, 13388}, {371, 1743}, {487, 4416}, {488, 3912}, {515, 7090}, {573, 31438}, {1100, 3594}, {1123, 31533}, {1124, 7074}, {1449, 3312}, {1587, 5393}, {2183, 19068}, {2951, 31545}, {3218, 21568}, {3219, 21567}, {3247, 6398}, {3305, 16441}, {3306, 21492}, {3311, 16670}, {3523, 30413}, {3576, 30557}, {3592, 16669}, {3723, 6438}, {3731, 6396}, {3911, 8957}, {3928, 21561}, {3929, 21560}, {3973, 6200}, {4292, 30324}, {4297, 31595}, {4357, 11291}, {5405, 13935}, {5437, 21548}, {6204, 15803}, {6351, 6460}, {6409, 16885}, {6411, 15492}, {6412, 16814}, {6420, 16667}, {6426, 16777}, {6430, 16672}, {6431, 16671}, {6432, 16666}, {6434, 16677}, {6450, 16676}, {6454, 16673}, {6469, 16674}, {6684, 14121}, {7308, 16433}, {9583, 13332}, {10164, 31594}, {11292, 17353}, {13411, 30325}, {21566, 27065}, {21569, 27003}

X(32555) = (excentral)-isogonal conjugate of-X(6213)
X(32555) = X(485)-of-excentral triangle
X(32555) = X(488)-of-1st circumperp triangle
X(32555) = X(641)-of-6th mixtilinear triangle
X(32555) = X(6289)-of-hexyl triangle
X(32555) = X(12257)-of-2nd circumperp triangle
X(32555) = X(40)-Ceva conjugate of X(32556)
X(32555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 9, 32556), (20, 30412, 31562), (84, 198, 32556), (610, 1490, 32556), (6502, 7133, 1)


X(32556) = X(1)X(371)∩X(3)X(9)

Barycentrics    a*(a*(-a^2 + b^2 + c^2) - (-a + b + c)*S) : :
Trilinears    1 + (sec A + tan A) - (sec B + tan B) - (sec C + tan C) : :
X(32556) = 2 s X[3] - (r + 4 R) X[9], s^2 X[1] - (SW + S) X[371]

X(32556) lies on the cubic K414, the Kiepert circumhyperbola of the excentral triangle, and on these lines: {1, 371}, {2, 31541}, {3, 9}, {7, 31540}, {20, 30413}, {37, 1151}, {40, 30557}, {41, 30401}, {43, 1686}, {44, 1152}, {45, 6409}, {48, 19068}, {57, 16433}, {63, 16441}, {101, 31563}, {165, 6213}, {169, 31564}, {223, 13389}, {372, 1743}, {487, 3912}, {488, 4416}, {505, 3645}, {515, 14121}, {572, 31438}, {846, 9582}, {950, 8957}, {1100, 3592}, {1335, 7074}, {1336, 31532}, {1449, 3311}, {1588, 5405}, {2183, 19067}, {2951, 31544}, {3218, 21565}, {3219, 21566}, {3247, 6221}, {3305, 16440}, {3306, 21553}, {3312, 16670}, {3523, 30412}, {3576, 30556}, {3594, 16669}, {3723, 6437}, {3731, 6200}, {3928, 21558}, {3929, 21559}, {3973, 6396}, {4292, 30325}, {4297, 31594}, {4357, 11292}, {5393, 9540}, {5437, 21547}, {6203, 15803}, {6352, 6459}, {6410, 16885}, {6411, 16814}, {6412, 15492}, {6419, 16667}, {6425, 16777}, {6429, 16672}, {6431, 16666}, {6432, 16671}, {6433, 16677}, {6449, 16676}, {6453, 16673}, {6468, 16674}, {6684, 7090}, {7308, 16432}, {10164, 31595}, {10436, 21909}, {11291, 17353}, {13411, 30324}, {21564, 27003}, {21567, 27065}

X(32556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9, 32555}, {20, 30413, 31561}, {84, 198, 32555}, {610, 1490, 32555}
X(32556) = excentral-isogonal conjugate of X(6212)
X(32556) = X(485)-of-excentral-triangle
X(32556) = X(487)-of-1st-circumperp-triangle
X(32556) = X(12257)-of-2nd-circumperp-triangle
X(32556) = X(642)-of-6th-mixtilinear-triangle
X(32556) = X(6290)-of-hexyl-triangle
X(32556) = X(i)-Ceva conjugate of X(j) for these (i,j): {40, 32555}, {30557, 1}


X(32557) = X(1)X(6702)∩X(2)X(2802)

Barycentrics    2*a^4 - a^3*b - 4*a^2*b^2 + a*b^3 + 2*b^4 - a^3*c + 6*a^2*b*c - 4*a^2*c^2 - 4*b^2*c^2 + a*c^3 + 2*c^4 : :
X(32557) = X[1] + 2 X[6702],5 X[1] + X[12531],2 X[1] + X[15863],X[1] + 5 X[31272],X[3] + 2 X[16174],2 X[5] + X[11715],X[10] + 2 X[1387],X[10] - 4 X[6667],2 X[11] + X[214],X[11] + 2 X[1125],5 X[11] + X[10609],7 X[11] - X[12690],X[80] + 5 X[3616],X[100] - 7 X[3624],X[104] + 5 X[8227],X[124] + 2 X[29008],X[149] + 11 X[5550],X[214] - 4 X[1125],5 X[214] - 2 X[10609],7 X[214] + 2 X[12690],4 X[551] - X[11274],5 X[631] + X[14217],X[946] + 2 X[6713],10 X[1125] - X[10609],14 X[1125] + X[12690],X[1145] - 4 X[3634],X[1317] - 4 X[3636],X[1320] + 5 X[1698],2 X[1385] + X[6246],X[1387] + 2 X[6667],5 X[1656] + X[12737],2 X[3035] - 5 X[19862],2 X[3035] + X[21630],2 X[3036] + X[3244],7 X[3090] - X[12751],5 X[3617] + X[26726],7 X[3622] - X[7972],2 X[3626] + X[25416],5 X[3698] + X[17652],2 X[3754] + X[12758],X[3874] - 4 X[18240],X[3874] + 2 X[18254],X[3878] + 2 X[12736],X[4973] + 2 X[11813],X[4973] - 4 X[15325],5 X[5439] + X[17638],2 X[5901] + X[12619],4 X[5901] - X[25485],2 X[6681] + X[30384],10 X[6702] - X[12531],4 X[6702] - X[15863],2 X[6702] - 5 X[31272],5 X[7987] + X[10724],7 X[9624] - X[10698],X[10265] + 2 X[11729],7 X[10609] + 5 X[12690],X[11813] + 2 X[15325],2 X[12019] + 7 X[15808],X[12515] + 5 X[18493],2 X[12531] - 5 X[15863],X[12531] - 25 X[31272],X[12532] + 5 X[18398],2 X[12619] + X[25485],2 X[13624] + X[22938],X[13996] - 10 X[31253],2 X[15528] + X[31803],X[15863] - 10 X[31272],2 X[18240] + X[18254],2 X[18857] + X[24042],5 X[19862] + X[21630],8 X[19878] - 5 X[31235],2 X[20418] + X[21635]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29037.

X(32557) lies these lines: {1, 6702}, {2, 2802}, {3, 16174}, {5, 11715}, {10, 1387}, {11, 214}, {80, 3616}, {100, 3624}, {104, 8227}, {124, 29008}, {149, 5550}, {499, 3878}, {515, 23513}, {516, 21154}, {528, 19883}, {547, 551}, {631, 14217}, {758, 3582}, {946, 6713}, {1145, 3634}, {1317, 3636}, {1320, 1698}, {1385, 6246}, {1656, 12737}, {2771, 3742}, {2800, 5883}, {2801, 5817}, {2829, 3817}, {3035, 14150}, {3036, 3244}, {3057, 20107}, {3086, 3874}, {3090, 12751}, {3617, 26726}, {3622, 7972}, {3626, 25416}, {3698, 17652}, {3754, 12758}, {3825, 8068}, {3892, 10072}, {4973, 11813}, {4996, 5259}, {5083, 11375}, {5248, 10090}, {5439, 17638}, {5443, 11570}, {5840, 10165}, {5901, 12619}, {6265, 30143}, {6681, 30384}, {7968, 8988}, {7969, 13976}, {7987, 10724}, {9624, 10698}, {10057, 10584}, {10058, 23708}, {10265, 11729}, {10527, 14740}, {10707, 15015}, {11108, 22560}, {11263, 12611}, {11376, 15558}, {11717, 24222}, {12019, 15808}, {12515, 18493}, {12532, 18398}, {12740, 30147}, {13205, 16408}, {13624, 22938}, {13902, 19077}, {13959, 19078}, {13996, 31253}, {15528, 31803}, {15950, 20118}, {17636, 20104}, {17724, 23869}, {18857, 24042}, {19878, 31235}, {20418, 21635}

X(32557) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 16173}, {10707, 15015}
X(32557) = centroid of X(1)X(10)X(11)
X(32557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6702, 15863}, {1, 31272, 6702}, {11, 1125, 214}, {1387, 6667, 10}, {5886, 10199, 5883}, {5901, 12619, 25485}, {11813, 15325, 4973}, {18240, 18254, 3874}, {19862, 21630, 3035}


X(32558) = X(2)X(2802)∩X(8)X(1387)

Barycentrics    3*a^4 - 2*a^3*b - 6*a^2*b^2 + 2*a*b^3 + 3*b^4 - 2*a^3*c + 11*a^2*b*c - a*b^2*c - 6*a^2*c^2 - a*b*c^2 - 6*b^2*c^2 + 2*a*c^3 + 3*c^4 : :
X(32558) = X[2] + 2 X[16173],X[8] + 8 X[1387],5 X[8] + 4 X[25416],X[8] - 10 X[31272],4 X[11] + 5 X[3616],8 X[11] + X[6224],X[20] + 8 X[16174],2 X[80] + 7 X[3622],2 X[100] - 11 X[5550],X[145] + 8 X[6702],X[149] + 8 X[1125],X[149] + 2 X[15015],X[153] - 10 X[8227],X[962] + 8 X[6713],4 X[1125] - X[15015],4 X[1145] - 13 X[19877],X[1320] + 8 X[6667],2 X[1320] + 7 X[9780],10 X[1387] - X[25416],4 X[1387] + 5 X[31272],8 X[3035] + X[9802],8 X[3036] + X[20050],7 X[3090] + 2 X[12737],5 X[3091] + 4 X[11715],7 X[3523] + 2 X[14217],10 X[3616] - X[6224],5 X[3623] + 4 X[15863],7 X[3624] + 2 X[21630],8 X[3634] + X[12653],8 X[3636] + X[9897],5 X[3890] + 4 X[6797],7 X[4678] + 2 X[26726],11 X[5056] - 2 X[12751],X[5180] + 8 X[15325],X[5541] - 10 X[19862],8 X[5901] + X[12247],16 X[6667] - 7 X[9780],7 X[9624] + 2 X[10265],X[9778] - 4 X[21154],X[9803] + 8 X[11729],X[9809] + 8 X[20418],8 X[9955] + X[12248],5 X[10595] + 4 X[12619],2 X[12531] + 7 X[20057],X[12532] + 8 X[18240],2 X[25416] + 25 X[31272]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29037.

X(32558) lies these lines: {2, 2802}, {8, 1387}, {11, 2476}, {20, 16174}, {80, 3622}, {100, 5550}, {145, 6702}, {149, 1125}, {153, 8227}, {214, 31418}, {952, 5055}, {962, 6713}, {1145, 19877}, {1320, 6667}, {2771, 5886}, {2829, 9779}, {3035, 9802}, {3036, 20050}, {3090, 12737}, {3091, 11715}, {3523, 14217}, {3623, 15863}, {3624, 21630}, {3634, 12653}, {3636, 9897}, {3890, 6797}, {4323, 12832}, {4678, 26726}, {5047, 22560}, {5056, 12751}, {5180, 15325}, {5541, 19862}, {5901, 12247}, {9624, 10265}, {9778, 21154}, {9803, 11729}, {9809, 20418}, {9955, 12248}, {10588, 20586}, {10595, 12619}, {11373, 27529}, {11376, 25414}, {12531, 20057}, {12532, 18240}, {13205, 17531}, {15558, 18220}

X(32558) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 3616, 6224}, {1320, 6667, 9780}, {1387, 31272, 8}

leftri

Mutual polar conics: X(32559)-X(32588)

rightri

This preamble and centers X(32559)-X(32588) were contributed by César Eliud Lozada, May 22, 2019.

Two triangles are mutually polar with respect to a conic if each edge of one is the polar of a vertex of the other.

Two triangles are perspective if and only if they are mutually polar with respect to a conic.. (Lord, Eric (2013). Symmetry and Pattern in Projective Geometry, (pp 88). London: Springer).

The conic with respect to which two perspective triangles T1 and T2 are mutually polar are here named the mutual polar conic of T1 and T2. A list of these conics involving ABC and some triangles can be seen in Wolfram's Polar Triangle.

If T' = A'B'C' is a central triangle perspective to ABC with perspector P = u:v:w (trilinears) then there exists a function f(a,b,c) such that AA'=f(a,b,c)*AP, BB'=f(b,c,a)*BP and CC'=f(c,a,b)*CP (in particular, if T' and ABC are homothetic then f(a,b,c) is a constant). The center O of the mutual polar conic of ABC and T' has trilinears O = u/f(a,b,c) : v/f(b,c,a) : w/f(c,a,b) (O=P if ABC and T' are homothetic). The perspector of this conic is P.

The appearance of (T, n) in the following list means that the center of the mutual polar conic of ABC and T is X(n) (ABC and T non-homothetic):

(Andromeda, 32559), (anti-Artzt, 2), (anti-Atik, 4), (1st anti-Brocard, 2), (4th anti-Brocard, 21448), (anti-Conway, 54), (2nd anti-Conway, 4), (anti-excenters-reflections, 64), (2nd anti-extouch, 6), (anti-Honsberger, 1176), (anti-Hutson intouch, 3), (anti-incircle-circles, 3), (anti-inverse-in-incircle, 69), (anti-McCay, 2), (6th anti-mixtilinear, 3), (anti-orthocentroidal, 6), (1st anti-orthosymmedial, 251), (1st anti-Sharygin, 54), (anti-tangential-midarc, 73), (3rd anti-tri-squares, 486), (4th anti-tri-squares, 485), (AAOA, 3), (Antlia, 32560), (Apollonius, 9560), (Apus, 32561), (Artzt, 2), (Atik, 8), (Ayme, 10), (BCI, 1489), (1st Brocard-reflected, 2), (1st Brocard, 2), (2nd Brocard, 574), (3rd Brocard, 3117), (4th Brocard, 5094), (circummedial, 10130), (circumorthic, 54), (2nd circumperp, 21), (circumsymmedial, 574), (Conway, 21), (2nd Conway, 8), (3rd Conway, 1), (4th Conway, 11679), (5th Conway, 17185), (Ehrmann-side, 3), (Ehrmann-vertex, 265), (2nd Ehrmann, 895), (2nd Euler, 3), (5th Euler, 5094), (excenters-midpoints, 9), (excenters-reflections, 3680), (excentral, 9), (1st excosine, 6), (2nd excosine, 1033), (extangents, 71), (extouch, 9), (2nd extouch, 9), (3rd extouch, 223), (4th extouch, 1038), (5th extouch, 1038), (inner-Fermat, 2), (outer-Fermat, 2), (3rd Fermat-Dao, 13), (4th Fermat-Dao, 14), (5th Fermat-Dao, 11080), (6th Fermat-Dao, 11085), (7th Fermat-Dao, 13), (8th Fermat-Dao, 14), (9th Fermat-Dao, 11080), (10th Fermat-Dao, 11085), (11th Fermat-Dao, 14), (12th Fermat-Dao, 13), (13th Fermat-Dao, 14), (14th Fermat-Dao, 13), (15th Fermat-Dao, 18), (16th Fermat-Dao, 17), (Feuerbach, 5949), (Hatzipolakis-Moses, 6), (1st Hatzipolakis, 17054), (2nd Hatzipolakis, 17054), (3rd Hatzipolakis, 6), (hexyl, 1), (Honsberger, 2346), (Hutson extouch, 9), (Hutson intouch, 1), (outer-Hutson, 7707), (2nd Hyacinth, 6), (incentral, 37), (incircle-circles, 1), (intouch, 1), (inverse-in-incircle, 7), (1st isodynamic-Dao, 17), (2nd isodynamic-Dao, 18), (3rd isodynamic-Dao, 4), (4th isodynamic-Dao, 4), (1st Kenmotu diagonals, 6413), (2nd Kenmotu diagonals, 6414), (Kosnita, 3), (Lemoine, 597), (1st Lemoine-Dao, 4), (2nd Lemoine-Dao, 4), (Lucas antipodal, 10132), (Lucas Brocard, 32562), (Lucas central, 10132), (Lucas inner, 32563), (Lucas inner tangential, 32564), (Lucas reflection, 184), (Lucas secondary central, 32565), (Lucas 1st secondary tangents, 32566), (Lucas 2nd secondary tangents, 32567), (Lucas tangents, 32568), (Lucas(-1) antipodal, 10133), (Lucas(-1) Brocard, 32569), (Lucas(-1) central, 10133), (Lucas(-1) inner, 32570), (Lucas(-1) inner tangential, 32571), (Lucas(-1) reflection, 184), (Lucas(-1) secondary central, 32572), (Lucas(-1) 1st secondary tangents, 32573), (Lucas(-1) 2nd secondary tangents, 32574), (Lucas(-1) tangents, 32575), (Macbeath, 5), (Malfatti, 32576), (Mandart-excircles, 6), (McCay, 2), (midarc, 2089), (2nd midarc, 1488), (midheight, 6), (mixtilinear, 55), (2nd mixtilinear, 220), (3rd mixtilinear, 32577), (4th mixtilinear, 32578), (6th mixtilinear, 1), (7th mixtilinear, 2124), (Montesdeoca-Hung, 32579), (1st Morley, 3604), (2nd Morley, 3602), (3rd Morley, 3603), (1st Morley-adjunct, 16839), (2nd Morley-adjunct, 16840), (3rd Morley-adjunct, 16841), (Moses-Hung, 32580), (inner-Napoleon, 2), (outer-Napoleon, 2), (1st Neuberg, 2), (2nd Neuberg, 2), (orthic, 6), (orthocentroidal, 6), (1st orthosymmedial, 251), (2nd orthosymmedial, 32581), (1st Pamfilos-Zhou, 32582), (2nd Pamfilos-Zhou, 7133), (1st Parry, 110), (2nd Parry, 111), (3rd Parry, 32583), (Pelletier, 11), (reflection, 6), (1st Sharygin, 21), (2nd Sharygin, 100), (Soddy, 3160), (inner-Soddy, 10134), (2nd inner-Soddy, 13389), (outer-Soddy, 10135), (2nd outer-Soddy, 13388), (inner-squares, 3068), (outer-squares, 3069), (Steiner, 523), (symmedial, 39), (tangential, 3), (tangential-midarc, 15997), (inner tri-equilateral, 32585), (outer tri-equilateral, 32586), (3rd tri-squares, 485), (4th tri-squares, 486), (Trinh, 3), (inner-Vecten, 2), (2nd inner-Vecten, 32587), (3er inner-Vecten, 32587), (outer-Vecten, 2), (2nd outer-Vecten, 32588), (3er outer-Vecten, 32588), (Walsmith, 74), (X-parabola-tangential, 523), (Yff central, 7707), (Yff contact, 514), (Yiu, 1154), (1st Zaniah, 1), (2nd Zaniah, 9).

X(32559) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND ANDROMEDA

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

X(32559) lies on these lines: {1,738}, {2,3677}, {37,32560}, {3666,21446}


X(32560) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND ANTLIA

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

X(32560) lies on these lines: {1,728}, {2,479}, {37,32559}, {10582,21450}


X(32561) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND APUS

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

X(32561) lies on these lines: {3,169}, {6,255}, {9,35}, {21,6554}, {32,16588}, {37,8573}, {41,55}, {56,17451}, {71,11434}, {101,10267}, {198,23843}, {218,11507}, {219,584}, {384,26068}, {411,5819}, {672,11509}, {958,1146}, {1376,26036}, {1466,5022}, {2082,26357}, {2170,10966}, {2178,7742}, {2183,15592}, {2225,7085}, {2246,5217}, {2478,6506}, {2911,15830}, {3208,8668}, {3295,6603}, {3560,5179}, {3730,11248}, {5251,23058}, {7367,8606}, {8069,16601}, {9310,11510}, {10306,21872}, {11496,17747}, {12329,23851}, {16367,30854}, {16865,27541}

X(32561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 15288, 1212), (1802, 8012, 220)


X(32562) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS BROCARD

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

X(32562) lies on these lines: {574,8373}, {1151,1584}


X(32563) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS INNER

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

X(32563) lies on these lines: {2,6568}, {110,32072}, {574,32570}, {6221,8854}, {6407,32564}


X(32564) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS INNER TANGENTIAL

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

X(32564) lies on the line {6407,32563}


X(32565) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS SECONDARY CENTRAL

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

X(32565) lies on these lines: {1152,32568}, {8407,10133}, {22112,32572}


X(32566) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS 1st SECONDARY TANGENTS

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

X(32566) lies on the line {1151,10133}


X(32567) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS 2nd SECONDARY TANGENTS

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

X(32567) lies on these lines: {22,6480}, {372,1600}, {3156,6431}


X(32568) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS TANGENTS

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

X(32568) lies on these lines: {2,7598}, {3,493}, {6,6216}, {22,6200}, {110,11199}, {154,1151}, {371,1599}, {574,20859}, {1152,32565}, {1501,9675}, {1583,15883}, {3167,6221}, {6413,8939}, {6560,11209}, {7484,9600}, {8216,21642}, {8414,10133}, {13882,32588}, {19358,26347}

X(32568) = isogonal conjugate of X(18819)
X(32568) = {X(3), X(493)}-harmonic conjugate of X(8577)


X(32569) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) BROCARD

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

X(32569) lies on these lines: {574,8374}, {1152,1583}


X(32570) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) INNER

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

X(32570) lies on these lines: {2,6569}, {110,32073}, {574,32563}, {6398,8855}, {6408,32571}


X(32571) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) INNER TANGENTIAL

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

X(32571) lies on the line {6408,32570}


X(32572) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) SECONDARY CENTRAL

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

X(32572) lies on these lines: {1151,32575}, {8400,10132}, {22112,32565}


X(32573) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) 1st SECONDARY TANGENTS

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

X(32573) lies on the line {1152,10132}


X(32574) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) 2nd SECONDARY TANGENTS

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

X(32574) lies on these lines: {22,6481}, {371,1599}, {3155,6432}


X(32575) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) TANGENTS

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

X(32575) lies on these lines: {2,7599}, {3,494}, {6,6397}, {22,6396}, {110,32074}, {154,1152}, {372,1600}, {574,20859}, {1151,32572}, {1584,15884}, {3167,6398}, {6414,8943}, {6561,11210}, {8219,21643}, {8406,10132}, {13934,32587}

X(32575) = isogonal conjugate of X(18820)
X(32575) = {X(3), X(494)}-harmonic conjugate of X(8576)


X(32576) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND MALFATTI

Barycentrics    a*(2*a*(cos(B/2)*cos(C/2)+cos(B/2)+cos(C/2))-cos(A/2)*(a-b-c)+a+b+c)*(cos(B/2)+1)*(cos(C/2)+1) : :
Barycentrics    Sin[A] (Sec[A / 4]^2) (1 + Sin[A / 2]) : : (Peter Moses, May 21, 2019)

X(32576) lies on this line: {258,483}

X(32576) = X(289)-isoconjugate of X(557)
X(32576) = barycentric product X(236)*X(483)
X(32576) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {7010, 21456}, {7014, 1488}


X(32577) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 3rd MIXTILINEAR

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

X(32577) lies on these lines: {1,88}, {3,1149}, {8,9350}, {25,8278}, {31,56}, {36,3915}, {38,19861}, {41,1015}, {42,3304}, {57,15839}, {200,7963}, {220,23649}, {227,1319}, {238,28370}, {355,28096}, {515,28018}, {551,16393}, {602,22765}, {604,17053}, {614,1420}, {748,2975}, {756,8583}, {899,12513}, {944,28074}, {956,27627}, {958,8688}, {976,17614}, {995,1203}, {999,1066}, {1064,16203}, {1125,5192}, {1253,10966}, {1357,16945}, {1385,19548}, {1388,17054}, {1450,26437}, {1458,15287}, {1477,9439}, {1496,22767}, {1647,1837}, {1739,22837}, {2209,20470}, {2267,8610}, {2275,9259}, {2650,3333}, {3086,21935}, {3120,11376}, {3303,17782}, {3576,28011}, {3616,4195}, {3720,16405}, {3752,20323}, {3756,10950}, {3890,17596}, {3953,30144}, {3976,4511}, {4251,9336}, {4298,24725}, {4310,24558}, {4694,22836}, {4861,24174}, {5193,10571}, {5288,17749}, {5303,8616}, {5450,32486}, {5484,25960}, {5731,28016}, {6762,21805}, {9619,21808}, {9708,28257}, {10165,28027}, {10459,17124}, {11260,16610}, {11682,18193}, {12635,17449}, {14986,26050}, {16466,23070}, {21842,30117}, {22437,23057}, {26561,30816}

X(32577) = isogonal conjugate of the isotomic conjugate of X(4862)
X(32577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 1054, 14923), (1, 4855, 3722), (1, 5253, 750)


X(32578) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 4th MIXTILINEAR

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

X(32578) lies on these lines: {9,100}, {31,15263}, {41,55}, {57,17451}, {165,169}, {200,15838}, {672,1405}, {899,6181}, {1155,1212}, {1253,14936}, {2078,9310}, {2280,2323}, {3730,5537}, {5745,24596}

X(32578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (55, 8012, 6602), (1212, 15855, 1155)


X(32579) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND MONTESDEOCA-HUNG

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

X(32579) lies on these lines: {}


X(32580) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND MOSES-HUNG

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

X(32580) lies on these lines: {4,6}, {37,115}, {3553,8818}, {6354,8736}


X(32581) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 2nd ORTHOSYMMEDIAL

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

X(32581) lies on these lines: {4,83}, {5,26224}, {25,14535}, {66,8801}, {112,251}, {406,27005}, {475,27067}, {1594,28724}, {1799,8889}, {5094,10130}, {5523,10549}, {7507,10547}, {7770,12220}

X(32581) = polar conjugate of X(23297)


X(32582) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 1st PAMFILOS-ZHOU

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

X(32582) lies on these lines: {2,31546}, {165,16441}, {1621,5314}


X(32583) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 3rd PARRY

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

X(32583) lies on these lines: {2,10558}, {110,249}, {111,352}, {323,895}, {647,9216}, {892,5466}, {1296,15406}, {2421,9186}, {2434,2444}, {3292,15899}, {3906,9146}, {5968,15066}, {6137,9202}, {6138,9203}, {9124,9178}, {9145,17414}, {9872,10510}, {10989,14833}, {11215,13241}, {15398,23061}

X(32583) = midpoint of X(9872) and X(10510)
X(32583) = isogonal conjugate of X(23287)
X(32583) = trilinear pole of the line {574, 8542}
X(32583) = homothetic center of ABC and 3rd Parry of 3rd Parry triangle
X(32583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 10559, 10558), (2, 10560, 21460), (10560, 21460, 10558)


X(32584) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND SCHROETER

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

X(32584) lies on the line {115,523}


X(32585) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND INNER TRI-EQUILATERAL

Barycentrics    a^2*(-a^2+b^2+c^2)*(2*sqrt(3)*S+a^2-b^2+c^2)*(2*sqrt(3)*S+a^2-c^2+b^2) : :
Barycentrics    Sin[A] Csc[A+Pi/6] Sin[2 A] : : (Peter Moses, May 21, 2019)

X(32585) lies on the Jerabek hyperbola and these lines: {2,10639}, {3,10661}, {4,15}, {6,3132}, {16,54}, {61,1173}, {62,13472}, {64,10675}, {65,7051}, {67,32301}, {68,10634}, {69,11515}, {74,3166}, {110,10640}, {184,10979}, {216,21648}, {290,32036}, {1176,11516}, {2963,3458}, {2992,19779}, {3131,30402}, {3431,10646}, {3527,11485}, {5238,16835}, {5352,13452}, {6145,32397}, {8795,19190}, {11081,11139}, {11144,11420}, {11421,14170}, {11481,14528}, {21647,22052}, {22466,22974}

X(32585) = isogonal conjugate of X(473)
X(32585) = isotomic conjugate of the polar conjugate of X(21461)
X(32585) = anticomplement of the complementary conjugate of X(465)
X(32585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (15, 8837, 10632), (184, 10979, 32586)


X(32586) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND OUTER TRI-EQUILATERAL

Barycentrics    a^2*(-a^2+b^2+c^2)*(-2*sqrt(3)*S+a^2-b^2+c^2)*(-2*sqrt(3)*S+a^2-c^2+b^2) : :
Barycentrics    Sin[A] Csc[A-Pi/6] Sin[2 A] : : (Peter Moses, May 21, 2019)

X(32586) lies on the Jerabek hyperbola and these lines: {2,10640}, {3,10662}, {4,16}, {6,3131}, {15,54}, {61,13472}, {62,1173}, {64,10676}, {65,10637}, {67,32302}, {68,10635}, {69,11516}, {74,3165}, {110,10639}, {184,10979}, {216,21647}, {290,32037}, {1176,11515}, {2963,3457}, {2992,11131}, {3132,30403}, {3431,10645}, {3527,11486}, {5237,16835}, {5351,13452}, {6145,32398}, {8795,19191}, {11143,11421}, {11420,14169}, {11480,14528}, {21648,22052}, {22466,22975}

X(32586) = isogonal conjugate of X(472)
X(32586) = isotomic conjugate of the polar conjugate of X(21462)
X(32586) = anticomplement of the complementary conjugate of X(466)
X(32586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16, 8839, 10633), (184, 10979, 32585)


X(32587) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 2nd INNER-VECTEN

Barycentrics    (a^2-b^2+c^2)*(a^2+b^2-c^2)*(b^2+c^2-2*S) : :
X(32587) = (4*R^2-SW)*X(3)+(2*R^2+S-SW)*X(4)

As a point on the Euler line, X(32587) has Shinagawa coefficients (F, E+F-2*S).

X(32587) lies on these lines: {2,3}, {51,12299}, {69,24243}, {136,5408}, {184,13749}, {275,14238}, {486,494}, {488,11395}, {490,12172}, {591,8754}, {615,8564}, {640,8946}, {1249,19041}, {1322,1899}, {1351,13439}, {1588,11245}, {1853,23261}, {2052,14231}, {2969,13387}, {2979,6400}, {3070,12232}, {3917,6406}, {5409,6290}, {5591,26376}, {6414,13960}, {6561,8940}, {6747,11474}, {7140,13386}, {11090,14593}, {11550,13748}, {12601,13428}, {13429,13951}, {13934,32575}, {14230,23292}

X(32587) = polar conjugate of the isogonal conjugate of X(1505)
X(32587) = anticomplement of X(8964)
X(32587) = X(22553)-of-4th tri-squares triangle, when ABC is obtuse
X(32587) = X(22554)-of-4th tri-squares triangle, when ABC is acute
X(32587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 427, 32588), (4, 1586, 25), (4, 3128, 427), (4, 5200, 428)


X(32588) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 2nd OUTER-VECTEN

Barycentrics    (a^2-b^2+c^2)*(a^2+b^2-c^2)*(b^2+c^2+2*S) : :
X(32588) = (4*R^2-SW)*X(3)+(2*R^2-S-SW)*X(4)

As a point on the Euler line, X(32587) has Shinagawa coefficients (F, E+F+2*S).

X(32588) lies on these lines: {2,3}, {51,12298}, {69,24244}, {136,5409}, {184,13748}, {275,14234}, {485,493}, {487,11394}, {489,12171}, {590,8563}, {639,8948}, {1249,19042}, {1321,1899}, {1351,13428}, {1587,11245}, {1853,23251}, {1991,8754}, {2052,14245}, {2969,13386}, {2979,6239}, {3071,12231}, {3917,6291}, {5408,6289}, {5590,26375}, {6413,8966}, {6560,8944}, {6564,8956}, {6747,11473}, {7140,13387}, {8976,13440}, {11091,14593}, {11550,13749}, {12602,13439}, {13882,32568}, {14233,23292}

X(32588) = polar conjugate of the isogonal conjugate of X(1504)
X(32588) = X(15891)-of-3rd outer-Vecten triangle
X(32588) = X(22553)-of-3rd tri-squares triangle
X(32588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 427, 32587), (4, 1585, 25), (4, 3535, 5200)


X(32589) = SS( S → -S) of X(8954)

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

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32589) lies on these lines: {1, 32591}, {3, 6}, {24, 6414}, {155, 10960}, {485, 6810}, {486, 1586}, {590, 8955}, {1075, 3069}, {1600, 26922}, {5562, 8963}, {6413, 7592}, {6565, 8887}, {6642, 10962}, {8855, 15199}, {10880, 26920}

X(32589) = SS( S → -S) of X(8954)
X(32589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (216, 389, 8954), (3371, 3372, 577), (3385, 3386, 578)

X(32590) = X(1)X(372)∩X(4)X(48)

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

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32590) lies on these lines: {1, 372}, {4, 48}, {41, 1588}, {101, 31562}, {572, 31561}, {604, 1587}, {610, 6212}, {637, 20769}, {1745, 2067}, {2066, 3362}, {2174, 3071}, {2286, 3093}, {3070, 7113}, {3092, 7124}, {5709, 19215}, {7330, 19216}

X(32590) = isogonal conjugate of X(32591)
X(32590) = {X(4),X(48)}-harmonic conjugate of X(32592)

X(32591) = ISOGONAL CONJUGATE OF X(32590)

Barycentrics    a*(-(a^2-b^2+c^2)*(a^2-b^2-c^2)*a*b+2*(a^2+b^2-c^2)*S*c^2)*(-(a^2-b^2-c^2)*(a^2+b^2-c^2)*a*c+2*(a^2-b^2+c^2)*S*b^2) : :
Barycentrics    a*(S^3+(a*b-S)*SA*SB)*(S^3+SA*(-S+c*a)*SC) : :
Trilinears    sin(A)*(2*cos(A)*cos(C)+sin(2*B))*(2*cos(A)*cos(B)+sin(2*C)) : :

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32591) lies on these lines: {1, 32589}, {1745, 6212}

X(32591) = isogonal conjugate of X(32590)

X(32592) = X(1)X(371)∩X(4)X(48)

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

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32592) lies on these lines: {1, 371}, {4, 48}, {41, 1587}, {101, 31561}, {572, 31562}, {604, 1588}, {610, 6213}, {638, 20769}, {1745, 6502}, {2174, 3070}, {2286, 3092}, {3071, 7113}, {3093, 7124}, {3362, 5414}, {5709, 19216}, {7330, 19215}

X(32592) = isogonal conjugate of X(32593)
X(32592) = {X(4),X(48)}-harmonic conjugate of X(32590)

X(32593) = ISOGONAL CONJUGATE OF X(32592)

Barycentrics    a*(-(a^2-b^2+c^2)*(a^2-b^2-c^2)*a*b-2*(a^2+b^2-c^2)*S*c^2)*(-(a^2-b^2-c^2)*(a^2+b^2-c^2)*a*c-2*(a^2-b^2+c^2)*S*b^2) : :
Barycentrics    a*(S^3+(a*b+S)*SA*SB)*(S^3+SA*(a*c+S)*SC) : :
Trilinears    sin(A)*(2*cos(A)*cos(C)-sin(2*B))*(2*cos(A)*cos(B)-sin(2*C)) : :

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32593) lies on these lines: {1, 8954}, {1745, 6213}

X(32593) = isogonal conjugate of X(32592)

X(32594) = X(3)X(8287)∩X(5)X(6)

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

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32594) lies on these lines: {3, 8287}, {5, 6}, {368, 18453}, {1736, 1893}, {2478, 25000}, {5221, 5729}, {5706, 14873}, {5740, 6835}


X(32595) = X(3)X(25424)∩X(6)X(1569)

Barycentrics    a^2 (a^12 b^4-4 a^10 b^6+6 a^8 b^8-4 a^6 b^10+a^4 b^12-2 a^12 b^2 c^2+4 a^10 b^4 c^2-11 a^8 b^6 c^2+13 a^6 b^8 c^2-2 a^4 b^10 c^2-2 a^2 b^12 c^2+a^12 c^4+4 a^10 b^2 c^4+a^8 b^4 c^4-9 a^6 b^6 c^4+25 a^4 b^8 c^4+4 a^2 b^10 c^4+b^12 c^4-4 a^10 c^6-11 a^8 b^2 c^6-9 a^6 b^4 c^6-21 a^4 b^6 c^6-11 a^2 b^8 c^6+2 b^10 c^6+6 a^8 c^8+13 a^6 b^2 c^8+25 a^4 b^4 c^8-11 a^2 b^6 c^8-6 b^8 c^8-4 a^6 c^10-2 a^4 b^2 c^10+4 a^2 b^4 c^10+2 b^6 c^10+a^4 c^12-2 a^2 b^2 c^12+b^4 c^12) : :
X(32595) = 3 X[3] - 2 X[25424]

X(32595) lies on the Stammler circle, the cubic K1105, and on these lines: {3,25424}, {6,1569}


X(32596) = X(4)X(3104)∩X(16)X(7709)

Barycentrics    Sqrt[3] (a^8 b^2+3 a^6 b^4-5 a^4 b^6+a^2 b^8+a^8 c^2+5 a^6 b^2 c^2-6 a^4 b^4 c^2-3 a^2 b^6 c^2-b^8 c^2+3 a^6 c^4-6 a^4 b^2 c^4+4 a^2 b^4 c^4+b^6 c^4-5 a^4 c^6-3 a^2 b^2 c^6+b^4 c^6+a^2 c^8-b^2 c^8)+2 (3 a^6 b^2-2 a^4 b^4-a^2 b^6+3 a^6 c^2+a^4 b^2 c^2-5 a^2 b^4 c^2+b^6 c^2-2 a^4 c^4-5 a^2 b^2 c^4-2 b^4 c^4-a^2 c^6+b^2 c^6) S : :
X(32596) = 3 X[7709] - 2 X[32465]

X(32596) lies on the cubic K1105 and on these lines: {4, 3104}, {16, 7709}, {98, 3098}, {511, 3180}, {616, 2782}, {3094, 16941}, {5980, 18906}, {9821, 22532}, {11257, 22531}, {12251, 14540}, {16940, 22707}, {31683, 31701}


X(32597) = X(4)X(3105)∩X(15)X(7709)

Barycentrics    Sqrt[3] (a^8 b^2+3 a^6 b^4-5 a^4 b^6+a^2 b^8+a^8 c^2+5 a^6 b^2 c^2-6 a^4 b^4 c^2-3 a^2 b^6 c^2-b^8 c^2+3 a^6 c^4-6 a^4 b^2 c^4+4 a^2 b^4 c^4+b^6 c^4-5 a^4 c^6-3 a^2 b^2 c^6+b^4 c^6+a^2 c^8-b^2 c^8)-2 (3 a^6 b^2-2 a^4 b^4-a^2 b^6+3 a^6 c^2+a^4 b^2 c^2-5 a^2 b^4 c^2+b^6 c^2-2 a^4 c^4-5 a^2 b^2 c^4-2 b^4 c^4-a^2 c^6+b^2 c^6) S : :
X(32597) = 3 X[7709] - 2 X[32466]

X(32597) lies on the cubic K1105 and these lines: {4, 3105}, {15, 7709}, {98, 3098}, {511, 3181}, {617, 2782}, {3094, 16940}, {5981, 18906}, {9821, 22531}, {11257, 22532}, {12251, 14541}, {16941, 22708}, {31684, 31702}


X(32598) = X(54)X(511)∩X(2916)X(2931)

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

X(32598) lies on the cubic K1107 and these lines: {54, 511}, {2916, 2931}, {7488, 29012}, {9019, 19129}, {13564, 32351}\


X(32599) = X(3)X(524)∩X(23)X(542)

Barycentrics    a^2*(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 + 7*a^6*b^2*c^2 - 13*a^4*b^4*c^2 + 11*a^2*b^6*c^2 - 4*b^8*c^2 - 2*a^6*c^4 - 13*a^4*b^2*c^4 - 4*a^2*b^4*c^4 + 5*b^6*c^4 + 2*a^4*c^6 + 11*a^2*b^2*c^6 + 5*b^4*c^6 + a^2*c^8 - 4*b^2*c^8 - c^10) : :
X(32599) = 3 X[186] - 2 X[12584],4 X[575] - 3 X[22151],3 X[2070] - X[32254],2 X[3292] - 3 X[15462],2 X[5609] - 3 X[18374],3 X[5622] - X[23061],4 X[12105] - 3 X[19596]

X(32599) lies on the cubic K1107 and these lines: {3, 524}, {23, 542}, {30, 16010}, {54, 20190}, {68, 7530}, {74, 511}, {110, 32315}, {182, 323}, {186, 12584}, {399, 32217}, {575, 1199}, {576, 5889}, {1154, 10510}, {1204, 15073}, {1352, 1995}, {1503, 9919}, {2070, 32254}, {2854, 3581}, {2930, 2931}, {3098, 15531}, {3292, 15462}, {5609, 18374}, {5622, 23061}, {5648, 15361}, {5965, 14049}, {6776, 7492}, {6795, 32515}, {7574, 25328}, {8537, 14865}, {8548, 11477}, {9027, 32110}, {9970, 13754}, {9972, 32352}, {10296, 32273}, {10990, 19924}, {11178, 16042}, {11180, 14002}, {12105, 19596}, {12106, 15069}, {15534, 18570}, {20423, 31861}

X(32599) = reflection of X(i) in X(j) for these lines: {i,j}: {323, 182}, {399, 32217}, {1352, 3580}, {2930, 7575}, {5648, 15361}, {7464, 32305}, {7574, 25328}, {10296, 32273}


X(32600) = X(3)X(2916)∩X(74)X(827)

Barycentrics    a^2*(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 - a^6*b^2*c^2 + 2*a^4*b^4*c^2 + 2*a^2*b^6*c^2 - 2*b^8*c^2 - 2*a^6*c^4 + 2*a^4*b^2*c^4 + 4*a^2*b^4*c^4 + 3*b^6*c^4 + 2*a^4*c^6 + 2*a^2*b^2*c^6 + 3*b^4*c^6 + a^2*c^8 - 2*b^2*c^8 - c^10) : :
X(32600) = 3 X[3] - X[2916]

X(32600) lies on the cubic K1107 and on these lines: {3, 2916}, {74, 827}, {141, 12901}, {182, 7689}, {206, 3357}, {511, 7691}, {549, 13289}, {1352, 16013}, {1495, 5888}, {1503, 32401}, {1531, 7550}, {1843, 3520}, {3098, 9019}, {5085, 11999}, {7512, 29323}, {8718, 15030}, {10226, 21167}, {14130, 29317}, {20190, 21637}

X(32600) = reflection of X(1176) in X(5092)


X(32601) = X(4)X(64)∩X(20)X(12164)

Barycentrics    7*a^10 - 3*a^8*b^2 - 30*a^6*b^4 + 38*a^4*b^6 - 9*a^2*b^8 - 3*b^10 - 3*a^8*c^2 + 52*a^6*b^2*c^2 - 38*a^4*b^4*c^2 - 20*a^2*b^6*c^2 + 9*b^8*c^2 - 30*a^6*c^4 - 38*a^4*b^2*c^4 + 58*a^2*b^4*c^4 - 6*b^6*c^4 + 38*a^4*c^6 - 20*a^2*b^2*c^6 - 6*b^4*c^6 - 9*a^2*c^8 + 9*b^2*c^8 - 3*c^10 : :
X(32601) - 3 X[4] - 4 X[9786],7 X[4] - 8 X[15873],7 X[9786] - 6 X[15873]

X(32601) lies on the cubic K1108 and on these lines: {4, 64}, {20, 12164}, {74, 3090}, {376, 1092}, {511, 3529}, {546, 15431}, {578, 20427}, {631, 11468}, {1204, 6622}, {1620, 2883}, {2777, 18909}, {3357, 8889}, {5878, 6353}, {5925, 6776}, {6225, 22750}, {6240, 20079}, {9825, 11469}, {11456, 17538}, {11457, 15682}, {12244, 15463}, {13347, 15740}, {18931, 22802}, {25712, 32139}

X(32601) = {X(5895),X(18913)}-harmonic conjugate of X(4)


X(32602) = X(20)X(154)∩X(25)X(64)

Barycentrics    a^2*(3*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 2*b^2*c^2 - c^4)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 - 4*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 28*a^2*b^6*c^2 - 19*b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 - 50*a^2*b^4*c^4 + 18*b^6*c^4 + 2*a^4*c^6 + 28*a^2*b^2*c^6 + 18*b^4*c^6 - 3*a^2*c^8 - 19*b^2*c^8 + c^10) : :

X(32602) lies on the cubic K1108 and these lines: {20, 154}, {25, 64}, {511, 1498}, {1181, 16105}, {1853, 16656}, {5085, 5893}, {8567, 10117}, {11744, 14528}, {13598, 17813}, {17812, 17818}, {17822, 18535}

X(32602) = reflection of X(64) in X(1192)
X(32602) = {X(9914),X(15811)}-harmonic conjugate of X(64)


X(32603) = X(3)X(3620)∩X(125)X(6353)

Barycentrics    15*a^12 - 20*a^10*b^2 - 17*a^8*b^4 + 24*a^6*b^6 + 5*a^4*b^8 - 4*a^2*b^10 - 3*b^12 - 20*a^10*c^2 + 78*a^8*b^2*c^2 - 32*a^6*b^4*c^2 + 12*a^4*b^6*c^2 - 44*a^2*b^8*c^2 + 6*b^10*c^2 - 17*a^8*c^4 - 32*a^6*b^2*c^4 - 34*a^4*b^4*c^4 + 48*a^2*b^6*c^4 + 3*b^8*c^4 + 24*a^6*c^6 + 12*a^4*b^2*c^6 + 48*a^2*b^4*c^6 - 12*b^6*c^6 + 5*a^4*c^8 - 44*a^2*b^2*c^8 + 3*b^4*c^8 - 4*a^2*c^10 + 6*b^2*c^10 - 3*c^12 : :

X(32603) lies on the cubic K1108 and on these lines: {3, 3620}, {125, 6353}, {185, 14912}, {376, 12283}, {5907, 25406}, {6776, 10606}


X(32604) = X(185)X(14914)∩X(511)X(6391)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(3*a^12 - 10*a^10*b^2 + 9*a^8*b^4 + 4*a^6*b^6 - 11*a^4*b^8 + 6*a^2*b^10 - b^12 - 10*a^10*c^2 + 74*a^8*b^2*c^2 - 68*a^6*b^4*c^2 - 12*a^4*b^6*c^2 - 18*a^2*b^8*c^2 + 34*b^10*c^2 + 9*a^8*c^4 - 68*a^6*b^2*c^4 + 110*a^4*b^4*c^4 + 12*a^2*b^6*c^4 - 127*b^8*c^4 + 4*a^6*c^6 - 12*a^4*b^2*c^6 + 12*a^2*b^4*c^6 + 188*b^6*c^6 - 11*a^4*c^8 - 18*a^2*b^2*c^8 - 127*b^4*c^8 + 6*a^2*c^10 + 34*b^2*c^10 - c^12) : :

X(32604) lies on the cubic K1108) and on these lines: {185, 14914}, {511, 6391}, {11820, 19458}


X(32605) = X(2)X(185)∩X(4)X(3167)

Barycentrics    (3*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - 5*a^4*b^2 + 7*a^2*b^4 - 3*b^6 - 5*a^4*c^2 - 6*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(32605) = 5 X[3091] - 2 X[15077],7 X[3523] - 4 X[3532]

X(32605) lies on the cubics K182, K329, K1108, the Thomson-Gibert-Moses hyperbola, the Feuerbach circumhyperbola of the orthic triangle, and on these lines: {2, 185}, {4, 3167}, {5, 5644}, {6, 3091}, {20, 154}, {25, 15741}, {30, 25712}, {52, 3089}, {110, 3146}, {113, 6193}, {155, 6623}, {193, 235}, {354, 1858}, {648, 6526}, {1498, 7396}, {1986, 3542}, {3090, 5544}, {3522, 6030}, {3523, 3532}, {3541, 22948}, {3546, 13491}, {3574, 3832}, {3839, 14516}, {5056, 18928}, {5068, 11442}, {5643, 15022}, {5646, 10303}, {5888, 11440}, {5889, 16879}, {6053, 14216}, {6225, 11064}, {6247, 30769}, {6622, 12164}, {6816, 19125}, {7398, 12233}, {7400, 7999}, {7487, 22660}, {7712, 11449}, {10151, 15751}, {10565, 16252}, {12174, 16051}, {12250, 15063}\

X(32605) = reflection of X(i) in X(j) for these lines: {i,j}: {20, 27082}, {5889, 16879}
X(32605) = {X(3091),X(11441)}-harmonic conjugate of X(5921)
X(32605) = Thomson-isogonal conjugate of X(9909)
X(32605) = orthic-isogonal conjugate of X(20)
X(32605) = X(4)-Ceva conjugate of X(20)
X(32605) = crosspoint of X(4) and X(6622)
X(32605) = barycentric product X(12164)*X(15466)
X(32605) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6622, 459}, {12164, 1073}


X(32606) = (name pending)

Barycentrics    a*(2*a^9 - 5*a^8*b - a^7*b^2 + 12*a^6*b^3 - 9*a^5*b^4 - 6*a^4*b^5 + 13*a^3*b^6 - 4*a^2*b^7 - 5*a*b^8 + 3*b^9 - 5*a^8*c + 20*a^7*b*c - 19*a^6*b^2*c - 19*a^5*b^3*c + 46*a^4*b^4*c - 22*a^3*b^5*c - 15*a^2*b^6*c + 21*a*b^7*c - 7*b^8*c - a^7*c^2 - 19*a^6*b*c^2 + 56*a^5*b^2*c^2 - 36*a^4*b^3*c^2 - 34*a^3*b^4*c^2 + 57*a^2*b^5*c^2 - 21*a*b^6*c^2 - 2*b^7*c^2 + 12*a^6*c^3 - 19*a^5*b*c^3 - 36*a^4*b^2*c^3 + 84*a^3*b^3*c^3 - 38*a^2*b^4*c^3 - 21*a*b^5*c^3 + 18*b^6*c^3 - 9*a^5*c^4 + 46*a^4*b*c^4 - 34*a^3*b^2*c^4 - 38*a^2*b^3*c^4 + 52*a*b^4*c^4 - 12*b^5*c^4 - 6*a^4*c^5 - 22*a^3*b*c^5 + 57*a^2*b^2*c^5 - 21*a*b^3*c^5 - 12*b^4*c^5 + 13*a^3*c^6 - 15*a^2*b*c^6 - 21*a*b^2*c^6 + 18*b^3*c^6 - 4*a^2*c^7 + 21*a*b*c^7 - 2*b^2*c^7 - 5*a*c^8 - 7*b*c^8 + 3*c^9) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29052.

X(32606) lies on this line: {1, 23279}


X(32607) = X(3)X(125)∩X(4)X(13289)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - 2*a^10*b^2 - a^8*b^4 + 4*a^6*b^6 - a^4*b^8 - 2*a^2*b^10 + b^12 - 2*a^10*c^2 + 7*a^8*b^2*c^2 - 5*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 5*a^2*b^8*c^2 - b^10*c^2 - a^8*c^4 - 5*a^6*b^2*c^4 + 10*a^4*b^4*c^4 - 3*a^2*b^6*c^4 - 5*b^8*c^4 + 4*a^6*c^6 - 4*a^4*b^2*c^6 - 3*a^2*b^4*c^6 + 10*b^6*c^6 - a^4*c^8 + 5*a^2*b^2*c^8 - 5*b^4*c^8 - 2*a^2*c^10 - b^2*c^10 + c^12) : :
X(32607) = X[74] + 2 X[11430],2 X[12041] + X[13352]

X(32607) lies on the cubic K1107 and these lines: {3, 125}, {4, 13289}, {24, 7687}, {26, 12295}, {49, 22584}, {54, 74}, {64, 17856}, {110, 5907}, {113, 7526}, {159, 32250}, {184, 5663}, {186, 13851}, {378, 2777}, {399, 19357}, {511, 2071}, {550, 11804}, {569, 14708}, {578, 1986}, {631, 18933}, {974, 1204}, {1092, 12358}, {1112, 11424}, {1147, 7723}, {1177, 12294}, {1181, 10620}, {1350, 32251}, {1425, 10081}, {1511, 15738}, {1593, 10117}, {1594, 19506}, {1658, 10113}, {2935, 3516}, {3043, 12281}, {3047, 12111}, {3270, 10065}, {3357, 17854}, {3448, 19467}, {5504, 5562}, {5621, 11410}, {5650, 15035}, {5890, 16219}, {5972, 7503}, {6146, 10264}, {6240, 32365}, {6467, 11579}, {6644, 23515}, {6723, 17928}, {6759, 12292}, {6776, 32305}, {7488, 10733}, {7728, 14130}, {9934, 11381}, {9970, 21637}, {9976, 15073}, {10114, 20417}, {10605, 15041}, {10606, 17853}, {10619, 18364}, {10681, 11476}, {10682, 11475}, {10721, 14865}, {11473, 13288}, {11474, 13287}, {11562, 12228}, {11801, 15331}, {12084, 16111}, {12133, 15647}, {12163, 19456}, {12168, 24981}, {12317, 18925}, {12412, 15063}, {12605, 23306}, {13358, 16270}, {13417, 15472}, {14049, 32333}, {14448, 17835}, {14585, 14901}, {15059, 22467}, {15081, 21844}, {15089, 22815}, {16010, 19459}, {18379, 20304}, {18563, 19479}

X(32607) = midpoint of X(74) and X(15463)
X(32607) = reflection of X(i) in X(j) for these lines: {i,j}: {15463, 11430}, {22109, 3}}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {{3, 265, 12893}, {3, 12302, 16163}, {3, 19457, 125}, {54, 74, 7722}, {54, 7722, 12227}, {74, 3520, 13293}, {74, 13198, 185}, {125, 21659, 265}, {974, 12041, 1204}, {1593, 10117, 13202}, {2935, 13171, 10990}, {3516, 13171, 2935}, {11425, 17835, 19504}, {12133, 15647, 26883}, {13367, 21650, 110}, {17835, 19504, 14448}


X(32608) = X(3)X(54)∩X(30)X(3448)

Barycentrics    a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 + a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 2*b^6*c^2 - 6*a^4*c^4 - 3*a^2*b^2*c^4 + 2*b^4*c^4 + 8*a^2*c^6 + 2*b^2*c^6 - 3*c^8) : :
X(32608) = 5 X[3] - 2 X[23061],5 X[399] - 8 X[1495],X[399] - 4 X[3581],3 X[399] - 4 X[10540],4 X[1495] - 5 X[2070],2 X[1495] - 5 X[3581],6 X[1495] - 5 X[10540],4 X[1568] - 5 X[1656],3 X[2070] - 2 X[10540],3 X[3581] - X[10540],9 X[5054] - 8 X[14156],5 X[15040] - 4 X[22115],5 X[15040] - 8 X[32110],3 X[15041] - 2 X[18859]

X(32608) lies on the cubic K1107 and these lines: {3, 54}, {30, 3448}, {52, 14130}, {74, 13391}, {185, 13564}, {323, 15646}, {381, 17810}, {382, 9927}, {389, 15047}, {399, 1495}, {511, 5621}, {539, 15085}, {567, 14831}, {568, 15004}, {1350, 15688}, {1568, 1656}, {1657, 11750}, {1658, 9544}, {3526, 9786}, {3534, 10605}, {3580, 18403}, {3830, 18392}, {5054, 14156}, {5055, 7699}, {5663, 5899}, {5876, 13621}, {5907, 18369}, {6241, 15086}, {6243, 7689}, {7545, 18435}, {7666, 32534}, {9306, 18436}, {9703, 18324}, {9818, 13321}, {10263, 11440}, {11438, 23039}, {12111, 18378}, {12308, 14157}, {12359, 31724}, {13403, 18442}, {13414, 28447}, {13415, 28448}, {14118, 14627}, {14128, 22462}, {14449, 14865}, {15040, 22115}, {15053, 15067}, {15060, 21308}, {15707, 21766}, {17835, 18400}

X(32608) = reflection of X(i) in X(j) for these lines: {i,j}: {323, 15646}, {399, 2070}, {2070, 3581}, {12308, 14157}, {18403, 3580}, {22115, 32110}
X(32608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5889, 195}, {7691, 13630, 3}


X(32609) = X(2)X(11694)∩X(3)X(74)

Barycentrics    - a^2*(3*a^8 - 8*a^6*b^2 + 6*a^4*b^4 - b^8 - 8*a^6*c^2 + 11*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 2*b^6*c^2 + 6*a^4*c^4 - 5*a^2*b^2*c^4 - 2*b^4*c^4 + 2*b^2*c^6 - c^8) : :
X(32609) = X[2] - 4 X[11694],5 X[3] - 2 X[74],X[3] + 2 X[110],2 X[3] + X[399],X[3] - 4 X[1511],5 X[3] + 4 X[5609],4 X[3] - X[10620],7 X[3] - 4 X[12041],5 X[3] + X[12308],7 X[3] + 2 X[14094],5 X[3] - 14 X[15020],19 X[3] - 10 X[15021],29 X[3] - 38 X[15023],X[3] - 10 X[15034],11 X[3] - 14 X[15036],2 X[3] + 7 X[15039],2 X[3] - 5 X[15040],10 X[3] - 13 X[15042],7 X[3] - 10 X[15051],11 X[3] - 2 X[15054],3 X[3] - 2 X[15055],X[4] - 4 X[10272],2 X[5] + X[12383],4 X[5] - X[12902],X[5] - 4 X[13392],X[6] + 2 X[12584],X[20] + 5 X[20125],X[40] + 2 X[11699],2 X[54] + X[5898],X[64] - 4 X[25564],X[74] + 5 X[110],4 X[74] + 5 X[399],X[74] - 10 X[1511],X[74] + 2 X[5609],8 X[74] - 5 X[10620],7 X[74] - 10 X[12041],2 X[74] + X[12308],7 X[74] + 5 X[14094],X[74] - 7 X[15020],19 X[74] - 25 X[15021],29 X[74] - 95 X[15023],X[74] - 25 X[15034],X[74] - 5 X[15035],11 X[74] - 35 X[15036],4 X[74] + 35 X[15039],4 X[74] - 25 X[15040],4 X[74] - 5 X[15041],4 X[74] - 13 X[15042],7 X[74] - 25 X[15051],11 X[74] - 5 X[15054],3 X[74] - 5 X[15055],4 X[110] - X[399],X[110] + 2 X[1511],5 X[110] - 2 X[5609],8 X[110] + X[10620],7 X[110] + 2 X[12041],10 X[110] - X[12308],7 X[110] - X[14094],5 X[110] + 7 X[15020],19 X[110] + 5 X[15021],29 X[110] + 19 X[15023],X[110] + 5 X[15034],11 X[110] + 7 X[15036],4 X[110] - 7 X[15039],4 X[110] + 5 X[15040],4 X[110] + X[15041],20 X[110] + 13 X[15042],7 X[110] + 5 X[15051],11 X[110] + X[15054],3 X[110] + X[15055]

X(32609) lies on the cubic K1107 and these lines: {2, 11694}, {3, 74}, {4, 7666}, {5, 12383}, {6, 11935}, {20, 20125}, {24, 3043}, {25, 15463}, {40, 11699}, {49, 9730}, {54, 5898}, {64, 25564}, {113, 382}, {125, 3526}, {140, 3448}, {141, 32306}, {146, 550}, {154, 2777}, {155, 12893}, {182, 2930}, {184, 17701}, {195, 568}, {265, 1656}, {323, 7575}, {373, 567}, {381, 5642}, {394, 22109}, {511, 2070}, {541, 15688}, {542, 5054}, {548, 12244}, {549, 9143}, {569, 15089}, {620, 15545}, {631, 10264}, {974, 19347}, {999, 10088}, {1092, 2937}, {1112, 3517}, {1151, 12376}, {1152, 12375}, {1350, 19140}, {1351, 6593}, {1385, 2948}, {1482, 11720}, {1498, 13293}, {1539, 5073}, {1598, 15472}, {1657, 7728}, {1658, 12307}, {1986, 3515}, {2079, 9696}, {2574, 28447}, {2575, 28448}, {2771, 3576}, {2778, 28450}, {2842, 22586}, {2854, 5050}, {2888, 10125}, {2935, 6759}, {3090, 11801}, {3200, 30439}, {3201, 30440}, {3233, 14934}, {3292, 3581}, {3295, 10091}, {3311, 10819}, {3312, 10820}, {3431, 14926}, {3516, 12292}, {3522, 14677}, {3523, 12317}, {3527, 5504}, {3628, 15081}, {3796, 15693}, {3843, 10733}, {3851, 10113}, {5013, 14901}, {5055, 14644}, {5070, 20304}, {5072, 7687}, {5079, 12900}, {5092, 16010}, {5093, 13321}, {5181, 11898}, {5204, 19470}, {5217, 7727}, {5465, 12355}, {5621, 17508}, {5640, 15038}, {5650, 18475}, {5651, 14805}, {5889, 11561}, {5907, 18364}, {6053, 16111}, {6101, 7731}, {6102, 12273}, {6243, 11557}, {6417, 19110}, {6418, 19111}, {6642, 12228}, {6644, 9703}, {6699, 15720}, {6723, 15027}, {7387, 20773}, {7517, 20771}, {7545, 13352}, {7574, 11064}, {7722, 32534}, {8909, 12892}, {8998, 19052}, {9129, 11258}, {9140, 15694}, {9545, 13472}, {9654, 18968}, {9669, 12896}, {9704, 17928}, {9705, 12284}, {9706, 12006}, {9786, 12227}, {9833, 23315}, {9904, 31663}, {9919, 15647}, {9934, 14530}, {9956, 12407}, {10117, 10282}, {10170, 13367}, {10540, 14915}, {10627, 13201}, {10628, 11202}, {10657, 11481}, {10658, 11480}, {10706, 15681}, {10721, 17800}, {11002, 12106}, {11426, 11746}, {11477, 25556}, {11562, 18436}, {11579, 12017}, {11598, 13093}, {11702, 12316}, {11999, 15748}, {12038, 12302}, {12083, 16165}, {12085, 25487}, {12165, 15750}, {12645, 12898}, {12903, 31479}, {13188, 18332}, {13289, 17821}, {13358, 15043}, {13434, 22462}, {13743, 16164}, {13990, 19051}, {14695, 32204}, {15033, 21308}, {15063, 15696}, {15141, 15577}, {17845, 19506}, {18440, 32233}, {18534, 20772}, {19145, 32292}, {19146, 32291}, {27866, 32046}

X(32609) = midpoint of X(i) and X(j) for these lines: {i,j}: {110, 15035}, {399, 15041}, {23515, 30714}
X(32609) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 15035}, {265, 23515}, {381, 14643}, {568, 16223}, {5050, 15462}, {5621, 17508}, {10620, 15041}, {14643, 5642}, {15035, 1511}, {15041, 3}, {23515, 5972}
X(32609) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 110, 399}, {3, 399, 10620}, {3, 1511, 15040}, {3, 12308, 74}, {5, 12383, 12902}, {24, 3043, 19504}, {74, 110, 5609}, {74, 5609, 12308}, {110, 1511, 3}, {110, 15020, 74}, {110, 15034, 1511}, {110, 15040, 10620}, {110, 15051, 14094}, {113, 12121, 382}, {265, 5972, 1656}, {381, 14643, 15046}, {399, 15039, 110}, {399, 15040, 3}, {399, 15042, 74}, {631, 14683, 10264}, {1511, 15039, 10620}, {5609, 12308, 399}, {5609, 15020, 3}, {5609, 15042, 10620}, {5972, 30714, 265}, {6644, 9703, 15087}, {7728, 16163, 1657}, {11720, 12778, 1482}, {12017, 32254, 11579}, {12038, 18350, 14130}, {12041, 15051, 3}, {12308, 15020, 15042}, {14094, 15051, 12041}, {15039, 15040, 399}, {16163, 16534, 7728}, {17821, 17847, 13289}

X(32609) = circumcircle- inverse of X(5609)
X(32609) = crosssum of X(523) and X(6070)
X(32609) = pole of line X(526)X(5607) wrt circumcircle


X(32610) = X(35)X(79)∩X(5010)X(20277)

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

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29057.

X(32610) lies on these lines: {35, 79}, {5010, 20277}

X(32610) = isogonal conjugate of X(32611)
X(32610) = {X(35), X(8606)}-harmonic conjugate of X(226)

X(32611) = ISOGONAL CONJUGATE OF X(32610)

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

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29057.

X(32611) lies on this line: {500, 9642}

X(32611) = isogonal conjugate of X(32610)

X(32612) = MIDPOINT OF X(3) AND X(56)

Barycentrics    a^2*(a^5-(b+c)*a^4-2*(b-c)^2*a^3+(b+c)*(2*b^2-3*b*c+2*c^2)*a^2+(b^4+c^4-4*b*c*(b^2-b*c+c^2))*a-(b^3+c^3)*(b-c)^2) : :
X(32612) = 3*X(3)-X(10310), 3*X(3)+X(10680), X(46)+3*X(3576), 3*X(56)+X(10310), 3*X(56)-X(10680), 5*X(631)-X(3436), 7*X(3523)+X(20076), 7*X(3526)-5*X(31246), 3*X(5054)-X(31141), 3*X(10165)-X(21616), X(11499)-3*X(16371), 3*X(21154)-X(32554)

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29059 and Hyacinthos 29062.

X(32612) lies these lines: {1, 3}, {4, 10584}, {5, 2829}, {10, 32153}, {12, 21154}, {24, 1828}, {30, 7681}, {84, 31828}, {104, 355}, {119, 13747}, {140, 993}, {182, 8679}, {214, 5884}, {388, 6961}, {474, 9956}, {496, 5840}, {499, 6923}, {515, 6924}, {528, 32214}, {529, 549}, {631, 3436}, {944, 4188}, {952, 8256}, {958, 11231}, {971, 15297}, {997, 5694}, {1006, 5303}, {1012, 9955}, {1125, 6914}, {1158, 22775}, {1478, 6958}, {1483, 5854}, {1656, 18515}, {1766, 21773}, {1837, 10090}, {2390, 11202}, {2975, 6940}, {3035, 10942}, {3086, 6948}, {3149, 28160}, {3523, 20076}, {3526, 5251}, {3560, 3824}, {3585, 6971}, {3616, 6950}, {3624, 7489}, {3653, 17549}, {3655, 11491}, {4190, 10785}, {4293, 6891}, {4299, 6928}, {4511, 26877}, {4640, 31838}, {4881, 21740}, {4973, 31806}, {5054, 31141}, {5229, 6978}, {5253, 5886}, {5267, 10165}, {5298, 15908}, {5322, 16434}, {5428, 17768}, {5433, 6842}, {5587, 26321}, {5690, 8666}, {5731, 6942}, {5818, 17572}, {5881, 12773}, {5882, 32141}, {5887, 17614}, {6256, 6959}, {6265, 18861}, {6850, 7288}, {6875, 11415}, {6882, 7354}, {6885, 18517}, {6905, 18481}, {6909, 12699}, {6911, 12114}, {6918, 18761}, {6921, 12115}, {6929, 10200}, {6944, 18516}, {6955, 10527}, {6966, 10532}, {6970, 12667}, {6980, 15446}, {7491, 15326}, {7741, 12764}, {8227, 13743}, {8583, 22936}, {8703, 12511}, {9657, 11929}, {10058, 11376}, {10943, 20418}, {11112, 26470}, {11263, 17009}, {11499, 16371}, {12737, 14923}, {13731, 27657}, {14988, 30144}, {15325, 15866}, {18446, 26201}, {19525, 19861}, {19548, 28096}, {22753, 22793}, {22836, 24475}, {28459, 30264}

X(32612) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 56}, {4299, 6928}, {10310, 10680}
X(32612) = reflection of X(i) in X(j) for these (i,j): (5, 6691), (1329, 140)
X(32612) = complement of complement of X(37002)
X(32612) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1,3,26285}, {3,36,26286}, {3,55,26086}, {3, 1385, 32613}, {3,999,11248}, {3,1482,2077}, {3,3428,31663}, {3,10246,35}, {3,10269,1385}, {3,10680,10310}, {3,11249,3579}, {3,16202,5217}, {3,16203,55}, {3,22765,40}, {36,14800,1}, {55,16203,15178}, {56,8069,24928}, {56,10310,10680}, {104,404,355}, {474,22758,9956}, {997,24467,5694}, {999,1466,31794}, {999,11248,10222}, {1319,25414,1}, {1385,23961,3}, {1470,22766,942}, {2077,5563,1482}, {2975,6940,26446}, {3086,6948,10525}, {3560,25524,11230}, {3576,7280,3}, {4293,6891,10526}, {5253,6906,5886}, {5885,13624,26287}, {5885,26287,1}, {6911,12114,18480}, {8071,22768,24929}, {9940,13624,1385}, {13528,20323,23340}, {15178,26086,55}, {31663,31797,3579}


X(32613) = MIDPOINT OF X(3) AND X(55)

Barycentrics    a^2*(a^5-(b+c)*a^4-2*(b^2+c^2)*a^3+(b+c)*(2*b^2-b*c+2*c^2)*a^2+(b^4+c^4)*a-(b^2-c^2)*(b^3-c^3)) : :
X(32613) = 3*X(3)-X(3428), 3*X(3)+X(10679), 3*X(55)+X(3428), 3*X(55)-X(10679), 5*X(631)-X(3434), 5*X(1656)-X(18499), X(3419)-3*X(26446), 7*X(3523)+X(20075), 7*X(3526)-5*X(31245), X(3870)+3*X(21165), 3*X(5054)-X(31140), 4*X(6690)-X(18407), 3*X(16370)-X(22758)

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29059 and Hyacinthos 29062.

X(32613) lies these lines: {1, 3}, {4, 10585}, {5, 5248}, {8, 6875}, {10, 32141}, {11, 21155}, {12, 7491}, {21, 355}, {24, 1824}, {30, 7680}, {31, 5396}, {42, 5398}, {47, 2594}, {100, 1006}, {104, 3655}, {119, 11113}, {140, 2886}, {153, 15677}, {182, 674}, {255, 5399}, {405, 9956}, {411, 12699}, {497, 6954}, {498, 6928}, {500, 601}, {515, 6914}, {528, 549}, {529, 32213}, {631, 3434}, {902, 1064}, {912, 4640}, {943, 5812}, {944, 4189}, {952, 993}, {962, 6876}, {971, 15296}, {991, 19624}, {997, 22935}, {1001, 6911}, {1012, 28160}, {1030, 2079}, {1125, 6924}, {1283, 14663}, {1324, 3185}, {1376, 6883}, {1479, 6863}, {1483, 5855}, {1490, 31828}, {1621, 5886}, {1656, 5259}, {1871, 14017}, {2771, 18446}, {2875, 18475}, {3085, 6868}, {3145, 9959}, {3149, 9955}, {3523, 20075}, {3526, 31245}, {3560, 11500}, {3583, 6980}, {3584, 15175}, {3616, 6942}, {3651, 16159}, {3652, 12528}, {3653, 13587}, {3654, 21161}, {3679, 12331}, {3811, 22937}, {3870, 21165}, {3877, 6265}, {4192, 29678}, {4220, 29665}, {4294, 6825}, {4302, 6923}, {4420, 26878}, {4421, 28466}, {4428, 22753}, {4512, 5720}, {4995, 28459}, {4996, 12737}, {4999, 10943}, {5054, 31140}, {5070, 25542}, {5218, 6827}, {5251, 5790}, {5258, 12645}, {5267, 5882}, {5281, 6987}, {5284, 6946}, {5310, 19544}, {5428, 5690}, {5432, 6882}, {5534, 31424}, {5552, 6936}, {5587, 7489}, {5691, 13743}, {5694, 12514}, {5731, 6950}, {5762, 8255}, {5818, 16865}, {5840, 6907}, {5844, 25439}, {5887, 20846}, {6097, 13754}, {6253, 6841}, {6284, 6842}, {6824, 18517}, {6872, 10786}, {6902, 27529}, {6906, 18481}, {6910, 12116}, {6913, 18491}, {6917, 10198}, {6930, 18516}, {6962, 10531}, {6970, 26105}, {6985, 11496}, {7301, 7609}, {7330, 22936}, {7483, 26470}, {7488, 20243}, {7580, 28146}, {8053, 14723}, {9670, 11928}, {10282, 10537}, {11604, 13199}, {13323, 22276}, {15623, 17524}, {15733, 31658}, {15865, 31789}, {15888, 30264}, {16139, 31660}, {16370, 22758}, {19524, 19861}, {19649, 29680}, {20999, 23206}, {24309, 29243}, {24466, 28458}, {28208, 28444}

X(32613) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 55}, {3428, 10679}, {4302, 6923}
X(32613) = reflection of X(i) in X(j) for these (i,j): (5, 6690), (993, 7508), (2886, 140), (5173, 13373), (10537, 10282), (18407, 5)
X(32613) = complement of complement of X(37000)
X(32613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1,3,26286}, {1,165,5535}, {1,1454,942} ,{3,35,26285}, {3, 1385, 32612}, {3,1482,11012}, {3,3295,11249}, {3,5217,26086}, {3,10246,36}, {3,10267,1385}, {3,10269,23961}, {3,10310,31663}, {3,10679,3428}, {3,11248,3579}, {3,11849,40}, {3,16202,56}, {3,16203,5204}, {21,11491,355}, {35,10902,3}, {35,14795,1}, {35,14799,5010}, {35,15931,2077}, {55,3428,10679}, {55,5172,1}, {55,8069,24929}, {56,16202,15178}, {100,1006,26446}, {405,11499,9956}, {1001,6911,11230}, {1376,6883,11231}, {1385,17502,18857}, {1385,23961,10269}, {1621,6905,5886}, {2077,10902,15931}, {2077,15931,3}, {3085,6868,10526}, {3295,11249,10222}, {3560,11500,18480}, {3576,5010,3}, {3746,11012,1482}, {3746,14804,1}, {4294,6825,10525}, {5248,6796,5}, {5267,5882,32153}, {6985,11496,22793}, {7489,18524,5587}, {8071,11510,24928}, {11508,26357,9957}, {13624,26086,3}, {26398,26422,1}

X(32613) = center of circle that is inverse-in-circumcircle of antiorthic axis


X(32614) = X(4)X(13414)∩X(20)X(13415)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2) - (5*a^4 - 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 6*b^2*c^2 - 3*c^4)*J*R^2 : :
X(32614) = J X[110] - X[3146]

X(32614) lies on the cubic K1108 and these lines: {4, 13414}, {20, 13415}, {64, 2574}, {110, 3146}, {185, 24651}, {511, 15156}, {1114, 21663}, {1495, 15157}, {2575, 12164}, {5907, 25407}, {13598, 24650}, {15155, 32608}

X(32614) = reflection of X(32615) in X(13346)
X(32614) = {X(110),X(3146)}-harmonic conjugate of X(32615)


X(32615) = X(4)X(13415)∩X(20)X(13414)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2) + (5*a^4 - 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 6*b^2*c^2 - 3*c^4)*J*R^2 : :
X(32615) = J X[110] + X[3146]

X(32615) lies on the cubic K1108 and these lines: {4, 13415}, {20, 13414}, {64, 2575}, {110, 3146}, {185, 24650}, {511, 15157}, {1113, 21663}, {1495, 15156}, {2574, 12164}, {5907, 25408}, {13598, 24651}, {15154, 32608}

X(32615) = reflection of X(32614) in X(13346)
X(32615) = {X(110),X(3146)}-harmonic conjugate of X(32614)


X(32616) = X(3)X(74)∩X(4)X(2575)

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

X(32616) lies on the cubic K1108 and these lines: {3, 74}, {4, 2575}, {20, 2574}, {64, 15461}, {185, 13415}, {511, 15156}, {1113, 6000}, {1114, 13754}, {1154, 15155}, {1344, 15305}, {1345, 5890}, {1347, 18388}, {5562, 25407}, {5889, 24651}, {5907, 13414}, {10751, 25739}, {12162, 14709}, {14915, 15157}, {18439, 20478}

X(32616) = reflection of X(i) in X(j) for these lines: {i,j}: {24650, 31955}, {31954, 13415}
X(32616) = reflection of X(32617) in X(3)
X(32616) = {X(74),X(6241)}-harmonic conjugate of X(32617)
X(32616) = {X(110),X(12111)}-harmonic conjugate of X(32617)


X(32617) = X(3)X(74)∩X(4)X(2574)

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

X(32617) lies on the cubic K1108 and these lines: {3, 74}, {4, 2574}, {20, 2575}, {64, 15460}, {185, 13414}, {511, 15157}, {1113, 13754}, {1114, 6000}, {1154, 15154}, {1344, 5890}, {1345, 15305}, {1346, 18388}, {5562, 25408}, {5889, 24650}, {5907, 13415}, {10750, 25739}, {12162, 14710}, {14915, 15156}, {18439, 20479}

X(32617) = reflection of X(i) in X(j) for these lines: {i,j}: {24651, 31954}, {31955, 13414}
X(32617) = reflection of X(32616) in X(3)
X(32617) = {X(74),X(6241)}-harmonic conjugate of X(32616)
X(32617) = {X(110),X(12111)}-harmonic conjugate of X(32616)


X(32618) = ISOGONAL CONJUGATE OF X(5000)

Barycentrics    1/(S*SB*SC + SA*Sqrt[SA*SB*SC*SW]) : :

X(32618) lies on the following curves: Jerabek circumhyperbola, K018, K270, K305, K336, K337, K1096, Q021, Q030, Q044, Q094, and on these lines: {2, 98}, {10264, 31665}

X(32618) = reflection of X(32619) in X(125)
X(32618) = isogonal conjugate of X(5000)
X(32618) = isogonal conjugate of the complement of X(5002)
X(32618) = Brocard-circle inverse of X(32619)
X(32618) = antigonal image of X(32619)
X(32618) = psi-transform of X(5001)
X(32618) = X(511)-cross conjugate of X(32619)
X(32618) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5000}, {240,32619}
X(32618) = barycentric product X(287)*X(5001)
X(32618) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 5000}, {248, 32619}, {5001, 297}
X(32618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6776, 32619}, {98, 287, 32619}, {110, 5622, 32619}, {182, 184, 32619}, {1352, 1899, 32619}, {1976, 17974, 32619}, {5921, 23291, 32619}, {13198, 15462, 32619}, {13414, 13415, 32619}


X(32619) = ISOGONAL CONJUGATE OF X(5001)

Barycentrics    1/(S*SB*SC - SA*Sqrt[SA*SB*SC*SW]) : :

X(32619) lies on the following curves: Jerabek circumhyperbola, K018, K270, K305, K336, K337, K1096, Q021, Q030, Q044, Q094, and on these lines: {2, 98}, {10264, 31664}

X(32619) = reflection of X(32618) in X(125)
X(32619) = Brocard-circle inverse of X(32618)
X(32619) = isogonal conjugate of X(5001)
X(32619) = isogonal conjugate of the complement of X(5003)
X(32619) = antigonal image of X(32618)
X(32619) = psi-transform of X(5000)
X(32619) = X(511)-cross conjugate of X(32618)
X(32619) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5001}, {240, 32618}
X(32619) = barycentric product X(287)*X(5000)
X(32619) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 5001}, {248, 32618}, {5000, 297}
X(32619 = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6776, 32618}, {98, 287, 32618}, {110, 5622, 32618}, {182, 184, 32618}, {1352, 1899, 32618}, {1976, 17974, 32618}, {5921, 23291, 32618}, {13198, 15462, 32618}, {13414, 13415, 32618}


X(32620) = X(3)X(1495)∩X(5)X(4549)

Barycentrics    a^2*(3*a^8 - 4*a^6*b^2 - 6*a^4*b^4 + 12*a^2*b^6 - 5*b^8 - 4*a^6*c^2 + 4*a^4*b^2*c^2 + 8*a^2*b^4*c^2 - 8*b^6*c^2 - 6*a^4*c^4 + 8*a^2*b^2*c^4 + 26*b^4*c^4 + 12*a^2*c^6 - 8*b^2*c^6 - 5*c^8) : :
X(32620) = 5 X[3] + X[3426],X[3] + 2 X[4550],5 X[3] - 2 X[8717],2 X[3] + X[11472],7 X[3] - X[11820],2 X[5] + X[4549],4 X[140] - X[4846],X[1350] + 2 X[31861],5 X[1656] - 2 X[7706],X[3426] - 10 X[4550],X[3426] + 2 X[8717],2 X[3426] - 5 X[11472],7 X[3426] + 5 X[11820],5 X[4550] + X[8717],4 X[4550] - X[11472],14 X[4550] + X[11820],4 X[8717] + 5 X[11472],14 X[8717] - 5 X[11820],7 X[11472] + 2 X[11820]

X(32620) lies on the cubic K1107 and on these lines: {3, 1495}, {5, 4549}, {6, 32599}, {22, 16261}, {30, 10516}, {54, 155}, {64, 7516}, {140, 3532}, {154, 15060}, {378, 7998}, {511, 9813}, {541, 5054}, {549, 10606}, {1154, 5102}, {1192, 3628}, {1350, 31861}, {1656, 7706}, {3066, 3581}, {3336, 7986}, {3796, 18435}, {5050, 13754}, {5085, 5621}, {5646, 12041}, {5891, 6090}, {6000, 17508}, {6800, 18451}, {7393, 16836}, {7395, 9730}, {7464, 21766}, {7509, 15072}, {7525, 15811}, {7526, 15067}, {9786, 13363}, {9827, 17834}, {10938, 19357}, {10982, 32352}, {11248, 15625}, {11284, 32110}, {11387, 11817}, {13154, 32138}, {16072, 23515}, {17811, 18570}, {18377, 20584}, {32607, 32609}

X(32620) = reflection of X(5085) in X(7514)
X(32620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3426, 8717}, {3, 4550, 11472}, {7395, 12163, 15805}


X(32621) = X(3)X(524)∩X(6)X(25)

Barycentrics    a^2*(a^6 + a^4*b^2 - a^2*b^4 - b^6 + a^4*c^2 - 10*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 + b^2*c^4 - c^6) : :
X(32621) = X[3] - 4 X[8546],X[1351] + 2 X[8547],X[5486] + 2 X[8550],X[15069] - 4 X[16511],X[16010] + 2 X[16510]

Let A'B'C' be the reflection of ABC in X(6). Let AB = BC∩C'A', AC = BC∩A'B', and define BC, BA, CA, CB cyclically. AB, AC, BC, BA, CA, CB lie on the 2nd Lemoine circle. Let A" be the intersection of the tangents to the 2nd Lemoine circle at BA and CA, and define B" and C" cyclically. X(32621) = X(4)-of-A"B"C". (see also X(5050)) (Randy Hutson, June 7, 2019)

X(32621) lies on the cubic K1107 and on these lines: {3, 524}, {6, 25}, {22, 1992}, {23, 5032}, {24, 11431}, {67, 32240}, {69, 7485}, {140, 9925}, {141, 16419}, {160, 8573}, {182, 8681}, {186, 14912}, {193, 6636}, {378, 6776}, {542, 9818}, {575, 6642}, {576, 7387}, {578, 8549}, {597, 5020}, {599, 7484}, {1181, 9914}, {1351, 8547}, {1353, 7502}, {1449, 1486}, {1503, 1597}, {1598, 15581}, {1609, 20775}, {2854, 5050}, {2930, 5642}, {2936, 18800}, {3158, 12329}, {3455, 5477}, {3517, 15582}, {3564, 7514}, {3576, 9004}, {4663, 9798}, {5012, 15531}, {5024, 9142}, {5085, 9027}, {5093, 5899}, {5095, 32262}, {5422, 11188}, {5480, 18535}, {5621, 11410}, {6515, 16789}, {7395, 15069}, {7517, 11482}, {7592, 15073}, {7666, 32154}, {8537, 11423}, {8540, 10833}, {8548, 9937}, {8584, 9909}, {8787, 9876}, {8889, 18935}, {10169, 18919}, {10249, 11430}, {10541, 14528}, {10601, 29959}, {11160, 15246}, {11255, 32136}, {11414, 11477}, {11416, 11422}, {12007, 15577}, {12161, 15074}, {15141, 32245}, {16010, 16510}, {18388, 23049}, {18534, 20423}, {18954, 19369}, {20583, 20850}, {23292, 23327}, {32254, 32274}

X(32621) = reflection of X(9813) in X(575)
X(32621) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 154, 19136}, {6, 184, 19153}, {6, 9924, 9969}, {6, 9971, 9777}, {6, 10602, 11216}, {6, 19459, 159}, {206, 22829, 6}, {6467, 13366, 8541}, {8541, 13366, 6}, {10602, 11402, 6}


X(32622) = 1st MOSES-STEVANOVIC POINT

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

"Tripolars" abbreviates "homogeneous tripolar coordinates"; i.e., to say that x : y : z are tripolars for a point X means that x, y, z, are respectively proportional to |AX|, |BX|, |CX|.

X(32622) is one of two points (X(32623) is the other) whose pedal antipodal perspector is X(7). Also, X(32622) is the perspector of the excentral triangles of ABC and the circumcevian triangle of X(3513). (Randy Hutson, June 5, 2019 )

X(32622) lies on the Stevanovic circle, the curves K352 and Q037, and on this line: {1, 3}

X(32622) = reflection of X(32623) in X(1155)
X(32622) = X(513)-vertex conjugate of X(32623)
X(32622) = X(972)-Ceva conjugate of X(32623)
X(32622) = circumcircle-inverse of X(32623)
X(32622) = Bevan-circle-inverse of X(32623)
X(32622) = isogonal conjugate of X(39144)
X(32622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 165, 32623}, {3, 55, 32623}, {35, 15931, 32623}, {36, 5537, 32623}, {40, 57, 32623}, {55, 3514, 1}, {56, 6244, 32623}, {354, 3579, 32623}, {484, 5536, 32623}, {942, 7964, 32623}, {1155, 3514, 36}, {1381, 1382, 32623}, {1617, 10310, 32623}, {2077, 2078, 32623}, {2448, 2449, 32623}, {3256, 11012, 32623}, {3660, 13528, 32623}, {3748, 31663, 32623}, {7987, 31508, 32623}, {7994, 15803, 32623}, {8186, 8187, 32623}, {10268, 10383, 32623}, {10270, 10388, 32623}


X(32623) = 2nd MOSES-STEVANOVIC POINT

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

X(32623) is one of two points (X(32622) is the other) whose pedal antipodal perspector is X(7). Also, X(32623) is the perspector of the excentral triangles of ABC and the circumcevian triangle of X(3514). (Randy Hutson, June 5, 2019 )

p> X(32623) lies on the Stevanovic circle, the curves K352 and Q037, and on this line: {1, 3}

X(32623) = reflection of X(32622) in X(1155)
X(32623) = isogonal conjugate of X(39145)
X(32623) = X(513)-vertex conjugate of X(32622)
X(32623) = X(972)-Ceva conjugate of X(32622)
X(32623) = circumcircle-inverse of X(32622)
X(32623) = Bevan-circle-inverse of X(32622)
X(32623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 165, 32622}, {3, 55, 32622}, {35, 15931, 32622}, {36, 5537, 32622}, {40, 57, 32622}, {55, 3513, 1}, {56, 6244, 32622}, {354, 3579, 32622}, {484, 5536, 32622}, {942, 7964, 32622}, {1155, 3513, 36}, {1381, 1382, 32622}, {1617, 10310, 32622}, {2077, 2078, 32622}, {2448, 2449, 32622}, {3256, 11012, 32622}, {3660, 13528, 32622}, {3748, 31663, 32622}, {7987, 31508, 32622}, {7994, 15803, 32622}, {8186, 8187, 32622}, {10268, 10383, 32622}, {10270, 10388, 32622}


X(32624) = CIRCUMCIRCLE-INVERSE OF X(7)

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

X(32624) lies on these lines: {3,7}, {1358,5172}, {4367,8638}, {5543,26357}, {7742,14878}, {9436,27086}, {23839,32613}

X(32624) = circumcircle-inverse of X(7)


X(32625) = CIRCUMCIRCLE-INVERSE OF X(9)

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

X(32625) lies on these lines: {3, 9}, {35, 3207}, {36, 910}, {48, 4262}, {101, 2077}, {104, 8074}, {404, 8568}, {667, 3900}, {934, 2391}, {1055, 2078}, {1108, 7297}, {1615, 15931}, {2170, 5193}, {2178, 18594}, {2183, 5030}, {2317, 4251}, {3911, 11349}, {4394, 4730}, {5537, 6603}, {7987, 32561}, {12114, 23058}

X(32625) = circumcircle-inverse of X(9)
X(32625) = crosspoint of X(2291) and X(3451)
X(32625) = crosssum of X(i) and X(j) for these (i,j): {527, 3452}, {5514, 6366}
X(32625) = crossdifference of every pair of points on line {3752, 6129}
X(32625) = {X(1436),X(1604)}-harmonic conjugate of X(9)


X(32626) = CIRCUMCIRCLE-INVERSE OF X(12)

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

X(32626) lies on these lines: {3, 12}, {2915, 14882}

X(32626) = circumcircle-inverse of X(12)


X(32627) = CIRCUMCIRCLE-INVERSE OF X(17)

Barycentrics    a^2*(a^2 + b^2 - c^2 + 2*Sqrt[3]*S)*(a^2 - b^2 + c^2 + 2*Sqrt[3]*S)*(Sqrt[3]*(a^6 - 2*a^4*b^2 + a^2*b^4 - 2*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4) - 2*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*S) : :

X(32627) lies on the cubic K937 and these lines: {3, 13}, {16, 16806}, {61, 1337}, {3130, 16530}, {3439, 11602}, {3442, 15444}, {5012, 21461}, {10677, 16257}, {11087, 22511}

X(32627) = isogonal conjugate of X(34219)
X(32627) = circumcircle-inverse of X(17)
X(32627) = {X(6104),X(31939)}-harmonic conjugate of X(3)


X(32628) = CIRCUMCIRCLE-INVERSE OF X(18)

Barycentrics    a^2*(a^2 + b^2 - c^2 - 2*Sqrt[3]*S)*(a^2 - b^2 + c^2 - 2*Sqrt[3]*S)*(Sqrt[3]*(a^6 - 2*a^4*b^2 + a^2*b^4 - 2*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4) + 2*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*S) : :

X(32628) lies on the cubic K937 and these lines: {3, 14}, {15, 16807}, {62, 1338}, {3129, 16529}, {3438, 11603}, {3443, 15445}, {5012, 21462}, {10678, 16258}, {11082, 22510}

X(32628) = isogonal conjugate of X(34220)
X(32628) = circumcircle-inverse of X(18)
X(32628) = {X(6105),X(31940)}-harmonic conjugate of X(3)


X(32629) = X(13624)X(28185)∩X(15178)X(28173)

Barycentrics    a*(a - b)*(a - c)*(3*a^3 + 13*a^2*b + 13*a*b^2 + 3*b^3 - 3*a^2*c - 7*a*b*c - 3*b^2*c - 3*a*c^2 - 3*b*c^2 + 3*c^3)*(3*a^3 - 3*a^2*b - 3*a*b^2 + 3*b^3 + 13*a^2*c - 7*a*b*c - 3*b^2*c + 13*a*c^2 - 3*b*c^2 + 3*c^3) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29066.

X(32629) lies on the circumcircle and these lines: {13624, 28185}, {15178, 28173}


X(32630) = X(1)X(28535)∩X(101)X(14422)

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

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29068.

X(32630) lies on the circumcircle and these lines: {1,28535}, {101,14422}, {103,10246}, {244,28317}, {2291,4860}, {3576,28159}, {5425,28471}, {14413,2899}


X(32631) = ISOGONAL CONJUGATE OF X(19654)

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

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29068.

X(32631) lies on these lines: {2,1155}, {4671,27756}, {4870,27761}, {4945,27741}, {4956,27753}, {5219,27737}, {5235,27740}, {5603,28537}, {9093,28899}

X(32631) = isogonal conjugate of X(19654)
X(32631) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {6,19654}, {45,5220}, {3679,17294}, {4777,28898}, {28899,4588}
X(32631) = trilinear product of X(i) and X(j) for these lines: {i,j}: {4791,28899}
X(32631) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {1,19654}, {3679,5220}, {4671,17294}


X(32632) = X(1)X(4127)∩X(9)X(19872)

Barycentrics    a*(9*a^3 + 9*a^2*b - 9*a*b^2 - 9*b^3 + 9*a^2*c - 13*a*b*c - 21*b^2*c - 9*a*c^2 - 21*b*c^2 - 9*c^3) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32632) lies on the Jerabek circumhyperbola of the excentral triangle and these lines: {1, 4127}, {9, 19872}, {40, 3627}, {191, 9780}, {2136, 4816}, {3219, 3337}, {3626, 5541}, {3646, 6763}, {3647, 13146}, {6326, 13624}

X(32632) = excentral isogonal conjugate of X(31663)
X(32632) = X(3634)-Ceva conjugate of X(1)


X(32633) = X(1)X(4757)∩X(3)X(5260)

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

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32633) lies on these lines: {1, 4757}, {3, 5260}, {8, 19704}, {21, 19862}, {100, 3626}, {404, 19872}, {1001, 4189}, {1621, 19535}, {2975, 3621}, {3634, 13587}, {3736, 16477}, {4816, 5010}, {5251, 22266}, {5284, 7280}, {5550, 16370}, {6265, 13624}, {7173, 15680}, {19705, 19877}, {21161, 22936}, {22355, 27026}

X(32633) = {X(7280),X(17574)}-harmonic conjugate of X(5284)


X(32634) = X(1)X(3968)∩X(8)X(381)

Barycentrics    a*(a^3 - 4*a^2*b - a*b^2 + 4*b^3 - 4*a^2*c + 23*a*b*c - 19*b^2*c - a*c^2 - 19*b*c^2 + 4*c^3) : :
X(32634) = 2 X[8148] - 5 X[16615]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32634) lies on these lines: {1, 3968}, {8, 381}, {10, 13606}, {100, 13624}, {2550, 3621}, {3617, 3813}, {3626, 21630}, {4420, 10222}, {4853, 5303}, {5178, 12751}, {5223, 14923}, {10914, 11684}, {11024, 20050}

X(32634) = reflection of X(13606) in X(10)


X(32635) = X(1)X(748)∩X(2)X(3296)

Barycentrics    a*(a - b - c)*(a + 2*b + c)*(a + b + 2*c) : :
X(32635) = X[1] - 3 X[5506],8 X[3634] - 3 X[5557],7 X[9780] - 3 X[9782]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32635) lies on Feuerbach circumhyperbola and these lines: {1, 748}, {2, 3296}, {4, 3617}, {7, 12}, {8, 3058}, {9, 3871}, {10, 79}, {21, 210}, {44, 2298}, {45, 941}, {80, 3626}, {84, 1796}, {100, 3065}, {104, 6986}, {191, 3956}, {256, 3214}, {314, 3701}, {354, 17546}, {404, 7284}, {484, 4540}, {517, 16615}, {518, 17536}, {519, 13606}, {943, 3935}, {958, 2320}, {960, 1320}, {1000, 3621}, {1171, 5297}, {1389, 11278}, {1392, 5330}, {2346, 15254}, {2478, 5686}, {2481, 6540}, {2891, 25479}, {3062, 7997}, {3219, 3579}, {3254, 6734}, {3475, 5550}, {3625, 5559}, {3634, 5557}, {3679, 5560}, {3680, 3877}, {3691, 4876}, {3740, 17531}, {3811, 16858}, {3869, 17098}, {3873, 17534}, {3885, 4900}, {3889, 7308}, {3983, 15481}, {4096, 27368}, {4430, 16842}, {4532, 16126}, {4537, 5425}, {4647, 4756}, {4661, 11108}, {4866, 5250}, {4943, 23836}, {5044, 15179}, {5251, 5424}, {5551, 5708}, {5665, 15556}, {5719, 17552}, {6595, 18259}, {6684, 13243}, {6763, 9342}, {7320, 20050}, {10266, 21031}, {11544, 17484}, {11604, 13272}, {11698, 16006}, {12019, 24298}, {17420, 23838}, {18483, 25006}, {21077, 31254}, {26792, 31419}, {27549, 30479}

X(32635) = isogonal conjugate of X(32636)
X(32635) = X(1268)-Ceva conjugate of X(1255)
X(32635) = X(i)-cross conjugate of X(j) for these (i,j): {3737, 3699}, {4041, 644}, {4662, 8}
X(32635) = X(i)-isoconjugate of X(j) for these (i,j): {6, 553}, {7, 2308}, {34, 3916}, {56, 1125}, {57, 1100}, {58, 3649}, {73, 31900}, {77, 2355}, {101, 30724}, {106, 5298}, {109, 4977}, {181, 30593}, {222, 1839}, {269, 3683}, {273, 23201}, {278, 22054}, {604, 4359}, {608, 4001}, {651, 4979}, {1014, 1962}, {1106, 3702}, {1213, 1412}, {1230, 16947}, {1269, 1397}, {1396, 3958}, {1400, 8025}, {1402, 16709}, {1407, 3686}, {1408, 4647}, {1411, 4973}, {1414, 4983}, {1415, 4978}, {1416, 4966}, {1417, 4975}, {1431, 4697}, {1434, 20970}, {1461, 4976}, {2163, 4870}, {2171, 30581}, {4565, 4988}, {4990, 6614}, {7341, 8013}
X(32635) = cevapoint of X(i) and X(j) for these (i,j): {1, 3579}, {9, 210}
X(32635) = crosspoint of X(1268) and X(4102)
X(32635) = trilinear pole of line {650, 4501}
X(32635) = barycentric product X(i) X(j) for these lines: {i,j}: {1, 4102}, {8, 1255}, {9, 1268}, {21, 6539}, {55, 32018}, {210, 32014}, {312, 1126}, {318, 1796}, {643, 31010}, {644, 4608}, {650, 6540}, {1171, 3701}, {1320, 31011}, {2185, 6538}, {3596, 28615}, {3700, 4596}, {4041, 4632}, {4086, 4629}, {4391, 8701}
X(32635) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {1, 553}, {8, 4359}, {9, 1125}, {21, 8025}, {33, 1839}, {37, 3649}, {41, 2308}, {44, 5298}, {45, 4870}, {55, 1100}, {60, 30581}, {78, 4001}, {200, 3686}, {210, 1213}, {212, 22054}, {219, 3916}, {220, 3683}, {312, 1269}, {333, 16709}, {346, 3702}, {513, 30724}, {522, 4978}, {607, 2355}, {644, 4427}, {650, 4977}, {663, 4979}, {1126, 57}, {1171, 1014}, {1172, 31900}, {1255, 7}, {1268, 85}, {1334, 1962}, {1796, 77}, {2185, 30593}, {2318, 3958}, {2321, 4647}, {2323, 4973}, {2325, 4975}, {2329, 4697}, {3158, 4856}, {3208, 4970}, {3239, 4985}, {3684, 4974}, {3686, 6533}, {3689, 4969}, {3693, 4966}, {3700, 30591}, {3701, 1230}, {3709, 4983}, {3900, 4976}, {4041, 4988}, {4069, 4115}, {4102, 75}, {4130, 4990}, {4420, 3578}, {4515, 4046}, {4526, 30592}, {4578, 30729}, {4596, 4573}, {4608, 24002}, {4629, 1414}, {4632, 4625}, {4873, 4717}, {4895, 4984}, {6538, 6358}, {6539, 1441}, {6540, 4554}, {7064, 21816}, {8701, 651}, {28615, 56}, {31010, 4077}, {32018, 6063}
X(32635) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {210, 5302, 4420}, {4420, 5302, 21}


X(32636) = MIDPOINT OF X(3336) AND X(5563)

Barycentrics    a*(a + b - c)*(a - b + c)*(2*a + b + c) : :
X(32636) = (r+3 R) X[1] - 3 r X[3], X[1] + 3 X[3336], X[1] - 3 X[5563], 2 X[1] - 3 X[20323], 3 X[404] - X[4420], 2 X[3336] + X[20323]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32636) lies on these lines: {1, 3}, {2, 5302}, {4, 17728}, {7, 5550}, {10, 5434}, {11, 1354}, {12, 3634}, {21, 3742}, {34, 17523}, {44, 583}, {45, 2285}, {58, 14158}, {60, 757}, {63, 25524}, {79, 3582}, {81, 4719}, {88, 961}, {89, 959}, {104, 7686}, {108, 1887}, {140, 13407}, {142, 24953}, {145, 9352}, {210, 474}, {226, 5433}, {229, 4228}, {244, 1104}, {329, 24954}, {355, 4317}, {388, 5435}, {404, 518}, {496, 1770}, {499, 17605}, {501, 1412}, {529, 24982}, {553, 1125}, {584, 604}, {595, 18360}, {603, 1418}, {614, 4252}, {631, 17718}, {749, 1469}, {758, 17614}, {896, 28352}, {908, 6691}, {910, 1475}, {936, 4005}, {946, 11246}, {950, 15326}, {956, 3698}, {958, 3306}, {960, 3218}, {976, 21342}, {978, 4641}, {993, 5439}, {997, 3962}, {1001, 4652}, {1042, 1450}, {1100, 17454}, {1106, 1427}, {1193, 1464}, {1203, 8614}, {1210, 7354}, {1357, 2842}, {1358, 10521}, {1386, 17092}, {1393, 1455}, {1398, 1452}, {1406, 16466}, {1434, 1447}, {1445, 5220}, {1458, 2594}, {1468, 3752}, {1478, 17606}, {1698, 11237}, {1708, 15650}, {1737, 18357}, {1768, 9856}, {1788, 3600}, {1836, 3086}, {1837, 4293}, {2096, 12679}, {2173, 2260}, {2306, 19373}, {2348, 4253}, {2975, 3812}, {3052, 28011}, {3058, 31730}, {3149, 12680}, {3296, 3524}, {3474, 12701}, {3475, 3523}, {3476, 3621}, {3485, 5265}, {3555, 3689}, {3556, 26866}, {3584, 5442}, {3585, 31776}, {3598, 24796}, {3616, 4640}, {3624, 4654}, {3625, 4315}, {3626, 10106}, {3669, 4782}, {3671, 4031}, {3674, 7181}, {3681, 17572}, {3720, 11553}, {3740, 17531}, {3753, 8666}, {3811, 16371}, {3848, 5047}, {3869, 23958}, {3873, 4188}, {3874, 5440}, {3925, 12436}, {3928, 8583}, {3983, 4413}, {4018, 30144}, {4295, 11376}, {4299, 5722}, {4301, 17613}, {4308, 20050}, {4311, 10950}, {4324, 31795}, {4325, 28160}, {4333, 9668}, {4340, 17723}, {4355, 5219}, {4383, 11512}, {4423, 31424}, {4650, 21214}, {4676, 26093}, {4857, 28146}, {4861, 10107}, {4999, 5249}, {5030, 16601}, {5044, 6763}, {5057, 20084}, {5083, 12432}, {5123, 20060}, {5218, 11037}, {5225, 10431}, {5229, 5704}, {5247, 16610}, {5267, 5427}, {5270, 9956}, {5290, 19872}, {5294, 25914}, {5393, 10910}, {5405, 10911}, {5432, 21620}, {5542, 15837}, {5586, 14150}, {5587, 9657}, {5714, 6832}, {5880, 10527}, {5905, 25681}, {6001, 26877}, {6284, 11019}, {6684, 15888}, {6692, 12527}, {6848, 12678}, {6904, 24477}, {6905, 12675}, {6906, 13374}, {6911, 14872}, {7173, 8226}, {7175, 16477}, {7198, 9436}, {7248, 27655}, {7989, 9656}, {8686, 8698}, {9579, 10896}, {9581, 12943}, {9655, 10826}, {9776, 30478}, {9965, 28647}, {10072, 12699}, {10074, 17636}, {10085, 19541}, {10090, 12738}, {10091, 11670}, {10308, 16141}, {10916, 11112}, {11038, 15717}, {11194, 19860}, {11544, 12047}, {12019, 20118}, {12688, 22753}, {12832, 18976}, {13369, 17637}, {13747, 21077}, {14027, 31524}, {15299, 31391}, {16736, 27660}, {17351, 25591}, {17736, 25066}, {17751, 24593}, {17863, 18661}, {18253, 24564}, {19861, 31165}, {20470, 22345}, {22344, 23383}, {22836, 24473}, {24628, 30038}, {31190, 31246}

X(32636) = isogonal conjugate of X(32635)
X(32636) = midpoint of X(3336) and X(5563)
X(32636) = reflection of X(20323) in X(5563)
X(32636) = X(i)-Ceva conjugate of X(j) for these (i,j): {553, 1100}, {1414, 3669}, {26700, 513}
X(32636) = X(2308)-cross conjugate of X(1100)
X(32636) = X(i)-isoconjugate of X(j) for these (i,j): {6, 4102}, {8, 1126}, {9, 1255}, {41, 32018}, {55, 1268}, {60, 6538}, {281, 1796}, {284, 6539}, {312, 28615}, {522, 8701}, {663, 6540}, {1171, 2321}, {1334, 32014}, {2316, 31011}, {3700, 4629}, {3709, 4632}, {3939, 4608}, {4041, 4596}, {5546, 31010}, {5547, 31013}
X(32636) = crosspoint of X(i) and X(j) for these (i,j): {1, 10308}, {57, 1014}
X(32636) = crosssum of X(i) and X(j) for these (i,j): {1, 3579}, {9, 210}
X(32636) = crossdifference of every pair of points on line {650, 4501}
X(32636) = barycentric product X(i) X(j) for these lines: {i,j}: {1, 553}, {7, 1100}, {12, 30581}, {34, 4001}, {56, 4359}, {57, 1125}, {65, 8025}, {77, 1839}, {81, 3649}, {85, 2308}, {88, 5298}, {89, 4870}, {100, 30724}, {109, 4978}, {269, 3686}, {273, 22054}, {278, 3916}, {279, 3683}, {331, 23201}, {348, 2355}, {552, 21816}, {604, 1269}, {651, 4977}, {664, 4979}, {934, 4976}, {1014, 1213}, {1214, 31900}, {1230, 1408}, {1400, 16709}, {1407, 3702}, {1412, 4647}, {1414, 4988}, {1432, 4697}, {1434, 1962}, {1461, 4985}, {1462, 4966}, {2006, 4973}, {2171, 30593}, {3669, 4427}, {4115, 7203}, {4565, 30591}, {4573, 4983}, {4617, 4990}, {4856, 19604}, {4970, 7153}, {4989, 21446}
X(32636) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {1, 4102}, {7, 32018}, {56, 1255}, {57, 1268}, {65, 6539}, {553, 75}, {603, 1796}, {604, 1126}, {651, 6540}, {1014, 32014}, {1100, 8}, {1125, 312}, {1213, 3701}, {1269, 28659}, {1319, 31011}, {1397, 28615}, {1408, 1171}, {1414, 4632}, {1415, 8701}, {1839, 318}, {1962, 2321}, {2171, 6538}, {2308, 9}, {2355, 281}, {3649, 321}, {3669, 4608}, {3683, 346}, {3686, 341}, {3916, 345}, {3958, 3710}, {4001, 3718}, {4017, 31010}, {4359, 3596}, {4427, 646}, {4565, 4596}, {4647, 30713}, {4697, 17787}, {4870, 4671}, {4969, 4723}, {4970, 4110}, {4974, 3975}, {4976, 4397}, {4977, 4391}, {4979, 522}, {4983, 3700}, {4984, 4768}, {4988, 4086}, {4989, 30854}, {5298, 4358}, {8025, 314}, {16709, 28660}, {17454, 4420}, {20970, 210}, {21816, 6057}, {22054, 78}, {22080, 3694}, {23201, 219}, {30581, 261}, {30724, 693}, {31900, 31623}
X(32636) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 36, 13624}, {1, 46, 12702}, {1, 57, 5221}, {1, 5221, 65}, {1, 5903, 11278}, {1, 11278, 5048}, {1, 12702, 3057}, {1, 13624, 2646}, {3, 3338, 354}, {3, 12704, 7957}, {7, 7288, 11375}, {35, 5045, 3748}, {36, 942, 2646}, {36, 3337, 942}, {40, 3304, 5919}, {46, 999, 3057}, {46, 3057, 5183}, {55, 3333, 17609}, {56, 57, 65}, {56, 65, 1319}, {56, 1388, 13462}, {56, 2099, 1420}, {56, 5221, 1}, {56, 11509, 1617}, {57, 1420, 3339}, {57, 3361, 56}, {63, 25524, 25917}, {65, 1319, 11011}, {79, 3582, 9955}, {388, 5435, 24914}, {553, 1125, 3649}, {553, 5298, 4870}, {942, 13624, 1}, {999, 12702, 1}, {1125, 3649, 4870}, {1125, 3916, 3683}, {1125, 4973, 3916}, {1418, 1471, 1456}, {1420, 3339, 2099}, {1434, 1447, 4059}, {1447, 4059, 24805}, {1788, 3600, 5252}, {2099, 3339, 65}, {2975, 27003, 3812}, {3218, 5253, 960}, {3333, 15803, 55}, {3340, 13462, 1388}, {3361, 15932, 13370}, {3474, 14986, 12701}, {3513, 3514, 3748}, {3555, 25440, 3689}, {3649, 5298, 1125}, {3746, 5131, 31663}, {3911, 4298, 12}, {4315, 4848, 10944}, {4860, 5204, 1}, {5045, 5122, 35}, {5049, 31663, 3746}, {5126, 31794, 1}, {5265, 21454, 3485}, {5903, 24928, 5048}, {7280, 18398, 24929}, {11278, 24928, 1}, {12009, 31794, 942}, {13388, 13389, 20182}, {15325, 24470, 12047}


X(32637) = ISOGONAL CONJUGATE OF X(27357)

Barycentrics    (a^4-2 a^2 b^2+b^4-a^2 c^2-b^2 c^2) (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) (a^4-a^2 b^2-2 a^2 c^2-b^2 c^2+c^4) (a^6-3 a^4 b^2+3 a^2 b^4-b^6-3 a^4 c^2-a^2 b^2 c^2+b^4 c^2+3 a^2 c^4+b^2 c^4-c^6)^2 : :
Barycentrics    (17 R^4-12 SB SC-4 R^2 SW-4 SW^2)S^4 + (-132 R^8-125 R^6 SB-125 R^6 SC-67 R^4 SB SC+293 R^6 SW+150 R^4 SB SW+150 R^4 SC SW+44 R^2 SB SC SW-225 R^4 SW^2-60 R^2 SB SW^2-60 R^2 SC SW^2-4 SB SC SW^2+72 R^2 SW^3+8 SB SW^3+8 SC SW^3-8 SW^4)S^2 + 12 S^6-18 R^8 SB SC+27 R^6 SB SC SW-9 R^4 SB SC SW^2 : :

See Antreas Hatzipolakis, Ercole Suppa and Peter Moses, Hyacinthos 29077 and Hyacinthos 29079.

X(32637) lies on these lines: {3,252}, {137,1487}, {1157,6592}, {3519,14072}, {19268,19552}, {27868,31392}

X(32637) = isogonal conjugate of X(27357)
X(32637) = barycentric quotient X(6)/X(27357)
X(32637) = trilinear quotient X(1)/X(27357)
X(32637) = {X(252),X(930)}-harmonic conjugate of X(24144)

X(32638) = X(5)X(49)∩X(1263)X(15038)

Barycentrics    (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) (2 a^16-11 a^14 b^2+25 a^12 b^4-31 a^10 b^6+25 a^8 b^8-17 a^6 b^10+11 a^4 b^12-5 a^2 b^14+b^16-11 a^14 c^2+34 a^12 b^2 c^2-31 a^10 b^4 c^2-4 a^8 b^6 c^2+31 a^6 b^8 c^2-38 a^4 b^10 c^2+27 a^2 b^12 c^2-8 b^14 c^2+25 a^12 c^4-31 a^10 b^2 c^4-5 a^6 b^6 c^4+34 a^4 b^8 c^4-51 a^2 b^10 c^4+28 b^12 c^4-31 a^10 c^6-4 a^8 b^2 c^6-5 a^6 b^4 c^6-14 a^4 b^6 c^6+29 a^2 b^8 c^6-56 b^10 c^6+25 a^8 c^8+31 a^6 b^2 c^8+34 a^4 b^4 c^8+29 a^2 b^6 c^8+70 b^8 c^8-17 a^6 c^10-38 a^4 b^2 c^10-51 a^2 b^4 c^10-56 b^6 c^10+11 a^4 c^12+27 a^2 b^2 c^12+28 b^4 c^12-5 a^2 c^14-8 b^2 c^14+c^16) : :
Barycentrics    (4 R^2+8 SB+8 SC)S^4 + (-93 R^6+14 R^4 SB+14 R^4 SC+52 R^2 SB SC+76 R^4 SW-8 R^2 SB SW-8 R^2 SC SW-16 SB SC SW-16 R^2 SW^2) S^2 -9 R^6 SB SC : :

See Antreas Hatzipolakis, Ercole Suppa and Peter Moses, Hyacinthos 29077 and Hyacinthos 29079.

X(32638) lies on these lines: {5,49}, {1263,15038}, {6343,13621}, {6592,11584}, {10096,14071}, {14627,31674}, {14857,24306}

X(32638) = barycentric quotient X(24385)/X(13582)
X(32638) = trilinear product of X(i) and X(j) for these lines: {i,j}: {1749,24385}, {1749,24385}

X(32639) = X(30)X(1141)∩X(140)X(10277)

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

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29079.

X(32639) lies on these lines: {30, 1141}, {140, 10277}

X(32639) = barycentric product X(8254)*X(13582)

leftri

Centers associated with barycentric products of circumcircle-P-antipodes: X(32640)-X(32741)

rightri

Let P = p : q : r (barycentrics). The locus of the barycentric product of circumcircle-P-antipodes is the circumconic with perspector X(6)*P = a2p : b2q : c2r.

Let L be a line. The barycentric product of the (real or nonreal) circumcircle intercepts of L is the trilinear pole of the isogonal conjugate of the isotomic conjugate of L (or equivalently, X(6)*L). These intercepts are also circumcircle-P-antipodes for all P on L.

Contributed by Randy Hutson, June 14, 2019.


X(32640) = BARYCENTRIC PRODUCT X(74)*X(110)

Barycentrics    a^4/((b^2 - c^2) (2 a^4 - a^2 (b^2 + c^2) - (b^2 - c^2)^2)) : :
Trilinears    (sin^2 A) (cos A)/((tan B - tan C) (2 tan A - tan B - tan C)) : :

As the barycentric product of circumcircle antipodes, X(32640) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32640) lies on these lines: {32, 14385}, {74, 187}, {110, 32681}, {112, 647}, {115, 14989}, {186, 3003}, {237, 14908}, {249, 4558}, {1384, 9717}, {1576, 32715}, {23357, 32320} et al

X(32640) = isogonal conjugate of polar conjugate of X(1304)
X(32640) = isotomic conjugate of polar conjugate of X(32715)
X(32640) = trilinear pole of line X(184)X(1576)
X(32640) = center of bianticevian conic of X(15) and X(16)
X(32640) = barycentric product X(i)*X(j) for these lines: {i,j}: {69, 32715}, {74, 110}, {112, 14919}, {163, 2349}, {249, 2433}, {476, 14385}, {691, 9717}, {4558, 8749}, {15066, 32681}
X(32640) = barycentric quotient X(i)/X(j) for these (i,j): (32, 1637), (74, 850), (110, 3260), (163, 14206), (2159, 32671), (2349, 20948), (2433, 338), (8749, 14618), (14385, 3268), (14919, 3267), (32715, 4)


X(32641) = BARYCENTRIC PRODUCT X(100)*X(104)

Barycentrics    a^2/((b - c) (b^3 + c^3 - (a^2 + b c) (b + c) + 2 a b c)) : :
Barycentrics    a^2/((b - c) (cos B + cos C - 1)) : :

As the barycentric product of circumcircle antipodes, X(32641) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32641) lies on these lines: {36, 909}, {44, 14578}, {100, 32685}, {101, 652}, {104, 294}, {112, 1309}, {248, 5291}, {644, 906}, {645, 4558}, {650, 1415}, {651, 905}, {654, 32675}, {666, 2401}, {692, 32723}, {1110, 3939}, {1576, 14776}, {1795, 2338}, {1983, 23703}, {2250, 2341}, {2323, 15629}, {2342, 4845}, {5546, 32661}, {8609, 15500}, {15627, 18877}, {23987, 32647} et al

X(32641) = isogonal conjugate of X(10015)
X(32641) = trilinear pole of line X(55)X(184)
X(32641) = crossdifference of every pair of points on line X(3259)X(3326)
X(32641) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 1309}, {6, 13136}, {69, 14776}, {100, 104}, {108, 1809}, {190, 909}, {662, 2250}, {664, 2342}, {692, 18816}, {906, 16082}, {1252, 2401}, {1795, 1897}, {6335, 14578}
X(32641) = barycentric quotient X(i)/X(j) for these (i,j): (6, 10015), (100, 3262), (101, 908), (104, 693), (109, 22464), (692, 517), (909, 514), (1252, 2397), (1309, 264), (1415, 1465), (1576, 859), (1795, 4025), (1983, 16586), (2250, 1577), (2342, 522), (2401, 23989), (3939, 6735), (13136, 76), (14578, 905), (14776, 4)


X(32642) = BARYCENTRIC PRODUCT X(101)*X(103)

Barycentrics    a^4/((b - c) (2 a^3 - a^2 (b + c) - (b - c)^2 (b + c))) : :
Barycentrics    a^4/((b - c) ((a - b) cot C + (a - c) cot B)) : :

As the barycentric product of circumcircle antipodes, X(32642) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32642) lies on these lines: {101, 32684}, {103, 32682}, {112, 21789}, {248, 17735}, {677, 4558}, {692, 24027}, {906, 1110}, {911, 2223}, {1415, 1946}, {6586, 8750}, {8608, 32699}, {23990, 32656}, {32659, 32719}, {32721, 32739} et al

X(32642) = isogonal conjugate of isotomic conjugate of X(677)
X(32642) = trilinear pole of line X(184)X(14827)
X(32642) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 677}, {100, 911}, {101, 103}, {109, 2338}, {18025, 32739}
X(32642) = barycentric quotient X(i)/X(j) for these (i,j): (32, 676), (103, 3261), (677, 76), (911, 693), (24027, 24015), (32656, 26006), (32739, 516)


X(32643) = BARYCENTRIC PRODUCT X(102)*X(109)

Barycentrics    a^4/((2 a^5 + a^4 (b + c) - 2 a^3 (b^2 + c^2) - (b + c) (b^2 - c^2)^2) (b - c) (b + c - a)) : :
Barycentrics    (sin^3 A)/((sin B (sec A - sec B) + sin C (sec A - sec C)) (cos B - cos C)) : :

As the barycentric product of circumcircle antipodes, X(32643) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32643) lies on these lines: {102, 32689}, {109, 32683}, {248, 17966}, {906, 2149}, {1415, 32667}, {1946, 32652}, {2425, 2432}, {5053, 15629}, {6589, 32653}, {7113, 14578}, {8607, 32707}, {23979, 32660}

X(32643) = isogonal conjugate of polar conjugate of X(36067)
X(32643) = barycentric product X(i)*X(j) for these lines: {i,j}: {63, 32667}, {102, 109}, {1262, 2432}, {1461, 15629}, {2399, 23979}
X(32643) = barycentric quotient X(i)/X(j) for these (i,j): (2432, 23978), (23979, 2406), (32667, 92)


X(32644) = BARYCENTRIC PRODUCT X(105)*X(1292)

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

As the barycentric product of circumcircle antipodes, X(32644) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32644) lies on these lines: {666, 2414}, {906, 919}, {2428, 2440}, {3290, 8751}, {32656, 32666}

X(32644) = barycentric product X(i)*X(j) for these lines: {i,j}: {105, 1292}, {277, 919}, {2428, 6185}
X(32644) = barycentric quotient X(i)/X(j) for these (i,j): (919, 344), (1292, 3263), (2428, 4437)


X(32645) = BARYCENTRIC PRODUCT X(106)*X(1293)

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

As the barycentric product of circumcircle antipodes, X(32645) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32645) lies on these lines: {1293, 32686}, {2429, 2441}, {4558, 4591}, {8610, 8752}, {32656, 32719}

X(32645) = barycentric product X(i)*X(j) for these lines: {i,j}: {106, 1293}, {2226, 2429}, {4373, 32719}
X(32645) = barycentric quotient X(i)/X(j) for these (i,j): (1293, 3264), (32719, 145)


X(32646) = BARYCENTRIC PRODUCT X(107)*X(1294)

Barycentrics    1/((b^2 - c^2) (a^2 - b^2 - c^2)^2 (a^6 (b^2 + c^2) - a^4 (3 b^4 - 4 b^2 c^2 + 3 c^4) + 3 a^2 (b^2 - c^2)^2 (b^2 + c^2) - (b^2 - c^2)^2 (b^4 + 4 b^2 c^2 + c^4))) : :

As the barycentric product of circumcircle antipodes, X(32646) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32646) lies on these lines: {112, 23590}, {1990, 15311}, {2404, 16077}, {2430, 2442}, {4558, 23582}, {6529, 6587}, {23964, 32661}

X(32646) = trilinear pole of line X(184)X(6525)
X(32646) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 1294}, {2416, 23590}
X(32646) = barycentric quotient X(i)/X(j) for these (i,j): (1294, 3265), (2416, 23974), (23590, 2404)


X(32647) = BARYCENTRIC PRODUCT X(108)*X(1295)

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

As the barycentric product of circumcircle antipodes, X(32647) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32647) lies on these lines: {906, 7115}, {1295, 32688}, {1415, 23985}, {1455, 14571}, {1457, 32667}, {2431, 2443}, {23987, 32641}

X(32647) = trilinear pole of line X(184)X(3195)
X(32647) = barycentric product X(i)*X(j) for these lines: {i,j}: {108, 1295}, {2417, 23985}, {2431, 23984}
X(32647) = barycentric quotient X(23985)/X(2405)


X(32648) = BARYCENTRIC PRODUCT X(111)*X(1296)

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

As the barycentric product of circumcircle antipodes, X(32648) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32648) lies on these lines: {691, 1296}, {892, 2418}, {2434, 2444}, {3291, 8753}, {10422, 15899}, {32661, 32729}

X(32648) = barycentric product X(i)*X(j) for these lines: {i,j}: {111, 1296}, {691, 21448}, {2434, 10630}, {5485, 32729}
X(32648) = barycentric quotient X(i)/X(j) for these (i,j): (691, 11059), (1296, 3266), (32729, 1992)


X(32649) = BARYCENTRIC PRODUCT X(112)*X(1297)

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

As the barycentric product of circumcircle antipodes, X(32649) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32649) lies on these lines: {112, 32687}, {186, 1297}, {232, 248}, {250, 4558}, {2409, 2966}, {2435, 2445}, {2485, 32713}, {18374, 18877}

X(32649) = trilinear pole of line X(184)X(17409)
X(32649) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 32687}, {112, 1297}, {2435, 23964}
X(32649) = barycentric quotient X(i)/X(j) for these (i,j): (112, 30737), (1297, 3267), (32687, 264)


X(32650) = BARYCENTRIC PRODUCT X(476)*X(477)

Barycentrics    1/((b^2 - c^2) ((a^2 - b^2 - c^2)^2 - b^2 c^2) (a^6 (b^2 + c^2) - a^4 (3 b^4 - 2 b^2 c^2 + 3 c^4) + a^2 (3 b^6 - 2 b^4 c^2 - 2 b^2 c^4 + 3 c^6) - (b^2 - c^2)^2 (b^4 + 3 b^2 c^2 + c^4))) : :
Barycentrics    (sin^2 A)/((1 + 2 cos 2A) sin(B - C) (4 cos A + cos(A - 2B) + cos(A - 2C) - 3 cos(B - C))) : :

As the barycentric product of circumcircle antipodes, X(32650) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32650) lies on these lines: {476, 32690}, {1637, 32640}, {1989, 18320}, {2436, 2437}, {3018, 32711}, {4558, 30528}, {14401, 32661}, {14560, 32733}, {23588, 32662}

X(32650) = trilinear pole of line X(184)X(14560)
X(32650) = barycentric product X(i)*X(j) for these lines: {i,j}: {476, 477}, {1989, 30528}
X(32650) = barycentric quotient X(i)/X(j) for these (i,j): (477, 3268), (30528, 7799)


X(32651) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(7)

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

As the barycentric product of circumcircle antipodes, X(32651) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32651) lies on these lines: {109, 15439}, {651, 906}, {943, 9372}, {1415, 32714}, {1461, 32660}, {1462, 32658}, {2259, 32657}, {2982, 14578}, {4558, 4573}, {4565, 32661} et al

X(32651) = trilinear pole of line X(56)X(184)
X(32651) = barycentric product X(i)*X(j) for these lines: {i,j}: {7, 15439}, {651, 2982}, {934, 943}
X(32651) = barycentric quotient X(i)/X(j) for these (i,j): (109, 6734), (943, 4397), (1576, 8021), (2982, 4391), (15439, 8)


X(32652) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(9)

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

As the barycentric product of circumcircle antipodes, X(32652) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32652) lies on these lines: {31, 2188}, {32, 7367}, {109, 8059}, {248, 1903}, {643, 4558}, {692, 32660}, {906, 3939}, {1415, 8750}, {1436, 2195}, {1946, 32643}, {2192, 2342}, {2208, 2352}, {6129, 32714}, {7151, 32655}, {21059, 32657} et al

X(32652) = isogonal conjugate of X(17896)
X(32652) = trilinear pole of line X(41)X(184)
X(32652) = crossdifference of every pair of points on line X(5514)X(16596)
X(32652) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 13138}, {9, 8059}, {84, 101}, {100, 1436}, {108, 268}, {109, 282}, {110, 1903}, {189, 692}, {190, 2208}, {280, 1415}, {644, 1413}, {651, 2192}, {653, 2188}, {934, 7367}, {1422, 3939}, {1332, 7151}, {7020, 32660}
X(32652) = barycentric quotient X(i)/X(j) for these (i,j): (6, 17896), (31, 14837), (32, 6129), (84, 3261), (101, 322), (692, 329), (1413, 24002), (1415, 347), (1436, 693), (1903, 850), (2188, 6332), (2192, 4391), (2208, 514), (7151, 17924), (7367, 4397), (8059, 85), (13138, 76), (32660, 7013)


X(32653) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(10)

Barycentrics    a^2/(b^2 (a - b) (a + b - c) - c^2 (a - c) (a - b + c)) : :
Barycentrics    a^2/((b - c) (b^3 + c^3 - a^2 b - a^2 c + a b c)) : :
Barycentrics    a^4/((cos C - cos A) (csc^2 B) + (cos A - cos B) (csc^2 C)) : :

As the barycentric product of circumcircle antipodes, X(32653) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32653) lies on these lines: {32, 1146}, {101, 32661}, {112, 26704}, {190, 4558}, {248, 15232}, {577, 23986}, {906, 1018}, {1576, 8750}, {2178, 32659}, {2217, 16968}, {2250, 14578}, {2425, 4559}, {4557, 32656}, {5301, 32655}, {6589, 32643} et al

X(32653) = trilinear pole of line X(42)X(184)
X(32653) = crossdifference of every pair of points on line X(124)X(2968)
X(32653) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 26704}, {100, 2217}, {101, 13478}, {109, 10570}, {110, 15232}, {692, 2995}, {4559, 19607}, {8687, 19608}
X(32653) = barycentric quotient X(i)/X(j) for these (i,j): (32, 6589), (101, 4417), (692, 3869), (2217, 693), (13478, 3261), (15232, 850), (26704, 264)


X(32654) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(512)

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

As the barycentric product of circumcircle antipodes, X(32654) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184), and as the barycentric product of circumcircle-X(512)-antipodes, X(32654) also lies on conic {{A,B,C,X(6),X(32),X(83),X(213),X(729)}} with perspector X(669).

Let A'B'C' be the circumcevian triangle of X(511). Let A" be the barycentric product B'*C', and define B" and C" cyclically. A", B", C" are collinear on line X(2491)X(3289). The lines AA", BB", CC" concur in X(32654). (Randy Hutson, August 19, 2019)

X(32654) lies on these lines: {6, 2987}, {24, 112}, {32, 1147}, {50, 32740}, {83, 3815}, {187, 5961}, {213, 906}, {230, 297}, {237, 14601}, {248, 2422}, {571, 1576}, {577, 1084}, {729, 10425}, {1691, 2065}, {1918, 32656} et al

X(32654) = isogonal conjugate of isotomic conjugate of X(2987)
X(32654) = isogonal conjugate of anticomplement of X(36212)
X(32654) = trilinear pole of line X(184)X(669)
X(32654) = crossdifference of every pair of points on line X(114)X(2974)
X(32654) = X(92)-isoconjugate of X(3564)
X(32654) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 3563}, {6, 2987}, {31, 8773}, {32, 8781}
X(32654) = barycentric quotient X(i)/X(j) for these (i,j): (31, 1733), (32, 230), (184, 3564), (237, 114), (1576, 4226), (2987, 76), (3563, 264), (8773, 561), (8781, 1502)


X(32655) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(513)

Barycentrics    a^3/(a^3 (b + c) - a^2 (b^2 + c^2) - a (b - c)^2 (b + c) + (b^2 - c^2)^2) : :
Barycentrics    (sin^3 A)/(sin B (cos A + cos B - 1) + sin C (cos A + cos C - 1)) : :

As the barycentric product of circumcircle antipodes, X(32655) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

Let A'B'C' be the circumcevian triangle of X(517). Let A" be the barycentric product B'*C', and define B" and C" cyclically. A", B", C" are collinear with X(3310). The lines AA", BB", CC" concur in X(32655). (Randy Hutson, August 19, 2019)

X(32655) lies on these lines: {6, 906}, {31, 32656}, {32, 23980}, {81, 2990}, {112, 915}, {248, 3657}, {563, 604}, {571, 608}, {577, 1015}, {654, 2423}, {739, 6099}, {1333, 32661}, {1576, 2203}, {5301, 32653}, {7151, 32652}, {8609, 15500} et al

X(32655) = isogonal conjugate of polar conjugate of X(915)
X(32655) = isogonal conjugate of isotomic conjugate of X(2990)
X(32655) = trilinear pole of line X(184)X(667)
X(32655) = X(92)-isoconjugate of X(912)
X(32655) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 915}, {6, 2990}, {110, 3657}, {905, 32698}
X(32655) = barycentric quotient X(i)/X(j) for these (i,j): (31, 1737), (32, 8609), (184, 912), (915, 264), (2990, 76), (3657, 850), (32698, 6335)


X(32656) = BARYCENTRIC PRODUCT X(3)*X(101)

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

X(32656) is the barycentric product of the circumcircle intercepts of line X(3)X(71). As the barycentric product of circumcircle antipodes, X(32656) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32656) lies on these lines: {31, 32655}, {42, 14910}, {48, 23203}, {71, 248}, {100, 15440}, {101, 112}, {109, 15439}, {110, 28624}, {184, 32659}, {190, 2966}, {212, 2638}, {560, 21059}, {577, 20776}, {692, 1415}, {1110, 3939}, {1331, 4558}, {1459, 1813}, {1576, 32739}, {1897, 16813}, {1918, 32654}, {4557, 32653}, {7649, 32699}, {23990, 32642}, {32644, 32666}, {32645, 32719} et al

X(32656) = isogonal conjugate of polar conjugate of X(101)
X(32656) = isotomic conjugate of polar conjugate of X(32739)
X(32656) = X(92)-isoconjugate of X(514)
X(32656) = trilinear pole of line X(184)X(2200)
X(32656) = crossdifference of every pair of points on X(116)X(2973)
X(32656) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 906}, {3, 101}, {6, 1331}, {8, 32660}, {10, 32661}, {31, 1332}, {32, 4561}, {41, 6516}, {42, 4558}, {48, 100}, {55, 1813}, {56, 4587}, {58, 4574}, {63, 692}, {69, 32739}, {71, 110}, {72, 163}, {108, 2289}, {109, 219}, {112, 3682}, {162, 3990}, {184, 190}, {212, 651}, {577, 1897}, {905, 1110}, {1252, 1459}, {1790, 4557}, {1918, 4563}, {3977, 32719}, {17780, 32659}, {25083, 32666}, {26006, 32642}
X(32656) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3261), (31, 17924), (32, 7649), (42, 14618), (48, 693), (71, 850), (72, 20948), (100, 1969), (101, 264), (109, 331), (163, 286), (184, 514), (190, 18022), (212, 4391), (560, 6591), (577, 4025), (649, 2973), (692, 92), (906, 75), (1110, 6335), (1331, 76), (1332, 561), (1459, 23989), (1813, 6063), (1897, 18027), (1918, 2501), (3682, 3267), (3990, 14208), (4558, 310), (4561, 1502), (4574, 313), (4587, 3596), (6516, 20567), (32659, 6548), (32660, 7), (32661, 86), (32719, 6336), (32739, 4)


X(32657) = BARYCENTRIC PRODUCT X(3)*X(103)

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

X(32657) is the barycentric product of the circumcircle intercepts of line X(3)X(4091). As the barycentric product of circumcircle antipodes, X(32657) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32657) lies on these lines: {41, 603}, {58, 103}, {255, 906}, {577, 20776}, {1795, 2338}, {1815, 2327}, {1886, 32701}, {2259, 32651}, {7335, 32660}, {21059, 32652} et al

X(32657) = isogonal conjugate of polar conjugate of X(103)
X(32657) = X(92)-isoconjugate of X(516)
X(32657) = crossdifference of every pair of points on line X(118)X(20622)
X(32657) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 103}, {6, 1815}, {63, 911}, {184, 18025}, {222, 2338}, {677, 1459}, {916, 15380}
X(32657) = barycentric quotient X(i)/X(j) for these (i,j): (32, 1886), (103, 264), (184, 516), (577, 26006), (911, 92), (1815, 76), (2338, 7017), (18025, 18022)


X(32658) = BARYCENTRIC PRODUCT X(3)*X(105)

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

X(32658) is the barycentric product of the circumcircle intercepts of line X(3)X(905). As the barycentric product of circumcircle antipodes, X(32658) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32658) lies on these lines: {3, 906}, {6, 3433}, {28, 105}, {32, 56}, {48, 23203}, {104, 294}, {248, 10099}, {448, 2481}, {603, 9247}, {665, 2440}, {911, 2223}, {1333, 1576}, {1384, 3420}, {1436, 2195}, {1437, 32661}, {1444, 1814}, {1462, 32651}, {2217, 16968}, {3053, 3435}, {5089, 32703} et al

X(32658) = isogonal conjugate of polar conjugate of X(105)
X(32658) = X(92)-isoconjugate of X(518)
X(32658) = crossdifference of every pair of points on line X(120)X(20621)
X(32658) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 105}, {6, 1814}, {31, 31637}, {48, 673}, {63, 1438}, {77, 2195}, {78, 1416}, {109, 23696}, {110, 10099}, {184, 2481}, {219, 1462}, {222, 294}, {603, 14942}, {905, 919}, {1437, 13576}, {6185, 20752}, {9247, 18031}
X(32658) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3263), (31, 1861), (32, 5089), (48, 3912), (105, 264), (184, 518), (222, 27818), (294, 7017), (577, 25083), (603, 9436), (604, 5236), (673, 1969), (919, 6335), (1333, 15149), (1416, 273), (1437, 30941), (1438, 92), (1462, 331), (1576, 4238), (1814, 76), (2195, 318), (2481, 18022), (9247, 672), (10099, 850), (20752, 4437), (31637, 561)


X(32659) = BARYCENTRIC PRODUCT X(3)*X(106)

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

X(32659) is the barycentric product of the circumcircle intercepts of line X(3)X(1459). As the barycentric product of circumcircle antipodes, X(32659) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32659) lies on these lines: {36, 909}, {48, 906}, {106, 112}, {184, 32656}, {604, 1415}, {903, 2966}, {1576, 2206}, {1790, 1797}, {2178, 32653}, {2208, 2352}, {2359, 22054}, {8756, 32705}, {32642, 32719} et al

X(32659) = isogonal conjugate of polar conjugate of X(106)
X(32659) = X(92)-isoconjugate of X(519)
X(32659) = crossdifference of every pair of points on line X(121)X(4768)
X(32659) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 106}, {6, 1797}, {48, 88}, {63, 9456}, {78, 1417}, {184, 903}, {222, 2316}, {577, 6336}, {603, 1320}, {901, 1459}, {905, 32665}, {906, 1022}, {4025, 32719}, {4049, 32661}, {6548, 32656}, {9247, 20568}
X(32659) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3264), (32, 8756), (48, 4358), (88, 1969), (106, 264), (184, 519), (577, 3977), (903, 18022), (906, 24004), (1417, 273), (1797, 76), (2316, 7017), (6336, 18027), (9247, 44), (9456, 92), (32656, 17780), (32665, 6335), (32719, 1897)


X(32660) = BARYCENTRIC PRODUCT X(3)*X(109)

Barycentrics    a^4 (a^2 - b^2 - c^2)/((b - c) (a - b - c)) : :
Trilinears    a^2 (cos A)/(cos B - cos C) : :

X(32660) is the barycentric product of the circumcircle intercepts of line X(3)X(73). As the barycentric product of circumcircle antipodes, X(32660) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

The trilinear polar of X(32660) passes through X(184).

X(32660) lies on these lines: {48, 14578}, {73, 248}, {101, 652}, {109, 112}, {563, 604}, {603, 9247}, {653, 16813}, {664, 2966}, {692, 32652}, {1400, 14910}, {1404, 2252}, {1415, 32739}, {1461, 32651}, {1813, 4558}, {2425, 4559}, {3064, 32707}, {7335, 32657}, {23979, 32643} et al

X(32660) = isogonal conjugate of polar conjugate of X(109)
X(32660) = X(92)-isoconjugate of X(522)
X(32660) = crossdifference of every pair of points on line X(124)X(20620)
X(32660) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 109}, {6, 1813}, {7, 32656}, {31, 6516}, {48, 651}, {63, 1415}, {65, 4575}, {71, 4565}, {73, 110}, {77, 692}, {100, 603}, {101, 222}, {108, 255}, {162, 22341}, {163, 1214}, {184, 664}, {212, 4397}, {219, 1461}, {226, 32661}, {228, 1414}, {307, 1576}, {348, 32739}, {577, 653}, {604, 1332}, {652, 1262}, {1400, 4558}, {1790, 4559}, {1897, 7335}, {4554, 9247}, {6332, 23979}, {7013, 32652}, {14578, 24029}
X(32660) = barycentric quotient X(i)/X(j) for these (i,j): (32, 3064), (48, 4391), (73, 850), (101, 7017), (109, 264), (163, 31623), (184, 522), (212, 934), (222, 3261), (228, 4086), (577, 6332), (603, 693), (604, 17924), (651, 1969), (652, 23978), (653, 18027), (664, 18022), (692, 318), (1214, 20948), (1332, 28659), (1400, 14618), (1415, 92), (1459, 59), (1461, 331), (1576, 29), (1813, 76), (4558, 28660), (4575, 314), (6516, 561), (7335, 4025), (9247, 650), (22341, 14208), (23979, 653), (32656, 8), (32661, 333), (32739, 281), (32652, 7020)


X(32661) = BARYCENTRIC PRODUCT X(3)*X(110)

Barycentrics    a^4 (a^2 - b^2 - c^2)/(b^2 - c^2) : :
Trilinears    sin 2A csc(B - C) : :

X(32661) is the barycentric product of the circumcircle intercepts of line X(3)X(49). As the barycentric product of circumcircle antipodes, X(32661) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32661) lies on these lines: {3, 248}, {5, 1970}, {6, 1511}, {30, 1971}, {32, 1147}, {39, 12038}, {49, 217}, {50, 15136}, {99, 249}, {101, 32653}, {110, 112}, {115, 17702}, {155, 3053}, {163, 1415}, {184, 14908}, {187, 13754}, {206, 2882}, {216, 5961}, {394, 18876}, {520, 9145}, {577, 18877}, {647, 32662}, {648, 16813}, {686, 23181}, {827, 26714}, {906, 4575}, {912, 5006}, {916, 1326}, {925, 32692}, {933, 6570}, {1092, 10316}, {1333, 32655}, {1384, 1501}, {1437, 32658}, {1562, 16163}, {1576, 14270}, {1691, 3564}, {1915, 18907}, {1968, 10539}, {2030, 8681}, {2071, 13509}, {2193, 14578}, {2421, 4611}, {2501, 32708}, {3060, 10986}, {3124, 12310}, {3202, 15257}, {3284, 32663}, {3289, 10317}, {3331, 10540}, {3767, 12118}, {4558, 8552}, {4565, 32651}, {5023, 12163}, {5206, 7689}, {5448, 7747}, {5449, 7749}, {5546, 32641}, {14401, 32650}, {23357, 32640}, {23964, 32646}, {32648, 32729} et al

X(32661) = isogonal conjugate of X(14618)
X(32661) = isotomic conjugate of polar conjugate of X(1576)
X(32661) = crosssum of X(i) and X(j) for these {i,j}: {6, 13558}, {523, 2501}, {647, 924}
X(32661) = crosspoint of X(i) and X(j) for these {i,j}: {110, 4558}, {648, 925}
X(32661) = X(i)-isoconjugate of X(j) for these lines: {i,j}: {1, 14618}, {4, 1577}, {92, 523}, {107, 20902}
X(32661) = trilinear pole of line X(184)X(418) (the tangent at X(577) to the inellipse that is the barycentric square of the Brocard axis)
X(32661) = crossdifference of every pair of points on line X(125)X(136)
X(32661) = crosspoint of X(371)-isoconjugate-of-X(1577) and X(372)-isoconjugate-of-X(1577)
X(32661) = crosssum of polar circle intercepts of Brocard axis
X(32661) = trilinear product of vertices of circumanticevian triangle of X(3)
X(32661) = barycentric product of MacBeath circumconic intercepts of Brocard axis
X(32661) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 4575}, {3, 110}, {5, 15958}, {6, 4558}, {31, 4592}, {32, 4563}, {48, 662}, {49, 930}, {54, 23181}, {58, 1331}, {63, 163}, {69, 1576}, {81, 906}, {86, 32656}, {99, 184}, {100, 1437}, {101, 1790}, {107, 1092}, {109, 283}, {112, 394}, {155, 13398}, {162, 255}, {216, 18315}, {219, 4565}, {222, 5546}, {248, 2421}, {249, 647}, {250, 520}, {284, 1813}, {287, 14966}, {323, 32662}, {476, 22115}, {577, 648}, {651, 2193}, {686, 18879}, {691, 3292}, {692, 1444}, {827, 3917}, {907, 3796}, {925, 1147}, {933, 5562}, {1332, 1333}, {1415, 1812}, {1511, 2425}, {2396, 14600}, {2407, 18877}, {2966, 3289}, {3167, 3565}, {3267, 23963}, {4230, 17974), {5468, 14908}, {6390, 32729}, {10317, 17708}, {10420, 13754}, {11064, 32640}, {15136, 16167}
X(32661) = barycentric quotient X(i)/X(j) for these (i,j): (3, 850), (6, 14618), (31, 24006), (32, 2501), (48, 1577), (63, 20948), (99, 18022), (110, 264), (112, 2052), (163, 92), (184, 523), (216, 18314), (217, 12077), (249, 6331), (250, 6528), (255, 14208), (394, 3267), (476, 18817), (520, 339), (577, 525), (647, 338), (648, 18027), (662, 1969), (906, 321), (930, 20572), (933, 8795), (1092, 3265), (1147, 6563), (1331, 313), (1332, 27801), (1333, 17924), (1437, 693), (1501, 2489), (1576, 4), (1790, 3261), (1813, 349), (2193, 4391), (3289, 2799), (3917, 23285), (4558, 76), (4563, 1502), (4565, 331), (4575, 75), (4592, 561), (5546, 7017), (10317, 9979), (14600, 2395), (14908, 5466), (14966, 297), (15958, 95), (18315, 276), (18877, 2394), (20975, 23105), (22115, 3268), (23181, 311), (23963, 112), (23964, 15352), (32640, 16080), (32656, 10), (32662, 94), (32729, 17983)


X(32662) = BARYCENTRIC PRODUCT X(3)*X(476)

Barycentrics    a^2 (a^2 - b^2 - c^2)/((b^2 - c^2) ((a^2 - b^2 - c^2)^2 - b^2 c^2)) : :
Trilinears    (sin 2A)/((1 + 2 cos 2A) sin(B - C)) : :

X(32662) is the barycentric product of the circumcircle intercepts of line X(3)X(125). As the barycentric product of circumcircle antipodes, X(32662) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32662) lies on these lines: {30, 50}, {32, 23967}, {94, 401}, {112, 476}, {187, 5961}, {248, 265}, {297, 18883}, {328, 15013}, {441, 18876}, {512, 1576}, {525, 4558}, {577, 32663}, {647, 32661}, {691, 23969}, {1415, 32678}, {1625, 2623}, {2420, 2433}, {2966, 14592}, {3284, 13754}, {14590, 16077}, {14591, 30510}, {14966, 23968}, {16813, 23582}, {23588, 32650}, {32708, 32711} et al

X(32662) = isogonal conjugate of polar conjugate of X(476)
X(32662) = isotomic conjugate of polar conjugate of X(14560)
X(32662) = X(92)-isoconjugate of X(526)
X(32662) = trilinear pole of line X(184)X(5158)
X(32662) = crossdifference of every pair of points on line X(3258)X(16186)
X(32662) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 476}, {63, 32678}, {69, 14560}, {94, 32661}, {110, 265}, {249, 14582}, {328, 1576}, {925, 5961}, {1141, 23181}, {1989, 4558}, {2166, 4575}, {2410, 32663}, {8552, 23588}, {14592, 23357}
X(32662) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3268), (48, 32679), (110, 340), (112, 14165), (184, 526), (265, 850), (476, 264), (577, 8552), (1576, 186), (1625, 14918), (1989, 14618), (2420, 14920), (3049, 2088), (3284, 5664), (4558, 7799), (5961, 6563), (8552, 23965), (14560, 4), (14582, 338), (14592, 23962), (14908, 9213), (23181, 1273), (23357, 14590), (32661, 323), (32663, 2411), (32678, 92)


X(32663) = BARYCENTRIC PRODUCT X(3)*X(477)

Barycentrics    a^2 (a^2 - b^2 - c^2)/(a^6 (b^2 + c^2) - a^4 (3 b^4 - 2 b^2 c^2 + 3 c^4) + a^2 (3 b^6 - 2 b^4 c^2 - 2 b^2 c^4 + 3 c^6) - (b^2 - c^2)^2 (b^4 + 3 b^2 c^2 + c^4)) : :
Trilinears    (sin 2A)/(4 cos A + cos(A - 2B) + cos(A - 2C) - 3 cos(B - C)) : :

X(32663) is the barycentric product of the circumcircle intercepts of line X(3)X(9033). As the barycentric product of circumcircle antipodes, X(32663) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32663) lies on these lines: {6, 32640}, {50, 112}, {248, 14220}, {577, 32662}, {647, 18877}, {841, 32690}, {1495, 1576}, {2966, 30528}, {3284, 32661}, {4558, 11064}, {6587, 14910}, {14586, 18365}

X(32663) = isogonal conjugate of polar conjugate of X(477)
X(32663) = X(92)-isoconjugate of X(5663)
X(32663) = trilinear pole of line X(184)X(9409)
X(32663) = crossdifference of every pair of points on line X(11251)X(18809)
X(32663) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 477}, {110, 14220}, {647, 30528}, {2411, 32662}
X(32663) = barycentric quotient X(i)/X(j) for these (i,j): (477, 264), (14220, 850), (30528, 6331), (32662, 2410)


X(32664) = CENTER OF LOCUS OF BARYCENTRIC PRODUCT OF CIRCUMCIRCLE-X(1)-ANTIPODES

Barycentrics    a^3 (a^3 - b^3 - c^3) : :

The locus of the barycentric product of circumcircle-X(1)-antipodes is a circumconic that is also the locus of the trilinear product of circumcircle-X(6)-antipodes, and the locus of trilinear poles of lines passing through X(31). The conic is the isogonal conjugate of line X(514)X(661), and passes through X(101), X(163), X(662), X(693), X(909), X(913), X(923), X(1415), X(1438), X(1461), X(1910), X(2159), X(2576), X(2577), X(4586), X(4593), X(8632), X(9456), X(18268), X(24019), X(32665), X(32666), X(32667), X(32668), X(32669), X(32670), X(32671), X(32672), X(32673), X(32674), X(32675), X(32676), X(32677), X(32678). The perspector of this conic is X(31).

X(32664) lies on these lines: {2, 7357}, {31, 1501}, {41, 6186}, {48, 354}, {101, 3681}, {184, 2225}, {379, 2140}, {561, 4586}, {572, 11220}, {604, 1401}, {748, 2112}, {1495, 16588}, {3185, 32739} et al

X(32664) = complement of X(7357)
X(32664) = perspector of circumconic centered at X(31)
X(32664) = X(2)-Ceva conjugate of X(31)


X(32665) = BARYCENTRIC PRODUCT X(100)*X(106)

Barycentrics    a^3/((b - c) (2 a - b - c)) : :

As the barycentric product of circumcircle-X(1)-antipodes, X(32665) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32665) lies on these lines: {36, 909}, {41, 16944}, {88, 2224}, {100, 32686}, {101, 649}, {106, 919}, {662, 1019}, {667, 692}, {813, 6551}, {859, 3285}, {913, 8752}, {1262, 1461}, {1320, 5011}, {1415, 2149}, {1783, 32705}, {7115, 32674}, {23981, 32675} et al

X(32665) = isogonal conjugate of X(3762)
X(32665) = trilinear pole of line X(31)X(692)
X(32665) = complement of anticomplementary conjugate of X(21222)
X(32665) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 901}, {6, 3257}, {31, 4555}, {75, 32719}, {88, 101}, {100, 106}, {109, 1320}, {110, 4674}, {163, 4080}, {244, 6551}, {649, 5376}, {692, 903}, {1332, 8752}, {1415, 4997}, {6335, 32659}
X(32665) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3762), (31, 900), (32, 1635), (41, 1639), (88, 3261), (100, 3264), (101, 4358), (106, 693), (163, 16704), (667, 1647), (692, 519), (901, 75), (1415, 3911), (3257, 76), (4080, 20948), (4555, 561), (4674, 850), (5376, 1978), (6551, 7035), (8752, 17924), (16944, 4453), (32659, 905), (32719, 1)


X(32666) = BARYCENTRIC PRODUCT X(101)*X(105)

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

As the barycentric product of circumcircle-X(1)-antipodes, X(32666) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32666) lies on these lines: {101, 663}, {105, 2224}, {662, 3737}, {666, 4586}, {667, 1415}, {692, 3063}, {884, 32675}, {909, 2195}, {911, 2223}, {1416, 1457}, {1438, 2210}, {1461, 24027}, {8750, 32703}, {8751, 32699}, {9456, 32719}, {32644, 32656}, {32724, 32739}

X(32666) = trilinear pole of line X(31)X(9447)
X(32666) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 919}, {31, 666}, {100, 1438}, {101, 105}, {109, 294}, {110, 18785}, {163, 13576}, {644, 1416}, {649, 5377}, {651, 2195}, {673, 692}, {884, 4564}, {1415, 14942}, {1461, 28071}, {2481, 32739}, {24027, 28132}
X(32666) = barycentric quotient X(i)/X(j) for these (i,j): (31, 918), (101, 3263), (105, 3261), (109, 27818), (110, 18157), (163, 30941), (663, 693), (666, 561), (692, 3912), (884, 4858), (919, 75), (1415, 9436), (1416, 24002), (2195, 4391), (5377, 1978), (13576, 20948), (18785, 850), (32656, 25083), (32739, 518)


X(32667) = BARYCENTRIC PRODUCT X(102)*X(108)

Barycentrics    a^3/((b - c) (a - b - c) (a^2 - b^2 - c^2) (2 a^5 + a^4 (b + c) - 2 a^3 (b^2 + c^2) - (b + c) (b^2 - c^2)^2)) : :
Barycentrics    a^3/((sec B - sec C) (sin B (sec A - sec B) + sin C (sec A - sec C))) : :

As the barycentric product of circumcircle-X(1)-antipodes, X(32667) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32667) lies on these lines: {101, 7115}, {102, 32688}, {108, 32683}, {909, 32702}, {1415, 32643}, {1457, 32647}, {2432, 2443}, {23985, 32674}

X(32667) = barycentric product X(i)*X(j) for these lines: {i,j}: {92, 32643}, {102, 108}, {2432, 7128}
X(32667) = barycentric quotient X(i)/X(j) for these (i,j): (32643, 63)


X(32668) = BARYCENTRIC PRODUCT X(103)*X(934)

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

As the barycentric product of circumcircle-X(1)-antipodes, X(32668) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32668) lies on these lines: {101, 1262}, {692, 24027}, {934, 32684}, {1019, 24019}, {1461, 23971}, {6614, 32674)}, {32701, 32714}

X(32668) = trilinear pole of line X(31)X(7099)
X(32668) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 24016}, {103, 934}, {1815, 32714}, {2400, 24027}
X(32668) = barycentric quotient X(i)/X(j) for these (i,j): (103, 4397), (1815, 15416), (23971, 24015), (24016, 75), (24027, 2398)


X(32669) = BARYCENTRIC PRODUCT X(104)*X(109)

Barycentrics    a^3/((b - c) (a - b - c) (b^3 + c^3 - (a^2 + b c) (b + c) + 2 a b c)) : :
Barycentrics    a^3/((cos B - cos C) (1 - cos B - cos C)) : :

As the barycentric product of circumcircle-X(1)-antipodes, X(32669) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32669) lies on these lines: {101, 652}, {109, 32685}, {649, 32674}, {692, 1946}, {909, 1404}, {1415, 23979}, {2423, 2425}, {7113, 14578}

X(32669) = isogonal conjugate of isotomic conjugate of X(37136)
X(32669) = isogonal conjugate of polar conjugate of X(36110)
X(32669) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 2720}, {63, 32702}, {104, 109}, {108, 1795}, {651, 909}, {653, 14578}, {2423, 4564}
X(32669) = barycentric quotient X(i)/X(j) for these (i,j): (109, 3262), (692, 6735), (909, 4391), (1415, 908), (2423, 4858), (2720, 75), (14578, 6332), (23979, 24029), (32702, 92)


X(32670) = BARYCENTRIC PRODUCT X(107)*X(26701)

Barycentrics    a^2/((b + c) (b^2 - c^2) (a^2 - b^2 - c^2)^2 (a^6 - a^4 (2 b^2 - 3 b c + 2 c^2) + a^2 (b - c)^2 (b^2 + c^2) - b c (b^2 - c^2)^2)) : :
Barycentrics    (a tan A)/((tan B - tan C) ((b + c) tan A - b tan B - c tan C)) : :

As the barycentric product of circumcircle-X(1)-antipodes, X(32670) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32670) lies on these lines: {163, 23964}, {662, 23582}, {2159, 32695}, {23590, 24019}, {26701, 32687}

X(32670) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 26701}
X(32670) = barycentric quotient X(i)/X(j) for these (i,j): (26701, 3265)


X(32671) = BARYCENTRIC PRODUCT X(110)*X(759)

Barycentrics    a^3/((b + c) (b^2 - c^2) (a^2 - b^2 - c^2 + b c)) : :
Barycentrics    a^2 csc(B - C)/((b + c) cot A - b cot B - c cot C) : :

As the barycentric product of circumcircle-X(1)-antipodes, X(32671) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32671) lies on these lines: {163, 23357}, {249, 662}, {759, 1910}, {923, 32729}, {2159, 32640}, {9274, 99500}, {23964,24019}

X(32671) = trilinear pole of line X(31)X(1576)
X(32671) = isogonal conjugate of isotomic conjugate of X(37140)
X(32671) = barycentric product X(i)*X(j) for these lines: {i,j}: {110, 759}, {163, 24624}, {1576, 14616}
X(32671) = barycentric quotient X(i)/X(j) for these (i,j): (163, 3936), (759, 850), (1576, 758), (23357, 4585), (24624, 20948)


X(32672) = BARYCENTRIC PRODUCT X(111)*X(8691)

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

As the barycentric product of circumcircle-X(1)-antipodes, X(32672) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32672) lies on these lines: {163, 32729}, {662, 691}


X(32673) = BARYCENTRIC PRODUCT X(112)*X(26702)

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

As the barycentric product of circumcircle-X(1)-antipodes, X(32673) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32673) lies on these lines: {250, 662}, {1910, 32696}, {2159, 32715}, {10423, 26702}


X(32674) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(1)X(4)

Barycentrics    a^2/((b - c) (a - b - c) (a^2 - b^2 - c^2)) : :
Barycentrics    a^3/(sec B - sec C) : :

As the barycentric product of circumcircle-X(1)-antipodes, X(32674) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31), and as the barycentric product of circumcircle-X(4)-antipodes, X(32674) also lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32674) lies on these lines: {1, 20613}, {6, 3209}, {19, 604}, {34, 1438}, {41, 208}, {48, 2331}, {56, 607}, {65, 2332}, {101, 108}, {109, 112}, {196, 2301}, {204, 2187}, {207, 7114}, {221, 3172}, {225, 1910}, {232, 17966}, {278, 2224}, {281, 3476}, {478, 21148}, {608, 8752}, {648, 653}, {649, 32669}, {692, 2498}, {906, 23981}, {923, 8753}, {1033, 3197}, {1249, 1630}, {1319, 5089}, {1400, 2159}, {1402, 1945}, {1411, 1474}, {1415, 2425}, {1420, 7719}, {1429, 5236}, {1461, 32714}, {1767, 7125}, {1826, 7120}, {1877, 2201}, {1886, 2202}, {2172, 21147}, {3192, 17408}, {6589, 32643}, {6591, 32675}, {6614, 32668}, {7115, 32665}, {8687, 32691}, {23985, 32667} et al

X(32674) = isogonal conjugate of X(6332)
X(32674) = polar conjugate of isotomic conjugate of X(109)
X(32674) = crossdifference of every pair of points on line X(2968)X(4082)
X(32674) = trilinear pole of line X(25)X(31) (the isogonal conjugate of the isotomic conjugate of line X(1)X(4))
X(32674) = barycentric product of PU(100)
X(32674) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 108}, {4, 109}, {6, 653}, {7, 8750}, {9, 32714}, {19, 651}, {25, 664}, {27, 4559}, {28, 4551}, {31, 18026}, {33, 934}, {34, 100}, {41, 13149}, {56, 1897}, {57, 1783}, {65, 162}, {73, 107}, {92, 1415}, {101, 278}, {102, 23987}, {104, 23706}, {110, 225}, {112, 226}, {190, 608}, {208, 13138}, {273, 692}, {281, 1461}, {388, 32691}, {514, 7115}, {521, 24033}, {604, 6335}, {607, 658}, {648, 1400}, {811, 1402}, {901, 1877}, {919, 5236}, {1411, 4242}, {1474, 4552}, {1826, 4565}, {1945, 1981}, {1973, 4554}, {3476, 9088}, {4564, 6591}, {6332, 23985}, {6614, 7046}, {17923, 32675}, {23979, 32707}
X(32674) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6332), (19, 4391), (25, 522), (28, 18155), (31, 521), (33, 4397), (34, 693), (56, 4025), (57, 15413), (65, 14208), (73, 3265), (100, 3718), (101, 345), (108, 75), (109, 69), (110, 332), (112, 333), (162, 314), (163, 1812), (208, 17896), (225, 850), (226, 3267), (278, 3261), (604, 905), (607, 3239), (608, 514), (648, 28660), (649, 26932), (651, 304), (653, 76), (664, 305), (692, 78), (906, 3719), (934, 7182), (1400, 525), (1402, 656), (1415, 63), (1461, 348), (1474, 4560), (1783, 312), (1897, 3596), (1973, 650), (3172, 14331), (3209, 14837), (4551, 20336), (4559, 306), (6335, 28659), (6591, 4858), (6614, 7056), (7115, 190), (7120, 17899), (8750, 8), (13149, 20567), (18026, 561), (23706, 3262), (23979, 1813), (23985, 653), (24027, 6516), (24033, 18026), (32676, 21), (32691, 30479), (32714, 85)


X(32675) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(1)X(5)

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

As the barycentric product of circumcircle-X(1)-antipodes, X(32675) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31), and as the barycentric product of circumcircle-X(5)-antipodes, X(32675) also lies on conic {{A,B,C,X(112),X(1987)}} with perspector X(51).

X(32675) lies on these lines: {101, 650}, {163, 1625}, {649, 1415}, {654, 32641}, {655, 662}, {663, 692}, {884, 32666}, {909, 1319}, {911, 1055}, {913, 14571}, {1404, 1457}, {1411, 1438}, {1429, 2006}, {1461, 3669}, {2159, 19297}, {2183, 32677}, {2423, 2425}, {17923, 32674}, {23981, 32665} et al

X(32675) = isogonal conjugate of X(3904)
X(32675) = trilinear pole of line X(31)X(51) (the isogonal conjugate of the isotomic conjugate of line X(1)X(5))
X(32675) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 2222}, {6, 655}, {80, 109}, {100, 1411}, {101, 2006}, {108, 1807}, {654, 23592}, {692, 18815}, {1415, 18359}, {14628, 32665}
X(32675) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3904), (109, 320), (655, 76), (692, 4511), (1411, 693), (1415, 3218), (2006, 3261), (2222, 75), (32674, 17923)


X(32676) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(1)X(19)

Barycentrics    a^3/((b^2 - c^2) (a^2 - b^2 - c^2)) : :
Trilinears    a^2/(sin 2B - sin 2C) : :

As the barycentric product of circumcircle-X(1)-antipodes, X(32676) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31), and as the barycentric product of circumcircle-X(19)-antipodes, X(32676) also lies on conic {{A,B,C,X(162),X(8750)}} with perspector X(1973).

X(32676) lies on these lines: {19, 560}, {28, 2224}, {31, 2159}, {101, 112}, {107, 15440}, {110, 32691}, {162, 662}, {648, 4586}, {692, 2873}, {811, 4593}, {823, 24000}, {909, 2206}, {911, 1333}, {923, 1973}, {1086, 14119}, {1415, 1576}, {1438, 1474}, {1582, 20883}, {1974, 18268}, {2194, 2288}, {2203, 9456} et al

X(32676) = isogonal conjugate of X(14208)
X(32676) = polar conjugate of X(20948)
X(32676) = X(i)-isoconjugate of X(j) for these lines: {i,j}: {1, 14208}, {2, 525}, {4, 3265}, {6, 3267}, {48, 20948}, {690, 30786}, {3566, 6340}
X(32676) = trilinear pole of line X(31)X(1932)
X(32676) = crossdifference of every pair of points on line X(3708)X(4466)
X(32676) = barycentric product of PU(108)
X(32676) = trilinear product of circumcircle intercepts of Moses radical circle
X(32676) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 112}, {3, 24019}, {4, 163}, {6, 162}, {19, 110}, {21, 32674}, {25, 662}, {27, 692}, {28, 101}, {29, 1415}, {31, 648}, {32, 811}, {33, 4565}, {34, 5546}, {48, 107}, {58, 1783}, {63, 32713}, {92, 1576}, {99, 1973}, {100, 1474}, {108, 284}, {109, 1172}, {184, 823}, {190, 2203}, {240, 2715}, {286, 32739}, {560, 6331}, {647, 24000}, {649, 5379}, {651, 2299}, {653, 2194}, {799, 1974}, {909, 4246}, {911, 4241}, {923, 4235}, {1333, 1897}, {1461, 4183}, {1969, 14574}, {2159, 4240}, {2206, 6335}, {2224, 4249}, {2303, 32691}, {4593, 27369}, {4630, 20883}
X(32676) = barycentric quotient X(i)/X(j) for these (i,j): (1, 3267), (4, 20948), (6, 14208), (19, 850), (25, 1577), (28, 3261), (31, 525), (32, 656), (48, 3265), (58, 15413), (101, 20336), (107, 1969), (108, 349), (109, 1231), (110, 304), (112, 75), (162, 76), (163, 69), (184, 24018), (560, 647), (648, 561), (662, 305), (669, 3708), (692, 306), (811, 1502), (823, 18022), (923, 14977), (1333, 4025), (1415, 307), (1474, 693), (1576, 63), (1783, 313), (1897, 27801), (1973, 523), (1974, 661), (2194, 6332), (2203, 514), (2206, 905), (2299, 4391), (2715, 336), (4565, 7182), (5379, 1978), (5546, 3718), (6331, 1928), (8750, 321), (9780, 4466), (14574, 48), (24000, 6331), (24019, 264), (27369, 8061), (32674, 1441), (32713, 92), (32739, 72)


X(32677) = BARYCENTRIC PRODUCT X(1)*X(102)

Barycentrics    a^3/(2 a^5 + a^4 (b + c) - 2 a^3 (b^2 + c^2) - (b + c) (b^2 - c^2)^2) : :
Trilinears    a/(sin B (sec A - sec B) + sin C (sec A - sec C)) : :
Trilinears    a/((b + c) sec A - b sec B - c sec C) : :

X(32677) is the barycentric product of the circumcircle intercepts of line X(1)X(521). As the barycentric product of circumcircle-X(1)-antipodes, X(32677) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32677) lies on these lines: {6, 3209}, {25, 2192}, {48, 1415}, {101, 102}, {163, 2193}, {197, 2875}, {212, 692}, {222, 1461}, {654, 909}, {662, 1812}, {1172, 1905}, {2182, 6001}, {2183, 32675}, {2194, 2288}, {2431, 8677}, {7113, 14578}

X(32677) = isogonal conjugate of isotomic conjugate of X(36100)
X(32677) = polar conjugate of isotomic conjugate of X(36055)
X(32677) = X(2)-isoconjugate of X(515)
X(32677) = trilinear pole of line X(31)X(1946)
X(32677) = trilinear product X(6)*X(102)
X(32677) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 102}, {57, 15629}, {651, 2432}, {1415, 2399}
X(32677) = barycentric quotient X(i)/X(j) for these (i,j): (31, 515), (102, 75), (1415, 2406), (2432, 4391), (15629, 312)


X(32678) = BARYCENTRIC PRODUCT X(1)*X(476)

Barycentrics    a/((b^2 - c^2) ((a^2 - b^2 - c^2)^2 - b^2 c^2)) : :
Trilinears    a/((1 + 2 cos 2A) sin(B - C)) : :

X(32678) is the barycentric product of the circumcircle intercepts of line X(1)X(564). As the barycentric product of circumcircle-X(1)-antipodes, X(32678) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32678) lies on these lines: {101, 476}, {163, 661}, {662, 1577}, {923, 8772}, {1415, 32662}, {1725, 2159}, {1910, 2166}, {9455, 11076}, {11060, 18268}

X(32678) = isogonal conjugate of X(32679)
X(32678) = trilinear pole of line X(31)X(2153)
X(32678) = polar conjugate of isotomic conjugate of X(36061)
X(32678) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 476}, {6, 32680}, {75, 14560}, {92, 32662}, {94, 163}, {110, 2166}, {162, 265}, {328, 32676}, {662, 1989}, {799, 11060}
X(32678) = barycentric quotient X(i)/X(j) for these (i,j): (1, 3268), (6, 32679), (48, 8552), (94, 20948), (162, 340), (163, 323), (265, 14208), (476, 75), (662, 7799), (923, 9213), (1989, 1577), (2166, 850), (11060, 661), (14560, 1), (32680, 76), (32662, 63), (32676, 186)


X(32679) = ISOGONAL CONJUGATE OF X(32678)

Barycentrics    a (b^2 - c^2) ((a^2 - b^2 - c^2)^2 - b^2 c^2) : :
Barycentrics    (1 + 2 cos 2A) sin(B - C) : :
Trilinears    directed distance from A to Fermat axis : :

X(32679) lies on these lines: {163, 662}, {323, 14838}, {442, 6366}, {514, 661}, {2349, 2631}, {2573, 19178}, {2610, 3960}, {4707, 5664}, {7202, 8287}, {8773, 23894}, {10015, 17056}, {16559, 16563}

X(32679) = isogonal conjugate of X(32678)
X(32679) = isotomic conjugate of X(32680)
X(32679) = crossdifference of every pair of points on line X(31)X(2153)
X(32679) = polar conjugate of X(36129)
X(32679) = pole wrt polar circle of trilinear polar of X(36129) (line X(19)X(23894))
X(32679) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 3268}, {50, 20948}, {75, 526}, {92, 8552}, {186, 14208}, {323, 1577}, {340, 656}, {561, 14270}, {661, 7799}, {799, 2088}, {850, 6149}, {2349, 5664}, {3219, 4707}, {3936, 14838}, {3960, 3969}, {4585, 8287}, {14590, 20902}
X(32679) = barycentric quotient X(i)/X(j) for these (i,j): (1, 476), (6, 32678), (31, 14560), (48, 32662), (50, 163), (186, 162), (323, 662), (340, 811), (526, 1), (656, 265), (661, 1989), (1577, 94), (2088, 661), (2610, 8818), (3268, 75), (3936, 15455), (4707, 30690), (5664, 14206), (6149, 110), (7799, 799), (8552, 63), (14208, 328), (14270, 31), (14838, 24624), (20902, 14592), (20948, 20573), (21828, 2160)


X(32680) = TRILINEAR PRODUCT X(2)*X(476)

Barycentrics    b c/((b^2 - c^2) ((a^2 - b^2 - c^2)^2 - b^2 c^2)) : :
Barycentrics    csc(B - C)/(1 + 2 cos 2A) : :

X(32680) is the trilinear product of the circumcircle intercepts of line X(2)X(94) (the isotomic conjugate of the isogonal conjugate of the Fermat axis). As the trilinear product of circumcircle-X(2)-antipodes, X(32680) lies on conic {{A,B,C,X(100),X(162)}} with center X(9) and perspector X(1). X(32680) is also the barycentric product of the circumcircle intercepts of line X(75)X(2166).

Let H be the rectangular hyperbola passing through X(1), X(5), X(30) and the excenters (centered at X(476)); then X(32680) is the perspector of ABC and the tangential triangle, wrt excentral triangle, of H.

X(32680) lies on these lines: {94, 24624}, {100, 476}, {162, 24006}, {662, 1577}, {799, 20948}, {897, 1733}, {1101, 2618}, {1492, 14560}, {1821, 16568}, {2349, 14206}, {5802, 10991}

X(32680) = isogonal conjugate of X(2624)
X(32680) = isotomic conjugate of X(32679)
X(32680) = X(6)-isoconjugate of X(526)
X(32680) = trilinear pole of line X(1)X(564)
X(32680) = polar conjugate of isogonal conjugate of X(36061)
X(32680) = trilinear product X(i)*X(j) for these lines: {i,j}: {2, 476}, {75, 32678}, {76, 14560}, {94, 110}, {99, 1989}, {112, 328}, {250, 14592}, {662, 2166}, {759, 15455}, {1576, 20573}, {3268, 23588}, {6742, 24624}
X(32680) = trilinear quotient X(i)/X(j) for these (i,j): (2, 526), (6, 14270), (75, 32679), (76, 3268), (94, 523), (99, 323), (110, 50), (250, 14591), (329, 3267), (476, 6), (526, 18334), (662, 6149), (1989, 512), (2166, 661), (6742, 2245), (14560, 32), (14592, 125), (15455, 758), (20573, 850), (23588, 14560), (24624, 2605), (32678, 31)
X(32680) = barycentric product X(i)*X(j) for these lines: {i,j}: {75, 476}, {76, 32678}, {94, 662}, {99, 2166}, {162, 328}, {163, 20573}, {561, 14560}, {799, 1989}, {6742, 14616}, {15455, 24624}
X(32680) = barycentric quotient X(i)/X(j) for these (i,j): (1, 526), (31, 14270), (63, 8552), (75, 3268), (94, 1577), (110, 6149), (162, 186), (328, 14208), (476, 1), (662, 323), (759, 2605), (799, 7799), (897, 9213), (1989, 661), (2166, 523), (3268, 32679), (6742, 758), (14206, 5664), (14560, 31), (14616, 4467), (15455, 3936), (20573, 20948), (24624, 14838), (32678, 6)


X(32681) = BARYCENTRIC PRODUCT X(74)*X(1302)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32681) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(30) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32681).

X(32681) lies on the circumcircle and these lines: {6, 841}, {74, 3003}, {110, 32640}, {1300, 1990}, {1302, 9209}, {2420, 10420}, {2433, 9060} et al

X(32681) = Λ(PU(168))
X(32681) = Λ(X(1637), X(5664))
X(32681) = Λ(X(8552), X(14566))
X(32681) = Ψ(X(2), X(74))
X(32681) = barycentric product X(74)*X(1302)
X(32681) = barycentric quotient X(i)/X(j) for these (i,j): (74, 30474), (1302, 3260), (32640, 15066)


X(32682) = BARYCENTRIC PRODUCT X(101)*X(675)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32682) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(31) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32682).

X(32682) lies on the circumcircle and these lines: {98, 17734}, {99, 4570}, {100, 1110}, {101, 6586}, {102, 13329}, {103, 32642}, {105, 2224}, {106, 32719}, {675, 3011}, {759, 5009}, {789, 5384}, {813, 1983}, {840, 4257}, {917, 32699}, {934, 24027}, {953, 995}, {1311, 1737} et al

X(32682) = isogonal conjugate of ideal point of 1st and 2nd isobarycs of X(101)
X(32682) = Ψ(X(2), X(101))
X(32682) = barycentric product X(i)*X(j) for these lines: {i,j}: {100, 2224}, {101, 675}
X(32682) = barycentric quotient X(i)/X(j) for these (i,j): (101, 3006), (2224, 693), (675, 3261)


X(32683) = BARYCENTRIC PRODUCT X(102)*X(9056)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32683) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(652) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32683).

X(32683) lies on the circumcircle and these lines: {102, 8607}, {108, 32667}, {109, 32643}, {8755, 32706}, {26704, 32700}, {26715, 32720}

X(32683) = Ψ(X(2), X(102))


X(32684) = BARYCENTRIC PRODUCT X(103)*X(9057)

Barycentrics    a^2/((b - c) (2 a^3 - a^2 (b + c) - (b - c)^2 (b + c)) (a^3 (b + c) - a^2 (b^2 + b c + c^2) - a (b^3 + b^2 c + b c^2 + c^3) + b^4 + b^3 c + 4 b^2 c^2 + b c^3 + c^4)) : :
Barycentrics    a^3/(((c - a) cot B - (a - b) cot C) ((b^3 - c^3) cos A + a^2 (b cos B - c cos C) + b c (b - c))) : :

As the barycentric product of circumcircle-X(2)-antipodes, X(32684) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(657) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32684).

X(32684) lies on the circumcircle and these lines: {101, 32642}, {103, 8608}, {917, 1886}, {934, 32668}, {26705, 32701}, {26716, 32721}

X(32684) = Ψ(X(2), X(103))


X(32685) = BARYCENTRIC PRODUCT X(104)*X(9058)

Barycentrics    a^2/((b - c) (b^3 + c^3 - (a^2 + b c) (b + c) + 2 a b c) (a^3- a^2 (b + c) - a (b - c)^2 + (b + c) (b^2 + c^2))) : :
Barycentrics    a^2/((cos B + cos C - 1) (2 (sin B - sin C) (cos A - 1) + sin 2B + sin 2C)) : :

As the barycentric product of circumcircle-X(2)-antipodes, X(32685) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(650) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32685).

X(32685) lies on the circumcircle and these lines: {100, 32641}, {102, 5053}, {104, 8609}, {108, 32702}, {109, 32669}, {915, 14571}, {998, 2717}, {1983, 2743}, {2427, 6099}, {32722, 32723}

X(32685) = Ψ(X(2), X(104))


X(32686) = BARYCENTRIC PRODUCT X(106)*X(9059)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32686) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(649) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32686).

X(32686) lies on the circumcircle and these lines: {99, 4582}, {100, 32665}, {101, 32719}, {106, 5053}, {110, 5548}, {996, 2726}, {1293, 32645}, {3257, 13396}, {32704, 32705}

X(32686) = Ψ(X(2), X(106))
X(32686) = barycentric product X(i)*X(j) for these lines: {i,j}: {106, 9059}, {901, 996}
X(32686) = barycentric quotient X(i)/X(j) for these (i,j): (901, 4389), (9059, 3264), (32719, 995)


X(32687) = BARYCENTRIC PRODUCT X(107)*X(1297)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32687) lies on the circumcircle.

Let A', B', C' be the intersections of the van Aubel line and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32687).

X(32687) lies on the circumcircle and these lines: {74, 8744}, {98, 6530}, {99, 20580}, {107, 6587}, {110, 23964}, {112, 32649}, {232, 1297}, {393, 2697}, {647, 1301}, {1289, 6529}, {26701, 32670}, {26717, 32725} et al

X(32687) = Λ(X(i), X(j)) for these lines: {i,j}: {2, 14345}, {287, 2419}, {648, 2404}, {3269, 15526}
X(32687) = Ψ(X(2), X(107))
X(32687) = Moses-radical-circle-inverse of X(1301)
X(32687) = polar-circle-inverse of X(33504)
X(32687) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 1297}, {264, 32649}
X(32687) = barycentric quotient X(i)/X(j) for these (i,j): (1297, 3265), (32649, 3)


X(32688) = BARYCENTRIC PRODUCT X(108)*X(26703)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32688) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(19) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32688).

X(32688) lies on the circumcircle and these lines: {100, 7115}, {102, 32667}, {104, 32702}, {108, 6588}, {1295, 32647}, {1415, 26706}, {5089, 26703}, {32726, 32727}

X(32688) = Ψ(X(2), X(108))
X(32688) = polar-circle-inverse of X(38972)


X(32689) = BARYCENTRIC PRODUCT X(109)*X(1311)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32689) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(41) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32689).

X(32689) lies on the circumcircle and these lines: {100, 2149}, {102, 32643}, {104, 32669}, {109, 6589}, {2291, 32728}, {3064, 26704}, {8558, 26703}, {32706, 32707}

X(32689) = Ψ(X(2), X(109))


X(32690) = BARYCENTRIC PRODUCT X(477)*X(9060)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32690) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(1637) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32690).

X(32690) lies on the circumcircle and these lines: {99, 30528}, {476, 32650}, {477, 3018}, {841, 32663}, {1304, 32712}, {32732, 32733}

X(32690) = Ψ(X(2), X(477))


X(32691) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(19)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32691) lies on the circumcircle, and as the barycentric product of circumcircle-X(19)-antipodes, X(32691) also lies on conic {{A,B,C,X(162),X(8750)}} with perspector X(1973).

Let P be a point of the line X(2)X(19), other than X(2). Let A'B'C' be the cevian triangle of P. Let A" be the {B,C}-harmonic conjugate of A' (i.e., A" = BC∩B'C'), and define B" and C" cyclically. The circumcircles of AB"C", BC"A", CA"B" concur in X(32691).

X(32691) lies on the circumcircle and these lines: {4, 5515}, {25, 28476}, {74, 1245}, {99, 162}, {100, 8750}, {102, 1036}, {103, 2221}, {104, 1039}, {105, 5338}, {110, 32676}, {595, 11383}, {689, 32691}, {759, 17520}, {833, 4242}, {1897, 8707}, {2249, 2281}, {2339, 26703}, {2370, 11319}, {8687, 32674}.

X(32691) = isogonal conjugate of X(23874)
X(32691) = trilinear pole of line X(6)X(1245)
X(32691) = inverse-in-polar-circle of X(5515)
X(32691) = cevapoint of X(8646) and X(21750)
X(32691) = Ψ(X(i), X(j)) for these (i,j): (1, 25), (2, 19), (3, 31), (6, 1245), (63, 6), (69, 1), (75, 4), (1010, 2)
X(32691) = X(834)-cross conjugate of X(4)
X(32691) = trilinear product of circumcircle intercepts of line X(1)X(25)
X(32691) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23874}, {2, 2522}, {3, 2517}, {63, 6590}, {69, 8678}, {100, 26933}, {304, 2484}, {305, 8646}, {388, 521}, {514, 5227}, {522, 1038}, {525, 2303}, {612, 4025}, {649, 19799}, {656, 1010}, {693, 7085}, {905, 2345}, {1019, 3610}, {1459, 4385}, {2285, 6332}, {2286, 4391}, {3265, 4206}, {4131, 7102}, {7004, 14594}, {8898, 15411}
X(32691) = barycentric product X(i)*X(j) for these lines: {i,j}: {19, 1310}, {108, 2339}, {648, 1245}, {651, 1039}, {653, 1036}, {811, 2281}, {1897, 2221}, {30479, 32674}
X(32691) = barycentric quotient X(i)/X(j) for these (i,j): (19, 2517), (25, 6590), (31, 2522), (100, 19799), (112, 1010), (1036, 6332), (1039, 4391), (1245, 525), (1310, 304), (1415, 1038), (2221, 4025), (2281, 656), (8750, 2345), (32674, 388), (32676, 2303)


X(32692) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(54)

Barycentrics    a^2/((b^2 - c^2) (a^4 + b^4 + c^4 - 2 a^2 b^2 - 2 a^2 c^2) (b^4 + c^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2)) : :
Barycentrics    a^2/(tan 2B - tan 2C) : :
Trilinears    (sin A)/(sin 4B - sin 4C) : :
Trilinears    sin A sec 2A csc(2B - 2C) : :

As the barycentric product of circumcircle-X(2)-antipodes, X(32692) lies on the circumcircle.

Let P be a point of the line X(2)X(54), other than X(2). Let A'B'C' be the cevian triangle of P. Let A" be the {B,C}-harmonic conjugate of A' (i.e., A" = BC∩B'C'), and define B" and C" cyclically. The circumcircles of AB"C", BC"A", CA"B" concur in X(32692).

X(32692) lies on the circumcircle and these lines: {4, 139}, {6, 2383}, {54, 3563}, {74, 15664}, {96, 98}, {99, 18315}, {110, 14586}, {112, 32734}, {759, 2168}, {847, 14585}, {925, 32661}, {1141, 2165}, {1297, 10625}, {1299, 8882}, {1300, 14533}, {1971, 5962}, {2623, 10420} et al

X(32692) = trilinear pole of line X(6)X(2351) (the tangent to hyperbola {A,B,C,X(5),X(6)} at X(6))
X(32692) = inverse-in-polar-circle of X(139)
X(32692) = Ψ(X(i), X(j)) for these (i,j): (2, 54), (5, 6), (6, 2351), (51, 31), (76, 95), (317, 2)
X(32692) = Λ(trilinear polar of isotomic conjugate of X(96))
X(32692) = X(52)-isoconjugate of X(1577)
X(32692) = barycentric product X(i)*X(j) for these lines: {i,j}: {54, 925}, {68, 933}, {95, 32692}, {96, 110}, {662, 2168}, {847, 15958}, {2165, 18315}, {2351, 18831}, {5392, 14586}, {14533, 30450}
X(32692) = barycentric quotient X(i)/X(j) for these (i,j): (54, 6563), (96, 850), (925, 311), (933, 317), (1576, 52), (2165, 18314), (2168, 1577), (2351, 6368), (5392, 15415), (14586, 1993), (15958, 9723), (18315, 7763), (32692, 5)


X(32693) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(65)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32693) lies on the circumcircle, and as the barycentric product of circumcircle-X(65)-antipodes, X(32693) also lies on conic {{A,B,C,X(651),X(1415)}} with perspector X(1402).

Let P be a point of the line X(2)X(65), other than X(2). Let A'B'C' be the cevian triangle of P. Let A" be the {B,C}-harmonic conjugate of A' (i.e., A" = BC∩B'C'), and define B" and C" cyclically. The circumcircles of AB"C", BC"A", CA"B" concur in X(32693).

X(32693) lies on the circumcircle and these lines: {99, 651}, {100, 4559}, {104, 941}, {105, 959}, {110, 1415}, {644, 8707}, {692, 8687}, {1311, 31359}, {1783, 26704}, {2258, 2291}, {2284, 6574} et al

X(32693) = trilinear pole of line X(6)X(1402)
X(32693) = Ψ(X(i), X(j)) for these (i,j): (2, 65), (6, 1402), (21, 6), (314, 2)
X(32693) = Λ(X(i), X(j)) for these lines: {i,j}: {650, 3975}, {693, 3669}, {905, 1577}
X(32693) = Λ(polar of X(10435) wrt Conway circle)
X(32693) = barycentric product X(i)*X(j) for these lines: {i,j}: {65, 931}, {100, 959}, {109, 31359}, {651, 941}, {664, 2258}
X(32693) = barycentric quotient X(i)/X(j) for these (i,j): (101, 11679), (109, 10436), (931, 314), (941, 4391), (959, 693), (1415, 940), (2258, 522)


X(32694) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(353)

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

As the barycentric product of circumcircle-X(2)-antipodes, X(32694) lies on the circumcircle.

X(32694) lies on the circumcircle and these lines: {6, 9831}, {32, 843}, {74, 2080}, {98, 8859}, {99, 3906}, {110, 17414}, {111, 1691}, {182, 842}, {187, 6323}, {249, 12074}, {511, 14388}, {512, 11636}, {805, 5467}, {1296, 9218}, {1297, 11416}, {2698, 11842}, {2710, 8722}, {2770, 9169} et al

X(32694) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(9208)
X(32694) = inverse-in-Schoute-circle of X(6323)
X(32694) = inverse-in-circle-{{X(1687),X(1688),PU(1),PU(2)}} of X(111)
X(32694) = Ψ(X(2), X(353))
X(32694) = Λ(X(i), X(j)) for these lines: {i,j}: {76, 9180}, {98, 14388}, {99, 5467}, {115, 17416}, {262, 14223}
X(32694) = barycentric quotient X(i)/X(j) for these (i,j): (32, 9208), (110, 7840)


X(32695) = BARYCENTRIC PRODUCT X(74)*X(107)

Barycentrics    a^2/((b^2 - c^2) (a^2 - b^2 - c^2)^2 (2 a^4 - a^2(b^2 + c^2) - (b^2 - c^2)^2)) : :
Trilinears    (tan A)/((tan B - tan C) (cos A - 2 cos B cos C)) : :

As the barycentric product of circumcircle-X(4)-antipodes, X(32695) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32695) lies on these lines: {74, 8744}, {112, 647}, {512, 32713}, {525, 648}, {878, 32696}, {1552, 16318}, {1990, 15311}, {2159, 32670}, {2433, 2442}, {2501, 6529} et al

X(32695) = polar conjugate of isotomic conjugate of X(1304)
X(32695) = trilinear pole of line X(25)X(8749) (the isogonal conjugate of the isotomic conjugate of line X(4)X(74))
X(32695) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 1304}, {6, 15459}, {25, 16077}, {74, 107}, {112, 16080}, {264, 32715}, {648, 8749}, {823, 2159}, {1494, 32713}, {2433, 23582}, {6529, 14919}
X(32695) = barycentric quotient X(i)/X(j) for these (i,j): (25, 9033), (32, 1636), (74, 3265), (107, 3260), (112, 11064), (512, 1650), (1304, 69), (2159, 24018), (2433, 15526), (8749, 525), (14919, 4143), (15459, 76), (16077, 305), (16080, 3267), (32713, 30), (32715, 3)


X(32696) = BARYCENTRIC PRODUCT X(98)*X(112)

Barycentrics    a^2/((b^2 - c^2) (a^2 - b^2 - c^2) (b^4 + c^4 - a^2 b^2 - a^2 c^2)) : :
Barycentrics    sin^2 A tan A sec(A + ω) csc(B - C) : :
Barycentrics    (sin^3 A)/(sec B sin^3 C - sec C sin^3 B) : :

As the barycentric product of circumcircle-X(4)-antipodes, X(32696) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32696) lies on these lines: {98, 403}, {112, 512}, {232, 248}, {250, 523}, {351, 1304}, {378, 14355}, {460, 6531}, {669, 23964}, {827, 22456}, {878, 32695}, {933, 6037}, {1783, 4705}, {1910, 32673}, {1976, 8749}, {2386, 11610}, {2422, 2445}, {2489, 32713}, {4079, 8750}, {4230, 32697}, {6529, 20031} et al

X(32696) = isogonal conjugate of X(6333)
X(32696) = polar conjugate of isotomic conjugate of X(2715)
X(32696) = trilinear pole of line X(25)X(1501) (the isogonal conjugate of the isotomic conjugate of line X(4)X(32))
X(32696) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 20031}, {4, 2715}, {6, 685}, {25, 2966}, {32, 22456}, {98, 112}, {107, 248}, {110, 6531}, {162, 1910}, {250, 2395}, {287, 32713}, {648, 1976}, {878, 23582}, {879, 23964}, {1289, 11610}, {2207, 17932}, {2422, 18020}, {2445, 9476}, {6037, 10311}, {6331, 14601}, {6528, 14600}, {6529, 17974}
X(32696) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6333), (25, 2799), (32, 684), (98, 3267), (112, 325), (248, 3265), (250, 2396), (685, 76), (878, 15526), (1910, 14208), (1974, 3569), (1976, 525), (2207, 16230), (2395, 339), (2422, 125), (2445, 15595), (2489, 868), (2715, 69), (2966, 305), (6531, 850), (14600, 520), (14601, 647), (17974, 4143), (20031, 264), (22456, 1502), (23964, 877), (32713, 297)


X(32697) = BARYCENTRIC PRODUCT X(99)*X(3563)

Barycentrics    a^2/((b^2 - c^2) (a^2 - b^2 - c^2) (2 a^4 + b^4 + c^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2)) : :
Barycentrics    sec A csc(B - C)/(b^2 cos^2 C + c^2 cos^2 B - b c cos A) : :

As the barycentric product of circumcircle-X(4)-antipodes, X(32697) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32697) lies on these lines: {112, 249}, {186, 691}, {230, 297}, {250, 7468}, {648, 4590}, {1783, 4567}, {2489, 4558}, {4230, 32696}, {18879, 32708} et al

X(32697) = polar conjugate of isotomic conjugate of X(10425)
X(32697) = trilinear pole of line X(25)X(110) (the isogonal conjugate of the isotomic conjugate of line X(4)X(99))
X(32697) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 10425}, {99, 3563}, {112, 8781}, {162, 8773}, {648, 2987}
X(32697) = barycentric quotient X(i)/X(j) for these (i,j): (110, 3564), (112, 230), (162, 1733), (250, 4226), (2987, 525), (3563, 523), (4230, 114), (8773, 14208), (8781, 3267), (10425, 69)


X(32698) = BARYCENTRIC PRODUCT X(100)*X(915)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32698) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32698) lies on these lines: {112, 6099}, {648, 4567}, {906, 6591}, {913, 8752}, {915, 919}, {1110, 8750}, {1252, 1783}, {1262, 32714}, {2149, 32674}, {8609, 15500} et al

X(32698) = polar conjugate of isotomic conjugate of X(6099)
X(32698) = trilinear pole of line X(25)X(692) (the isogonal conjugate of the isotomic conjugate of line X(4)X(100))
X(32698) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 6099}, {100, 915}, {190, 913}, {1783, 2990}, {6335, 32655}
X(32698) = barycentric quotient X(i)/X(j) for these (i,j): (101, 914), (913, 514), (915, 693), (2990, 15413), (6099, 69), (8750, 1737), (32655, 905)


X(32699) = BARYCENTRIC PRODUCT X(101)*X(917)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32699) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32699) lies on these lines: {648, 4570}, {917, 32682}, {1110, 1783}, {7649, 32656}, {8608, 32642}, {8750, 23990}, {8751, 32666}, {8752, 32719}, {24027, 32714}

X(32699) = barycentric product X(i)*X(j) for these lines: {i,j}: {101, 917}, {2989, 8750}
X(32699) = barycentric quotient X(i)/X(j) for these (i,j): (917, 3261)


X(32700) = BARYCENTRIC PRODUCT X(102)*X(26704)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32700) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32700) lies on these lines: {6589, 32643}, {26704, 32683}


X(32701) = BARYCENTRIC PRODUCT X(103)*X(26705)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32701) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32701) lies on these lines: {1734, 1783}, {1886, 32657}, {6586, 8750}, {6589, 32643}, {26705, 32684}, {32668, 32714}


X(32702) = BARYCENTRIC PRODUCT X(104)*X(108)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32702) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32702) lies on these lines: {104, 32688}, {108, 32685}, {112, 2720}, {648, 4560}, {649, 32669}, {650, 1415}, {663, 8750}, {909, 32667}, {1309, 8687}, {1455, 14571}, {2423, 2443}, {3669, 32714}, {6591, 23985}

X(32702) = polar conjugate of isotomic conjugate of X(2720)
X(32702) = trilinear pole of line X(25)X(1397)
X(32702) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 2720}, {7, 14776}, {56, 1309}, {92, 32669}, {104, 108}, {653, 909}, {1415, 16082}
X(32702) = barycentric quotient X(i)/X(j) for these (i,j): (108, 3262), (909, 6332), (1309, 3596), (2720, 69), (8750, 6735), (14776, 8), (32669, 63)


X(32703) = BARYCENTRIC PRODUCT X(105)*X(26706)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32703) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32703) lies on these lines: {919, 1783}, {5089, 32658}, {8750, 32666}


X(32704) = CIRCUMCIRCLE-X(4)-ANTIPODE OF X(106)

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

X(32704) lies on the circumcircle and these lines: {3, 2370}, {4, 106}, {25, 9083}, {186, 2758}, {901, 1897}, {972, 30273}, {1311, 15626}, {32686, 32705}

X(32704) = reflection of X(i) in X(j) for these (i,j): (4, 20619), (2370, 3)
X(32704) = isogonal conjugate of X(32475)
X(32704) = circumcircle antipode of X(2370)
X(32704) = trilinear pole of line X(6)X(8756)
X(32704) = inverse-in-polar-circle of X(5510)
X(32704) = Λ(X(3), X(1459))
X(32704) = Ψ(X(i), X(j)) for these (i,j): (3, 519), (6, 8756), (106, 4), (1797, 2)
X(32704) = barycentric product X(3264)*X(32705)
X(32704) = 2nd-circumperp-isogonal conjugate of X(2390)
X(32704) = circumorthic-isogonal conjugate of X(2390) if ABC is acute


X(32705) = BARYCENTRIC PRODUCT X(106)*X(32704)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32705) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32705) lies on these lines: {648, 4591}, {1783, 32665}, {8756, 32659}, {32686, 32704}

X(32705) = barycentric quotient X(32704)/X(3264)


X(32706) = CIRCUMCIRCLE-X(4)-ANTIPODE OF X(109)

Barycentrics    1/((a^2 - b^2 - c^2) (a^4 (b^2 + c^2) - a^3 b c (b + c) - a^2 (b - c)^2 (2 b^2 + 3 b c + 2 c^2) + a b c (b - c)^2 (b + c) + (b^2 - c^2)^2 (b^2 - b c + c^2))) : :
Trilinears    (tan A)/(cos B csc C (cos A - cos B) + cos C csc B (cos A - cos C)) : :

X(32706) lies on the circumcircle and these lines: {3, 21666}, {4, 109}, {24, 26704}, {25, 9056}, {29, 110}, {99, 7436}, {100, 318}, {101, 281}, {108, 158}, {112, 8748}, {186, 2689}, {242, 2728}, {273, 934}, {411, 13397}, {476, 2075}, {925, 4225}, {944, 7040}, {1294, 7454}, {1295, 7456}, {1297, 7441}, {1305, 7420}, {1766, 29014}, {2370, 7457}, {2373, 7439}, {3518, 26709}, {3565, 7415}, {5176, 6099}, {7424, 10420}, {7443, 26703}, {8750, 32719}, {8755, 32683}, {32689, 32707}

X(32706) = reflection of X(4) in X(20620)
X(32706) = trilinear pole of line X(6)X(3064)
X(32706) = inverse-in-polar-circle of X(117)
X(32706) = X(63)-isoconjugate of X(8607)
X(32706) = Λ(X(3), X(73))
X(32706) = Ψ(X(i), X(j)) for these (i,j): (3, 522), (6, 3064), (109, 4), (1813, 2)


X(32707) = BARYCENTRIC PRODUCT X(109)*X(32706)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32707) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32707) lies on these lines: {1783, 2149}, {3064, 32660}, {8607, 32643}, {23979, 32674}, {32689, 32706}


X(32708) = BARYCENTRIC PRODUCT X(110)*X(1300)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32708) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32708) lies on these lines: {112, 6753}, {186, 3003}, {249, 648}, {297, 2986}, {1300, 2715}, {2501, 32661}, {4240, 14591}, {6529, 23964}, {8753, 32729}, {18879, 32697}, {32662, 32711}

X(32708) = isogonal conjugate of X(6334)
X(32708) = polar conjugate of isotomic conjugate of X(10420)
X(32708) = trilinear pole of line X(25)X(1576)
X(32708) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 10420}, {6, 687}, {25, 18878}, {107, 5504}, {110, 1300}, {112, 2986}, {250, 15328}, {648, 14910}, {2501, 18879}, {4240, 10419}, {15421, 23964}
X(32708) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6334), (32, 686), (112, 3580), (687, 76), (1300, 850), (2986, 3267), (5504, 3265), (10420, 69), (14910, 525), (15328, 339), (18878, 305), (18879, 4563), (23964, 16237), (32713, 403)


X(32709) = BARYCENTRIC PRODUCT X(111)*X(30247)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32709) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32709) lies on these lines: {112, 32729}, {468, 10422}, {648, 691}, {8753, 14580}


X(32710) = CIRCUMCIRCLE-X(4)-ANTIPODE OF X(476)

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

X(32710) lies on the circumcircle and these lines: {2, 16167}, {3, 10420}, {4, 476}, {24, 1304}, {25, 9060}, {30, 925}, {74, 924}, {99, 340}, {107, 403}, {110, 186}, {112, 3003}, {250, 1986}, {378, 691}, {468, 1302}, {523, 1300}, {562, 930}, {935, 18533}, {1287, 7576}, {1290, 7414}, {1291, 3520}, {1825, 2222}, {1835, 26700}, {2071, 13398}, {23969, 32711} et al

X(32710) = reflection of X(i) in X(j) for these (i,j): (4, 16221), (10420, 3)
X(32710) = isogonal conjugate of X(17702)
X(32710) = inverse-in-polar-circle of X(25641)
X(32710) = circumcircle antipode of X(10420)
X(32710) = X(63)-isoconjugate of X(3018)
X(32710) = trilinear pole of line X(6)X(686)
X(32710) = Λ(X(3), X(125))
X(32710) = Λ(X(4), X(110))
X(32710) = Ψ(X(i), X(j)) for these (i,j): (3, 526), (6, 686), (476, 4), (687, 2)
X(32710) = barycentric quotient X(i)/X(j) for these (i,j): (25, 3018), (112, 7471)


X(32711) = BARYCENTRIC PRODUCT X(476)*X(32710)

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

As the barycentric product of circumcircle-X(4)-antipodes, X(32711) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32711) lies on these lines: {3018, 32650}, {23969, 32710}, {32662, 32708}

X(32711) = trilinear pole of line X(25)X(14560)


X(32712) = BARYCENTRIC PRODUCT X(477)*X(1304)

Barycentrics    a^2/((b^2 - c^2) (a^2 - b^2 - c^2) (2 a^4 - b^4 - c^4 - a^2 b^2 - a^2 c^2 + 2 b^2 c^2) (a^6 (b^2 + c^2) - a^4 (3 b^4 - 2 b^2 c^2 + 3 c^4) + a^2 (3 b^6 - 2 b^4 c^2 - 2 b^2 c^4 + 3 c^6) - (b^2 - c^2)^2 (b^4 + 3 b^2 c^2 + c^4))) : :
Trilinears    (sin^2 A)/((tan B - tan C) (2 tan A - tan B - tan C) (4 cos A + cos(A - 2B) + cos(A - 2C) - 3 cos(B - C))) : :

As the barycentric product of circumcircle-X(4)-antipodes, X(32712) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32712) lies on these lines: {648, 5664}, {1304, 32690}, {1637, 32640}, {2088, 8749}, {32715, 32733}


X(32713) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF VAN AUBEL LINE

Barycentrics    a^2/((b^2 - c^2) (a^2 - b^2 - c^2)^2) : :
Trilinears    (sin A) (tan A)/(sin 2B - sin 2C) : :

As the barycentric product of circumcircle-X(4)-antipodes, X(32713) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25), and as the barycentric product of circumcircle-X(6)-antipodes, X(32713) also lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32713) lies on these lines: {4, 1177}, {25, 8749}, {107, 110}, {112, 1576}, {132, 23583}, {133, 9934}, {159, 15259}, {162, 1633}, {182, 10002}, {184, 6525}, {206, 1249}, {250, 7468}, {393, 1974}, {512, 32695}, {520, 15384}, {685, 15352}, {692, 1783}, {823, 1492}, {1304, 9064}, {1632, 2409}, {1660, 3079}, {1990, 18374}, {2207, 8753}, {2393, 15262}, {2445, 14398}, {2485, 32649}, {2489, 32696}, {4230, 4558}, {4577, 6528}, {5317, 8751}, {6523, 6759}, {6526, 26883}, {6529, 23977}, {8743, 20410}, {8745, 19118}, {10561, 23964}, {14569, 18384}, {20031, 32716}, {23590, 32725}

X(32713) = isogonal conjugate of X(3265)
X(32713) = polar conjugate of X(3267)
X(32713) = pole wrt polar circle of trilinear polar of X(3267) (line X(125)X(339))
X(32713) = trilinear pole of line X(25)X(32) (the isogonal conjugate of the isotomic conjugate of the van Aubel line)
X(32713) = center of bianticevian conic of X(6) and X(25)
X(32713) = X(i)-isoconjugate of X(j) for these lines: {i,j}: {1, 3265}, {2, 24018}, {3, 14208}, {48, 3267}
X(32713) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 24019}, {3, 6529}, {4, 112}, {6, 107}, {19, 162}, {25, 648}, {27, 8750}, {28, 1783}, {30, 32695}, {31, 823}, {32, 6528}, {51, 16813}, {53, 933}, {92, 32676}, {99, 2207}, {100, 5317}, {101, 8747}, {108, 1172}, {109, 8748}, {110, 393}, {158, 163}, {184, 15352}, {232, 685}, {250, 2501}, {297, 32696}, {403, 32708}, {511, 20031}, {512, 23582}, {520, 23590}, {523, 23964}, {662, 1096}, {811, 1973}, {925, 8745}, {1249, 1301}, {1289, 8743}, {1297, 23977}, {1304, 1990}, {1474, 1897}, {1576, 2052}, {1974, 6331}, {2445, 6330}, {2489, 18020}, {4230, 6531}, {4235, 8753}, {4238, 8751}, {4240, 8749}, {4558, 6524}, {6587, 15384}, {14569, 18315}, {14590, 18384}, {15262, 22239}
X(32713) = barycentric quotient X(i)/X(j) for these (i,j): (3, 4143), (4, 3267), (6, 3265), (19, 14208), (25, 525), (28, 15413), (31, 24018), (32, 520), (107, 76), (108, 1231), (110, 3926), (112, 69), (158, 20948), (162, 304), (163, 326), (232, 6333), (250, 4563), (393, 850), (512, 15526), (520, 23974), (648, 305), (692, 3998), (823, 561), (1096, 1577), (1474, 4025), (1576, 394), (1783, 20336), (1973, 656), (1974, 647), (2207, 523), (2445, 441), (2489, 125), (2501, 339), (4230, 6393), (4558, 4176), (5317, 693), (6524, 14618), (6528, 1502), (6529, 264), (8745, 6563), (8747, 3261), (8750, 306), (14398, 1650), (14569, 18314), (15352, 18022), (18384, 14592), (20031, 290), (23582, 670), (23590, 6528), (23964, 99), (23977, 30737), (24019, 75), (32676, 63), (32695, 1494), (32696, 287)


X(32714) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(4)X(7)

Barycentrics    a/((a - b - c)^2 (b - c) (a^2 - b^2 - c^2)) : :
Barycentrics    a^2 (tan A/2)/(sec B - sec C) : :
Barycentrics    a^2 (tan A)/((1 + cos A) (cos B - cos C)) : :
Barycentrics    a^2 tan A sec^2(A/2)/(cos B - cos C) : :

As the barycentric product of circumcircle-X(4)-antipodes, X(32713) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25), and as the barycentric product of circumcircle-X(7)-antipodes, X(32713) also lies on conic {{A,B,C,X(109),X(651)}} with center X(478) and perspector X(56).

X(32714) lies on these lines: {4, 9372}, {19, 269}, {28, 1042}, {108, 109}, {112, 934}, {196, 222}, {207, 1394}, {223, 1767}, {240, 5018}, {278, 1086}, {281, 6180}, {513, 24033}, {608, 1119}, {648, 4569}, {651, 653}, {1118, 1406}, {1172, 3668}, {1262, 32698}, {1415, 32651}, {1419, 2331}, {1426, 7316}, {1427, 8749}, {1435, 8752}, {1461, 32674}, {1712, 2956}, {3669, 32702}, {6129, 32652}, {24027, 32699}, {32668, 32701}

X(32714) = isogonal conjugate of complement of X(17896)
X(32714) = isotomic conjugate of X(15416)
X(32714) = trilinear pole of line X(25)X(34)
X(32714) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 934}, {6, 13149}, {7, 108}, {19, 658}, {25, 4569}, {28, 4566}, {56, 18026}, {57, 653}, {85, 32674}, {92, 1461}, {99, 1426}, {100, 1119}, {101, 1847}, {107, 1439}, {109, 273}, {112, 1446}, {162, 3668}, {190, 1435}, {269, 1897}, {278, 651}, {281, 4617}, {331, 1415}, {608, 4554}, {648, 1427}, {811, 1042}, {1118, 6516}, {1262, 17924}, {4025, 24033}
X(32714) = barycentric quotient X(i)/X(j) for these (i,j): (4, 4397), (19, 3239), (25, 3900), (28, 7253), (56, 521), (57, 6332), (100, 1265), (101, 3692), (108, 8), (109, 78), (110, 1792), (112, 2287), (162, 1043), (269, 4025), (278, 4391), (513, 2968), (608, 650), (651, 345), (653, 312), (658, 304), (934, 69), (1042, 656), (1119, 693), (1262, 1332), (1415, 219), (1426, 523), (1427, 525), (1435, 514), (1439, 3265), (1446, 3267), (1461, 63), (1847, 3261), (1897, 341), (3668, 14208), (3669, 26932), (4566, 20336), (4569, 305), (4617, 348), (6516, 1264), (8059, 271), (13149, 76), (17924, 23978), (18026, 3596), (24027, 1331), (24033, 1897), (32668, 1815), (32674, 9)


X(32715) = BARYCENTRIC PRODUCT X(74)*X(112)

Barycentrics    a^4/((b^2 - c^2) (a^2 - b^2 - c^2) (2 a^4 - a^2 (b^2 + c^2) - (b^2 - c^2)^2)) : :
Barycentrics    a^4/(SA (SB - SC) (SA SB + SA SC - 2 SB SC)) : :
Barycentrics    a^4/((tan B - tan C) (2 tan A - tan B - tan C)) : :
Barycentrics    a^4/((sin 2B - sin 2C) (2 sin 2A - sin 2B - sin 2C)) : :
Barycentrics    a^3/((sin 2B - sin 2C) (cos A - 2 cos B cos C)) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32715) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

The trilinear polar of X(32715) passes through X(32) and the barycentric square of X(647).

X(32715) lies on these lines: {74, 1177}, {110, 250}, {112, 32738}, {512, 32695}, {685, 879}, {687, 4240}, {1576, 32640}, {1976, 8749}, {2159, 32673}, {2211, 32740}, {2393, 15291}, {2433, 2445}, {18374, 18877}, {32712, 32733} et al

X(32715) = polar conjugate of isotomic conjugate of X(32640)
X(32715) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 32695}, {4, 32640}, {6, 1304}, {32, 16077}, {74, 112}, {110, 8749}, {162, 2159}, {250, 2433}, {1301, 15291}, {1576, 16080}
X(32715) = barycentric quotient X(i)/X(j) for these (i,j): (32, 9033), (74, 3267), (112, 3260), (1304, 76), (1576, 11064), (2159, 14208), (2433, 339), (8749, 850), (16077, 1502), (32695, 264), (32640, 69)


X(32716) = BARYCENTRIC PRODUCT X(98)*X(26714)

Barycentrics    a^2/((b^2 - c^2) (b^4 + c^4 - a^2 b^2 - a^2 c^2) (a^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2)) : :
Barycentrics    a^3 sec(A + ω)/((b^2 - c^2) sin 2A + b^2 sin 2C - c^2 sin 2B) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32716) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32716) lies on these lines: {110, 2966}, {262, 14355}, {1177, 11653}, {1576, 2715}, {1976, 9418}, {4577, 17932}, {20031, 32713}

X(32716) = trilinear pole of line X(32)X(263)
X(32716) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 6037}, {98, 26714}, {262, 2715}, {263, 2966}
X(32716) = barycentric quotient X(i)/X(j) for these (i,j): (263, 2799), (2715, 183), (2966, 20023), (6037, 76), (26714, 325)


X(32717) = BARYCENTRIC PRODUCT X(99)*X(729)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32717) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32717) lies on these lines: {110, 4590}, {249, 1576}, {691, 729}, {692, 4567}, {886, 4577}, {892, 5027}, {1976, 2966}, {5467, 17938} et al

X(32717) = isogonal conjugate of X(9148)
X(32717) = trilinear pole of line X(32)X(110)
X(32717) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 9150}, {32, 886}, {99, 729}, {110, 3228}, {691, 14608}
X(32717) = barycentric quotient X(i)/X(j) for these (i,j): (6, 9148), (32, 888), (99, 30736), (110, 538), (729, 523), (886, 1502), (1576, 3231), (3228, 850), (9150, 76)


X(32718) = BARYCENTRIC PRODUCT X(100)*X(739)

Barycentrics    a^3/((b - c) (a b + a c - 2 b c)) : :
Barycentrics    a^4/((csc B - csc C) (2 csc A - csc B - csc C)) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32718) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32718) lies on these lines: {110, 898}, {692, 1252}, {739, 919}, {889, 4577}, {1110, 32739}, {1492, 4607}, {2210, 32665}

X(32718) = trilinear pole of line X(32)X(692)
X(32718) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 898}, {31, 4607}, {32, 889}, {100, 739}, {692, 3227}, {31002, 32739}
X(32718) = barycentric quotient X(i)/X(j) for these (i,j): (31, 4728), (32, 891), (101, 6381), (692, 536), (739, 693), (889, 1502), (898, 76), (4607, 561), (32739, 899)


X(32719) = BARYCENTRIC PRODUCT X(101)*X(106)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32719) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32719) lies on these lines: {59, 4057}, {101, 32686}, {106, 32682}, {110, 901}, {667, 692}, {898, 6551}, {900, 13136}, {1492, 3257}, {1919, 23990}, {2426, 2441}, {5548, 32736}, {8750, 32705}, {8752, 32699}, {9456, 32666}, {32642, 32659}, {32645, 32656} et al

X(32719) = isogonal conjugate of isotomic conjugate of X(901)
X(32719) = isogonal conjugate of complement of polar conjugate of isogonal conjugate of X(23184)
X(32719) = isogonal conjugate of anticomplement of X(3310)
X(32719) = trilinear pole of line X(32)X(1977)
X(32719) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 32665}, {6, 901}, {31, 3257}, {32, 4555}, {88, 692}, {100, 9456}, {101, 106}, {145, 32645}, {649, 9268}, {667, 5376}, {902, 4638}, {903, 32739}, {995, 32686}, {1015, 6551}, {1331, 8752}, {1797, 8750}, {1897, 32659}, {6336, 32656}, {6635, 23990}
X(32719) = barycentric quotient X(i)/X(j) for these (i,j): (31, 3762), (32, 900), (101, 3264), (106, 3261), (692, 4358), (901, 76), (1919, 1647), (3257, 561), (4555, 1502), (5376, 6386), (6551, 31625), (9268, 1978), (9456, 693), (23990, 6550), (32645, 4373), (32656, 3977), (32659, 4025), (32665, 75), (32739, 519)


X(32720) = BARYCENTRIC PRODUCT X(102)*X(26715)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32720) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32720) lies on the line {26715, 32683}


X(32721) = BARYCENTRIC PRODUCT X(103)*X(26716)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32721) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32721) lies on these lines: {26716, 32684}, {32642, 32739}


X(32722) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(104)

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

X(32722) lies on the circumcircle and these lines: {6, 104}, {100, 2427}, {103, 4256}, {105, 957}, {187, 2699}, {644, 9059}, {739, 1384}, {1309, 1783}, {1415, 2720}, {2726, 3230}, {2751, 5526}, {32685, 32723} et al

X(32722) = Λ(X(2), X(905))
X(32722) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(650)
X(32722) = circumcircle intercept, other than X(104), of circle {{X(15),X(16),X(104)}} (or V(X(104))
X(32722) = inverse-in-Schoute-circle of X(2699)
X(32722) = barycentric product X(100)*X(957)
X(32722) = barycentric quotient X(957)/X(693)


X(32723) = BARYCENTRIC PRODUCT X(104)*X(32722)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32723) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32723) lies on these lines: {692, 32641}, {32685, 32722}


X(32724) = BARYCENTRIC PRODUCT X(105)*X(8693)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32724) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32724) lies on these lines: {692, 919}, {32666, 32739}

X(32724) = barycentric product X(i)*X(j) for these lines: {i,j}: {105, 8693}, {919, 1002}
X(32724) = barycentric quotient X(i)/X(j) for these (i,j): (919, 4441), (8693, 3263)


X(32725) = BARYCENTRIC PRODUCT X(107)*X(26717)

Barycentrics    a^2/((b^2 - c^2) (a^2 - b^2 - c^2)^2 (a^6 (b^2 + c^2) - 2 a^4 (b^4 - b^2 c^2 + c^4) + a^2 (b^2 - c^2)^2 (b^2 + c^2) - 2 b^2 c^2 (b^2 - c^2)^2)) : :
Barycentrics    a^4/((csc 2B - csc 2C) (2 csc 2A - csc 2B - csc 2C)) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32725) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32725) lies on these lines: {110, 23582}, {1576, 23964}, {1976, 20031}, {23590, 32713}, {26717, 32687}

X(32725) = trilinear pole of line X(32)X(32713)
X(32725) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 26717}
X(32725) = barycentric quotient X(i)/X(j) for these (i,j): (26717, 3265)


X(32726) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(108)

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

X(32726) lies on the circumcircle and these lines: {6, 108}, {48, 109}, {99, 1812}, {100, 219}, {101, 212}, {107, 1172}, {110, 2193}, {112, 2194}, {187, 2714}, {222, 934}, {927, 1814}, {1055, 1949}, {1295, 2431}, {1951, 14733}, {2720, 14578}, {2722, 13509}, {2730, 5526}, {32688, 32727} et al

X(32726) = trilinear pole of line X(6)X(1946)
X(32726) = Ψ(X(i), X(j)) for these (i,j): (4, 650), (6, 1946), (651, 3), (18026, 2)
X(32726) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(19)
X(32726) = circumcircle intercept, other than X(108), of circle {{X(15),X(16),X(108)}} (or V(X(108))
X(32726) = inverse-in-Schoute-circle of X(2714)
X(32726) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 23707}
X(32726) = barycentric quotient X(i)/X(j) for these (i,j): (23707, 75), (32727, 108)


X(32727) = BARYCENTRIC PRODUCT X(108)*X(32726)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32727) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32727) lies on these lines: {692, 7115}, {32688, 32726}


X(32728) = BARYCENTRIC PRODUCT X(109)*X(2291)

Barycentrics    a^4/((b - c) (a - b - c) (a (2 a - b - c) - (b - c)^2)) : :
Barycentrics    a^4/((cos B - cos C) (2 cos A - cos B - cos C)) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32728) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32728) lies on these lines: {110, 14733}, {692, 2149}, {884, 32735}, {2291, 32689}

X(32728) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 14733}, {109, 2291}
X(32728) = barycentric quotient X(i)/X(j) for these (i,j): (14733, 76)


X(32729) = BARYCENTRIC PRODUCT X(110)*X(111)

Barycentrics    a^4/((b^2 - c^2) (2 a^2 - b^2 - c^2)) : :
Barycentrics    a^4/((cot B - cot C) (2 cot A - cot B - cot C)) : :
Barycentrics    (SB + SC)^2/((SB - SC) (2 SA - SB - SC)) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32729) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

Let A1B1C1 and A2B2C2 be the 1st and 2nd Parry triangles. Let A' be the barycentric product A1*A2, and define B', C' cyclically. The lines AA', BB', CC' concur in X(32729).

X(32729) lies on these lines: {6, 32741}, {23, 895}, {110, 249}, {111, 1495}, {112, 32709}, {163, 32672}, {184, 10558}, {187, 9215}, {237, 14908}, {669, 1576}, {685, 4240}, {690, 17708}, {881, 17938}, {892, 4577}, {923, 32671}, {2420, 2444}, {2966, 9147}, {5968, 6800}, {8753, 32708}, {9178, 9206}, {9544, 10559}, {10561, 23964}, {11003, 21460}, {14567, 18374}, {14602, 19626}, {32648, 32661}

X(32729) = isogonal conjugate of X(35522)
X(32729) = trilinear pole of line X(32)X(1084)
X(32729) = X(92)-isoconjugate of X(14417)
X(32729) = barycentric product of PU(62)
X(32729) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 691}, {15, 9206}, {16, 9207}, {32, 892}, {110, 111}, {112, 895}, {163, 897}, {249, 9178}, {250, 10097}, {648, 14908}, {662, 923}, {670, 19626}, {671, 1576}, {1992, 32648}, {2420, 9139}, {2715, 5968}, {4558, 8753}, {11634, 15387}, {14574, 18023}, {17983, 32661}
X(32729) = barycentric quotient X(i)/X(j) for these (i,j): (32, 690), (110, 3266), (111, 850), (163, 14210), (184, 14417), (691, 76), (892, 1502), (895, 3267), (897, 20948), (923, 1577), (1576, 524), (8753, 14618), (9178, 338), (9206, 300), (9207, 301), (10097, 339), (14567, 1649), (14574, 187), (14602, 11183), (14908, 525), (19626, 512), (32648, 5485), (32661, 6390)


X(32730) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(476)

Barycentrics    a^2/(a^6 (b^2 + c^2) - 2 a^4 (b^4 + c^4) + a^2 (b^6 + c^6) - 2 b^2 c^2 (b^2 - c^2)^2) : :
Trilinears    a^2/(csc B sin(A - B) (1 + 2 cos 2C) + csc C sin(A - C) (1 + 2 cos 2B)) : :

X(32730) lies on the circumcircle and these lines: {6, 476}, {50, 110}, {98, 5996}, {99, 323}, {187, 9160}, {325, 9066}, {477, 2436}, {691, 10560}, {805, 15080}, {1141, 2623}, {1384, 32732}, {2222, 21741}, {2715, 9463}, {23969, 32731}

X(32730) = trilinear pole of line X(6)X(14270)
X(32730) = Ψ(X(6), X(14270))
X(32730) = Λ(X(2), X(94))
X(32730) = trilinear pole, wrt circumsymmedial triangle, of Fermat axis
X(32730) = circumcircle intercept, other than X(476), of circle {X(15),X(16),X(476)} (or V(X(476))
X(32730) = barycentric product X(3268)*X(32731)
X(32730) = barycentric quotient X(32731)/X(476)


X(32731) = BARYCENTRIC PRODUCT X(476)*X(32730)

Barycentrics    a^2/((b^2 - c^2) ((a^2 - b^2 - c^2)^2 - b^2 c^2) (a^6 (b^2 + c^2) - 2 a^4 (b^4 + c^4) + a^2 (b^6 + c^6) - 2 b^2 c^2 (b^2 - c^2)^2)) : :
Barycentrics    a^4/(sin(B - C) (1 + 2 cos 2A) (csc B sin(A - B) (1 + 2 cos 2C) + csc C sin(A - C) (1 + 2 cos 2B))) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32731) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32731) lies on these lines: {14560, 23588}, {23969, 32730}

X(32731) = trilinear pole of line X(32)X(14560)
X(32731) = barycentric quotient X(32730)/X(3268)


X(32732) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(477)

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

X(32732) lies on the circumcircle and these lines: {6, 477}, {98, 12112}, {187, 9161}, {476, 2437}, {1297, 3581}, {1384, 32730}, {32690, 32733}

X(32732) = Λ(X(2), X(2411))
X(32732) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(1637)
X(32732) = circumcircle intercept, other than X(477), of circle {X(15),X(16),X(477)} (or V(X(477))


X(32733) = BARYCENTRIC PRODUCT X(477)*X(32732)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32733) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32733) lies on these lines: {110, 30528}, {14560, 32650}, {32690, 32732}, {32712, 32715}


X(32734) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(5)X(6)

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

As the barycentric product of circumcircle-X(5)-antipodes, X(32734) lies on conic {{A,B,C,X(112),X(1987)}} with perspector X(51), and as the barycentric product of circumcircle-X(6)-antipodes, X(32734) also lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32734) lies on these lines: {68, 542}, {110, 925}, {112, 32692}, {154, 2351}, {159, 2871}, {184, 8754}, {206, 1976}, {485, 30427}, {486, 30428}, {685, 30450}, {847, 1614}, {924, 4558}, {1498, 16391}, {1576, 1625} et al

X(32734) = isogonal conjugate of X(6563)
X(32734) = trilinear pole of line X(32)X(51) (the isogonal conjugate of the isotomic conjugate of line X(5)X(6))
X(32734) = barycentric product X(i)*X(j) for these lines: {i,j}: {5, 32692}, {6, 925}, {68, 112}, {96, 1625}, {184, 30450}, {648, 2351}, {847, 32661}, {1576, 5392}, {4558, 14593}, {6529, 16391}
X(32734) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6563), (68, 3267), (112, 317), (847, 32661), (925, 76), (1576, 1993), (2351, 525), (14593, 14618), (16391, 4143), (30450, 18022), (32692, 95), (32661, 9723)


X(32735) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(7)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32735) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(7)-antipodes, X(32735) also lies on conic {{A,B,C,X(109),X(651)}} with center X(478) and perspector X(56).

X(32735) lies on these lines: {59, 513}, {100, 30626}, {105, 2720}, {109, 649}, {110, 927}, {294, 2182}, {666, 4581}, {667, 1262}, {677, 926}, {883, 3573}, {884, 32728}, {885, 14776}, {971, 28071}, {1404, 1438}, {1428, 1456}, {1458, 2195}, {1461, 24027}, {1576, 3733}, {1814, 3827}, {1876, 15382}, {1960, 14733}, {4617, 7339}, {7316, 32740} et al

X(32735) = trilinear pole of line X(32)X(56) (the isogonal conjugate of the isotomic conjugate of line X(6)X(7))
X(32735) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 927}, {7, 919}, {56, 666}, {100, 1462}, {105, 651}, {108, 1814}, {109, 673}, {294, 934}, {658, 2195}, {664, 1438}, {884, 1275}, {885, 1262}, {1461, 14942}, {4617, 28071}, {7339, 28132}
X(32735) = barycentric quotient X(i)/X(j) for these (i,j): (56, 918), (105, 4391), (109, 3912), (294, 4397), (651, 3263), (666, 3596), (667, 17435), (884, 1146), (885, 23978), (919, 8), (927, 76), (934, 27818), (1262, 883), (1438, 522), (1461, 9436), (1462, 693), (2195, 3239)


X(32736) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(8)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32736) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(8)-antipodes, X(32736) also lies on conic {{A,B,C,X(101),X(651)}} with center X(5452) and perspector X(55).

X(32736) lies on these lines: {101, 8687}, {110, 645}, {294, 2264}, {644, 692}, {666, 4581}, {1169, 2311}, {1576, 4557}, {1976, 14624}, {2308, 2316}, {2338, 2359}, {3939, 32739}, {5547, 32740}, {5548, 32719} et al

X(32736) = isogonal conjugate of X(3004)
X(32736) = trilinear pole of line X(32)X(55) (the isogonal conjugate of the isotomic conjugate of line X(6)X(8))
X(32736) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 8707}, {8, 8687}, {55, 6648}, {100, 2298}, {101, 1220}, {110, 14624}, {644, 961}, {692, 30710}, {1169, 3952}, {1240, 32739}, {1252, 4581}, {1897, 2359}, {4557, 14534}
X(32736) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3004), (55, 3910), (100, 20911), (101, 4357), (110, 16705), (692, 3666), (961, 24002), (1169, 7192), (1220, 3261), (2298, 693), (2359, 4025), (3952, 1228), (4557, 1211), (4581, 23989), (6648, 6063), (8687, 7), (8707, 76), (14624, 850), (32739, 1193)


X(32737) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF NAPOLEON AXIS

Barycentrics    a^2/((b^2 - c^2) (a^4 + b^4 + c^4 - 2 a^2 b^2 - 2 a^2 c^2 - b^2 c^2)) : :
Barycentrics    a^3/((3 sin^2 A - cos^2 A)(cos B sin C - sin B cos C)) : :
Barycentrics    a^2/(sin^2 A sin(2B - 2C) - sin^2 B sin(2C - 2A) - sin^2 C sin(2A - 2B)) : :
Trilinears    csc(B - C)/(3 - cot^2 A) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32737) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32737) lies on these lines: {110, 930}, {156, 25043}, {184, 11082}, {252, 1614}, {1177, 3519}, {1510, 18315}, {1576, 6140}, {1976, 2963} et al

X(32737) = isogonal conjugate of isotomic conjugate of X(930)
X(32737) = trilinear pole of line X(32)X(8565)
X(32737) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 930}, {17, 16807}, {18, 16806}, {110, 2963}, {112, 3519}, {163, 2962}, {252, 1625}, {1576, 11140}, {14586, 25043}
X(32737) = barycentric quotient X(i)/X(j) for these (i,j): (110, 7769), (930, 76), (1576, 1994), (2962, 20948), (2963, 850), (3519, 3267), (16806, 303), (16807, 302), (25043, 15415)


X(32738) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(30)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32738) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(30)-antipodes, X(32738) also lies on conic {{A,B,C,X(6),X(112)}} with perspector X(1495).

X(32738) lies on these lines: {110, 1302}, {112, 32715}, {182, 1177}, {1576, 2420}, {1974, 16240}

X(32738) = isogonal conjugate of X(30474)
X(32738) = trilinear pole of line X(32)X(1495) (the isogonal conjugate of the isotomic conjugate of line X(6)X(30))
X(32738) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 1302}, {112, 4846}
X(32738) = barycentric quotient X(i)/X(j) for these (i,j): (6, 30474), (1302, 76), (1576, 15066), (4846, 3267)


X(32739) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(31)

Barycentrics    a^4/(b - c) : :

As the barycentric product of circumcircle-X(6)-antipodes, X(32739) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(31)-antipodes, X(32739) also lies on conic {{A,B,C,X(163),X(825)}} with perspector X(560).

X(32739) lies on these lines: {31, 9447}, {32, 1977}, {41, 9247}, {42, 1976}, {71, 1177}, {99, 769}, {100, 825}, {101, 110}, {109, 649}, {112, 28624}, {184, 14827}, {190, 4577}, {514, 15378}, {657, 14776}, {685, 1897}, {692, 2874}, {1110, 32718}, {1415, 32660}, {1576, 32656}, {1918, 32740}, {1919, 23990}, {1922, 2205}, {2225, 2361}, {3185, 32664}, {3234, 9057}, {3939, 32736}, {23989, 24279}, {32666, 32724}, {32642, 32721} et al

X(32739) = isogonal conjugate of X(3261)
X(32739) = polar conjugate of isotomic conjugate of X(32656)
X(32739) = trilinear pole of line X(32)X(560) (the isogonal conjugate of the isotomic conjugate of line X(6)X(31))
X(32739) = crossdifference of every pair of points on line X(1111)X(3120)
X(32739) = barycentric product of vertices of 1st circumperp triangle
X(32739) = complement of anticomplementary conjugate of X(21225)
X(32739) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 692}, {4, 32656}, {6, 101}, {9, 1415}, {10, 1576}, {19, 906}, {31, 100}, {32, 190}, {37, 163}, {41, 651}, {42, 110}, {48, 1783}, {55, 109}, {56, 3939}, {71, 112}, {72, 32676}, {99, 1918}, {103, 2426}, {106, 23344}, {107, 4055}, {108, 212}, {162, 228}, {184, 1897}, {281, 32660}, {513, 1110}, {514, 23990}, {516, 32642}, {518, 32666}, {519, 32719}, {648, 2200}, {649, 1252}, {657, 1262}, {658, 14827}, {799, 2205}, {825, 2276}, {899, 32718}, {1011, 28624}, {1016, 1919}, {1193, 32736}, {1292, 21059}, {1501, 1978}, {1922, 3570}, {1977, 6632}, {2222, 2361}, {4554, 9447}, {6335, 9247}, {6586, 15378}, {14776, 22350}
X(32739) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3261), (31, 693), (32, 514), (37, 20948), (41, 4391), (42, 850), (48, 15413), (71, 3267), (100, 561), (101, 76), (109, 6063), (110, 310), (163, 274), (184, 4025), (190, 1502), (228, 14208), (649, 23989), (651, 20567), (657, 23978), (692, 75), (906, 304), (1110, 668), (1252, 1978), (1415, 85), (1501, 649), (1576, 86), (1783, 1969), (1897, 18022), (1918, 523), (1919, 1086), (1922, 4444), (1977, 6545), (2200, 525), (2205, 661), (3939, 3596), (4055, 3265), (9247, 905), (9447, 650), (14827, 3239), (15378, 31624), (23344, 3264), (23990, 190), (32642, 18025), (32656, 69), (32660, 348), (32666, 2481), (32718, 31002), (32719, 903), (32736, 1240), (32676, 286)


X(32740) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(512)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32740) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(512)-antipodes, X(32740) also lies on conic {{A,B,C,X(6),X(32),X(83),X(213),X(729)}} with perspector X(669).

X(32740) lies on these lines: {2, 9516}, {3, 15268}, {6, 110}, {23, 5166}, {32, 1084}, {50, 32654}, {67, 1648}, {83, 597}, {115, 15118}, {182, 14609}, {187, 13493}, {213, 692}, {512, 32741}, {524, 9225}, {575, 9966}, {685, 1990}, {691, 729}, {892, 3225}, {897, 1492}, {1177, 2492}, {1613, 10559}, {1692, 11060}, {1918, 32739}, {1976, 2422}, {2030, 9192}, {2056, 8584}, {2207, 8753}, {2211, 32715}, {3051, 10558}, {3114, 18023}, {3228, 17941}, {3589, 30786}, {5023, 6091}, {5095, 6791}, {5104, 11643}, {5106, 9145}, {5181, 10418}, {5380, 27810}, {5547, 32736}, {5618, 10036}, {6792, 11061}, {7316, 32735}, {9084, 15638}, {9407, 14601}, {9463, 10560}, {9468, 17938}, {11646, 25328}, {14567, 18374}, {16092, 16306}

X(32740) = isogonal conjugate of X(3266)
X(32740) = trilinear pole of line X(32)X(669) (the isogonal conjugate of the isotomic conjugate of line X(6)X(512))
X(32740) = crossdifference of every pair of points on line X(690)X(5181)
X(32740) = barycentric product of circumcircle-intercepts of Schoute circle
X(32740) = isotomic conjugate of isogonal conjugate of X(19626)
X(32740) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 923}, {3, 8753}, {4, 14908}, {6, 111}, {25, 895}, {31, 897}, {32, 671}, {55, 7316}, {56, 5547}, {76, 19626}, {110, 9178}, {163, 23894}, {184, 17983}, {187, 10630}, {237, 9154}, {669, 892}, {729, 14609}, {1501, 18023}, {1974, 30786}, {1976, 5968}, {3455, 14246}, {5380, 9780}, {6091, 14248}, {10415, 18374}
X(32740) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3266), (31, 14210), (32, 524), (111, 76), (163, 24039), (184, 6390), (669, 690), (671, 1502), (892, 4609), (895, 305), (897, 561), (923, 75), (1084, 1648), (1501, 187), (1974, 468), (5380, 28626), (5547, 3596), (7316, 6063), (8753, 264), (9154, 18024), (9178, 850), (9407, 5642), (9426, 351), (10630, 18023), (14567, 2482), (14601, 5967), (14609, 30736), (14908, 69), (17983, 18022), (18374, 7664), (19626, 6), (23894, 20948)


X(32741) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(690)

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

As the barycentric product of circumcircle-X(6)-antipodes, X(32741) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(690)-antipodes, X(32741) also lies on hyperbola {{A,B,C,X(6),X(187),X(249),X(512),X(524),X(598),X(843)}} with perspector X(351).

X(32741) lies on these lines: {6, 32729}, {110, 524}, {182, 9192}, {187, 1576}, {249, 6593}, {512, 32740}, {692, 21839}, {1177, 3566}, {10630, 28662}, {10765, 12367}, {17938, 18872}

X(32741) = trilinear pole of line X(32)X(351) (the isogonal conjugate of the isotomic conjugate of line X(6)X(690))
X(32741) = barycentric product X(6)*X(2770)
X(32741) = barycentric quotient X(i)/X(j) for these (i,j): (32, 2854), (2770, 76)


X(32742) = (name pending)

Barycentrics    12 a^12 b^2-46 a^10 b^4+64 a^8 b^6-54 a^6 b^8+32 a^4 b^10-8 a^2 b^12+12 a^12 c^2-40 a^10 b^2 c^2+8 a^8 b^4 c^2+65 a^6 b^6 c^2-88 a^4 b^8 c^2+47 a^2 b^10 c^2-4 b^12 c^2-46 a^10 c^4+8 a^8 b^2 c^4-10 a^6 b^4 c^4+32 a^4 b^6 c^4-82 a^2 b^8 c^4+14 b^10 c^4+64 a^8 c^6+65 a^6 b^2 c^6+32 a^4 b^4 c^6+86 a^2 b^6 c^6-10 b^8 c^6-54 a^6 c^8-88 a^4 b^2 c^8-82 a^2 b^4 c^8-10 b^6 c^8+32 a^4 c^10+47 a^2 b^2 c^10+14 b^4 c^10-8 a^2 c^12-4 b^2 c^12 : :
Barycentrics    (54 R^2 SB SC SW^2-18 SB SC SW^3+SB SW^4+SC SW^4)S^2 + (-54 R^2 SB SW-54 R^2 SC SW-18 R^2 SW^2+12 SB SW^2+12 SC SW^2-2 SW^3)S^4 + (108 R^2 + 27 SB + 27 SC - 18 SW)S^6 -2 SB SC SW^5 : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29086.

X(32742) lies on this line: {597,6055}


X(32743) = COMPLEMENT OF X(13289)

Barycentrics    a^14 b^2-3 a^12 b^4+a^10 b^6+5 a^8 b^8-5 a^6 b^10-a^4 b^12+3 a^2 b^14-b^16+a^14 c^2-4 a^12 b^2 c^2+6 a^10 b^4 c^2-5 a^8 b^6 c^2+9 a^4 b^10 c^2-11 a^2 b^12 c^2+4 b^14 c^2-3 a^12 c^4+6 a^10 b^2 c^4-6 a^8 b^4 c^4+5 a^6 b^6 c^4-13 a^4 b^8 c^4+15 a^2 b^10 c^4-4 b^12 c^4+a^10 c^6-5 a^8 b^2 c^6+5 a^6 b^4 c^6+10 a^4 b^6 c^6-7 a^2 b^8 c^6-4 b^10 c^6+5 a^8 c^8-13 a^4 b^4 c^8-7 a^2 b^6 c^8+10 b^8 c^8-5 a^6 c^10+9 a^4 b^2 c^10+15 a^2 b^4 c^10-4 b^6 c^10-a^4 c^12-11 a^2 b^2 c^12-4 b^4 c^12+3 a^2 c^14+4 b^2 c^14-c^16 : :
Barycentrics    (84 R^4 + R^2 SB + R^2 SC - 37 R^2 SW + 4 SW^2)S^2 + 36 R^4 SB SC-27 R^2 SB SC SW+4 SB SC SW^2 : :
X(32743) = 3*X[2]-X[13289], X[3]+X[19506], X[4]+X[13293], X[66]+X[19140], X[110]+X[18381], 3*X[381]+X[2935], X[399]+3*X[1853], 5*X[1656]-X[10117], X[2892]+3*X[14561], 7*X[3090]+X[13203], X[3357]+X[7728], 9*X[5055]-X[9919], 2*X[5972]-X[10282], X[6759]-3*X[14643], X[9976]-3*X[23327], X[10264]-3*X[23332], X[10606]+X[23043], X[10733]-3*X[18376], X[12893]+X[18569], X[12901]-3*X[18281], X[14864]+2*X[16534], 5*X[15040]-X[17845], 5*X[20125]+3*X[32064]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29086.

X(32743) lies on these lines: {2,13289}, {3,19506}, {4,13293}, {5,1539}, {30,15090}, {66,19140}, {74,7577}, {110,18381}, {113,2072}, {125,389}, {265,13352}, {381,2935}, {399,1853}, {403,13202}, {427,7687}, {511,15116}, {542,23300}, {858,16163}, {974,18388}, {1503,10272}, {1511,14156}, {1568,12825}, {1656,10117}, {1899,12227}, {2778,9955}, {2781,6697}, {2892,14561}, {3043,25739}, {3090,13203}, {3357,7728}, {5055,9919}, {5092,12900}, {5094,19457}, {5097,20300}, {5448,5663}, {5576,23515}, {5972,10282}, {6759,14643}, {7579,17835}, {7722,23294}, {7741,10118}, {7951,19505}, {8889,18933}, {9976,23327}, {10024,16111}, {10113,12897}, {10254,11204}, {10264,23332}, {10576,13287}, {10577,13288}, {10606,23043}, {10721,16868}, {10733,18376}, {11572,17701}, {11597,15139}, {12219,23293}, {12358,21243}, {12893,18569}, {12901,18281}, {13371,17702}, {14864,16534}, {15040,17845}, {15051,31101}, {15472,18390}, {20125,32064}

X(32743) = complement of X(13289)
X(32743) = midpoint of X(i) and X(j) for these lines: {i,j}: {3,19506}, {4,13293}, {5,23315}, {66,19140}, {110,18381}, {3357,7728}, {12893,18569}, {15131,23325}
X(32743) = reflection of X(i) in X(j) for these lines: {i,j}: {10282,5972}, {12041,25563}, {20301,20300}

X(32744) = X(3)X(14140)∩X(5)X(252)

Barycentrics    2 a^16-11 a^14 b^2+25 a^12 b^4-29 a^10 b^6+15 a^8 b^8+3 a^6 b^10-9 a^4 b^12+5 a^2 b^14-b^16-11 a^14 c^2+34 a^12 b^2 c^2-33 a^10 b^4 c^2+4 a^8 b^6 c^2+5 a^6 b^8 c^2+12 a^4 b^10 c^2-17 a^2 b^12 c^2+6 b^14 c^2+25 a^12 c^4-33 a^10 b^2 c^4+4 a^8 b^4 c^4+a^6 b^6 c^4-2 a^4 b^8 c^4+21 a^2 b^10 c^4-16 b^12 c^4-29 a^10 c^6+4 a^8 b^2 c^6+a^6 b^4 c^6-2 a^4 b^6 c^6-9 a^2 b^8 c^6+26 b^10 c^6+15 a^8 c^8+5 a^6 b^2 c^8-2 a^4 b^4 c^8-9 a^2 b^6 c^8-30 b^8 c^8+3 a^6 c^10+12 a^4 b^2 c^10+21 a^2 b^4 c^10+26 b^6 c^10-9 a^4 c^12-17 a^2 b^2 c^12-16 b^4 c^12+5 a^2 c^14+6 b^2 c^14-c^16 : :
Barycentrics    2 S^4 + (R^4+10 R^2 SB+10 R^2 SC-6 SB SC-6 R^2 SW-4 SB SW-4 SC SW+2 SW^2)S^2 -3 R^4 SB SC-2 R^2 SB SC SW+2 SB SC SW^2 : :
X(32744) = X[3]-X[14140], X[5]-X[252], X[12]-X[14102], X[30]-X[511], X[137]-X[24147], X[140]-X[6150], X[546]-X[16337], X[550]-X[14141], X[930]-X[6345], X[1263]-X[19553], X[3628]-X[10615], X[5501]-X[20414], X[10096]-X[10227], X[10126]-X[13856], X[10205]-X[14095], X[13372]-X[27090], X[22051]-X[27246], X[25043]-X[28237], X[27868]-X[30484]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29089.

X(32744) lies on these lines: {3, 14140}, {5, 252}, {12, 14102}, {30, 511}, {137, 24147}, {140, 6150}, {546, 16337}, {550, 14141}, {930, 6345}, {1263, 19553}, {3628, 10615}, {5501, 20414}, {10096, 10227}, {10126, 13856}, {10205, 14095}, {13372, 27090}, {16881, 32409}, {20030, 32536}, {22051, 27246}, {25043, 28237}, {27868, 30484}, {30480, 32638}

X(32744) = isogonal conjugate of X(32749)

X(32745) = (name pending)

Barycentrics    4 a^16-5 a^14 b^2-23 a^12 b^4+45 a^10 b^6-3 a^8 b^8-39 a^6 b^10+23 a^4 b^12-a^2 b^14-b^16-5 a^14 c^2+12 a^12 b^2 c^2-30 a^10 b^4 c^2-21 a^8 b^6 c^2+84 a^6 b^8 c^2-33 a^4 b^10 c^2-13 a^2 b^12 c^2+6 b^14 c^2-23 a^12 c^4-30 a^10 b^2 c^4+94 a^8 b^4 c^4-55 a^6 b^6 c^4-51 a^4 b^8 c^4+49 a^2 b^10 c^4-8 b^12 c^4+45 a^10 c^6-21 a^8 b^2 c^6-55 a^6 b^4 c^6+106 a^4 b^6 c^6-35 a^2 b^8 c^6-6 b^10 c^6-3 a^8 c^8+84 a^6 b^2 c^8-51 a^4 b^4 c^8-35 a^2 b^6 c^8+18 b^8 c^8-39 a^6 c^10-33 a^4 b^2 c^10+49 a^2 b^4 c^10-6 b^6 c^10+23 a^4 c^12-13 a^2 b^2 c^12-8 b^4 c^12-a^2 c^14+6 b^2 c^14-c^16 : :
Barycentrics    (162 R^4+27 R^2 SB+27 R^2 SC-99 R^2 SW-9 SB SW-9 SC SW+15 SW^2)S^4 + (-486 R^4 SB SC+243 R^2 SB SC SW+18 R^2 SB SW^2+18 R^2 SC SW^2-27 SB SC SW^2+6 R^2 SW^3-5 SB SW^3-5 SC SW^3-SW^4)S^2 + 18 R^2 SB SC SW^3-3 SB SC SW^4 : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29086.

X(32745) lies on this line: {541,597}


X(32746) = X(2)-CEVA CONJUGATE OF X(194)

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

X(32746) lies on these lines: {69, 25319}, {126, 7897}, {141, 5025}, {160, 9491}, {194, 6374}, {670, 2998}, {1368, 3314}, {3662, 3741}, {3739, 17448}, {6383, 24621}, {6389, 7836}

X(32746) = complement of X(38262)
X(32746) = complement of the isogonal conjugate of X(21001)
X(32746) = complement of the isotomic conjugate of X(20081)
X(32746) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 194}, {21001, 20081}
X(32746) = crosspoint of X(2) and X(20081)
X(32746) = barycentric product X(i)*X(j) for these lines: {i,j}: {194, 20081}, {1740, 20945}, {6374, 21001}, {16571, 17149}
X(32746) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {16571, 3223}, {20081, 2998}, {20945, 18832}, {21001, 3224}, {22152, 3504}
X(32746) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 194}, {16571, 141}, {17091, 17046}, {20081, 2887}, {20945, 626}, {21001, 10}, {21095, 21245}, {21206, 21252}, {22152, 18589}


X(32747) = X(194)-CEVA CONJUGATE OF X(2)

Barycentrics    a^4*b^4 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 + a^4*c^4 + 2*a^2*b^2*c^4 - 3*b^4*c^4 : :
X(32747) = 3 X[2] - 4 X[6374],9 X[2] - 8 X[6375],3 X[2998] - 4 X[6375],3 X[6374] - 2 X[6375]

X(32747) lies on these lines: {2, 2998}, {69, 698}, {75, 330}, {192, 17149}, {193, 25332}, {194, 15968}, {670, 8264}, {1278, 17135}, {1370, 7779}, {3186, 8782}, {3797, 18750}, {7774, 19583}, {9865, 14615}, {20245, 20535}, {21080, 21219}

X(32747) = anticomplement of X(2998)
X(32747) = reflection of X(2998) and X(6374)
X(32747) = anticomplement of the isogonal conjugate of X(1613)
X(32747) = anticomplement of the isotomic conjugate of X(194)
X(32747) = isotomic conjugate of the isogonal conjugate of X(3360)
X(32747) = X(194)-Ceva conjugate of X(2)
X(32747) = crosspoint of X(3360) and X(15965)
X(32747) = {X(2998),X(6374)}-harmonic conjugate of X(2)
X(32747) = trilinear pole, wrt anticomplementary triangle, of Lemoine axis
X(32747) = barycentric product X(i)*X(j) for these lines: {i,j}: {76, 3360}, {6374, 15965}
X(32747) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {194, 15968}, {3360, 6}, {15965, 3224}
X(32747) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6, 21299}, {31, 20081}, {32, 21223}, {101, 20983}, {163, 669}, {194, 6327}, {560, 2998}, {662, 3221}, {692, 20979}, {923, 20977}, {1333, 17157}, {1415, 23655}, {1424, 3434}, {1438, 20863}, {1613, 8}, {1740, 69}, {3186, 21270}, {3221, 21221}, {6374, 21275}, {7075, 3436}, {9456, 23633}, {9491, 21220}, {11325, 5905}, {17082, 21285}, {17149, 315}, {20794, 4329}, {21080, 21287}, {21191, 21293}, {21877, 1330}, {23301, 21294}, {23503, 148}, {23572, 149}, {24037, 4609}


X(32748) = X(1)X(6)∩X(31)X(7104)

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

X(32748) lies on the cubic K789 and these lines: {2, 6}, {31, 7104}, {32, 9490}, {187, 9427}, {237, 9468}, {669, 688}, {699, 805}, {1186, 7772}, {1197, 23576}, {1501, 15389}, {1576, 18902}, {1692, 9419}, {1914, 21762}, {1922, 19554}, {3224, 3552}, {3499, 7839}, {4173, 14820}, {6380, 9150}, {8023, 23200}, {9431, 13586}

X(32748) = isogonal conjugate of the isotomic conjugate of X(3229)
X(32748) = crosspoint of X(6) and X(9468)
X(32748) = crosssum of X(i) and X(j) for these (i,j): {2, 3978}, {3225, 8858}, {3766, 6377}, {3948, 6382}
X(32748) = crossdifference of every pair of points on line {76, 512}
X(32748) = X(i)-Ceva conjugate of X(j) for these (i,j): {805, 669}, {1691, 237}, {8789, 3051}
X(32748) = X(i)-isoconjugate of X(j) for these (i,j): {75, 3225}, {92, 8858}, {561, 699}, {1934, 32544}
X(32748) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 3229}, {31, 2227}, {32, 698}, {99, 9429}, {511, 32540}
X(32748) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {32, 3225}, {184, 8858}, {698, 1502}, {1501, 699}, {2227, 561}, {3229, 76}, {9429, 523}, {14602, 32544}, {32540, 290}
X(32748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1613, 7766}, {6, 3329, 20965}, {6, 18899, 3051}


X(32749) = ISOGONAL CONJUGATE OF X(32744)

Barycentrics    a^2 (a^16-6 a^14 b^2+16 a^12 b^4-26 a^10 b^6+30 a^8 b^8-26 a^6 b^10+16 a^4 b^12-6 a^2 b^14+b^16-5 a^14 c^2+17 a^12 b^2 c^2-21 a^10 b^4 c^2+9 a^8 b^6 c^2+9 a^6 b^8 c^2-21 a^4 b^10 c^2+17 a^2 b^12 c^2-5 b^14 c^2+9 a^12 c^4-12 a^10 b^2 c^4+2 a^8 b^4 c^4+2 a^6 b^6 c^4+2 a^4 b^8 c^4-12 a^2 b^10 c^4+9 b^12 c^4-3 a^10 c^6-5 a^8 b^2 c^6-a^6 b^4 c^6-a^4 b^6 c^6-5 a^2 b^8 c^6-3 b^10 c^6-15 a^8 c^8-4 a^6 b^2 c^8-4 a^4 b^4 c^8-4 a^2 b^6 c^8-15 b^8 c^8+29 a^6 c^10+33 a^4 b^2 c^10+33 a^2 b^4 c^10+29 b^6 c^10-25 a^4 c^12-34 a^2 b^2 c^12-25 b^4 c^12+11 a^2 c^14+11 b^2 c^14-2 c^16) (a^16-5 a^14 b^2+9 a^12 b^4-3 a^10 b^6-15 a^8 b^8+29 a^6 b^10-25 a^4 b^12+11 a^2 b^14-2 b^16-6 a^14 c^2+17 a^12 b^2 c^2-12 a^10 b^4 c^2-5 a^8 b^6 c^2-4 a^6 b^8 c^2+33 a^4 b^10 c^2-34 a^2 b^12 c^2+11 b^14 c^2+16 a^12 c^4-21 a^10 b^2 c^4+2 a^8 b^4 c^4-a^6 b^6 c^4-4 a^4 b^8 c^4+33 a^2 b^10 c^4-25 b^12 c^4-26 a^10 c^6+9 a^8 b^2 c^6+2 a^6 b^4 c^6-a^4 b^6 c^6-4 a^2 b^8 c^6+29 b^10 c^6+30 a^8 c^8+9 a^6 b^2 c^8+2 a^4 b^4 c^8-5 a^2 b^6 c^8-15 b^8 c^8-26 a^6 c^10-21 a^4 b^2 c^10-12 a^2 b^4 c^10-3 b^6 c^10+16 a^4 c^12+17 a^2 b^2 c^12+9 b^4 c^12-6 a^2 c^14-5 b^2 c^14+c^16) : :
Barycentrics    (68 R^2+4 SB+4 SC-20 SW)S^6 + (-142 R^6-116 R^4 SB-116 R^4 SC-92 R^2 SB SC+296 R^4 SW+64 R^2 SB SW+64 R^2 SC SW+20 SB SC SW-160 R^2 SW^2-8 SB SW^2-8 SC SW^2+24 SW^3)S^4 +(12 R^10-59 R^8 SB-59 R^8 SC-82 R^6 SB SC+53 R^8 SW-8 R^6 SB SW-8 R^6 SC SW-72 R^4 SB SC SW-14 R^6 SW^2+68 R^4 SB SW^2+68 R^4 SC SW^2+112 R^2 SB SC SW^2-48 R^4 SW^3-32 R^2 SB SW^3-32 R^2 SC SW^3-24 SB SC SW^3+28 R^2 SW^4+4 SB SW^4+4 SC SW^4-4 SW^5)S^2 -18 R^10 SB SC -21 R^8 SB SC SW+30 R^6 SB SC SW^2+16 R^4 SB SC SW^3-20 R^2 SB SC SW^4+4 SB SC SW^5 : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29089.

X(32749) lies on the circumcircle and these lines: {110,15345}, {930,10205}, {1510,6345}

X(32749) = isogonal conjugate of X(32744)

X(32750) = X(2)X(15351)∩X(14401)X(15183)

Barycentrics    (2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)^2*(a^8-(b^2+c^2)*a^6-((2*b^2-2*c^2)^2-b^2*c^2)*a^4+7*(b^4-c^4)*(b^2-c^2)*a^2-(3*b^4+7*b^2*c^2+3*c^4)*(b^2-c^2)^2)*(a^8-(b^2+c^2)*a^6-(2*b^2-c^2)*(b^2-2*c^2)*a^4+3*(b^4-c^4)*(b^2-c^2)*a^2-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2) : :
Barycentrics    (4*S^2+3*(SB+SC)*(12*R^2-SA-3*SW))*(5*S^2-4*(6*SA-SW)*R^2+6*SA^2-4*SB*SC-SW^2)*(9*S^2-4*(12*SA+SW)*R^2+12*SA^2-8*SB*SC+SW^2) : :

See Tran Quang Hung and César Lozada, Hyacinthos 29090.

X(32750) lies on these lines: {2, 15351}, {14401, 15183}

X(32750) = medial-isotomic conjugate of-X(15184)
X(32750) = complement of the isotomic conjugate of X(402)
X(32750) = barycentric product X(402)*X(15184)

leftri

Points Selected for Their Tripolar Coordinates: X(32751)-X(32766)

rightri

This preamble and centers X(32751)-X(32766) were contributed by Peter Moses and Clark Kimberling, June 18, 2019.

Homogeneous tripolar coordinates (henceforth simply tripolars) for a point X are any triple x : y : z of numbers (or functions of a,b,c) that are respectively proportional to the distances |AX|, |BX|, |CX|. A point X and its circumcircle-inverse have identical tripolars. The appearance of i, j; f(a,b,c) in the following table means that X(i) and X(j) are such a pair, with tripolars f(a,b,c,) : f(b,c,a) : f(c,a,b).

1 36 Sqrt[b c(b + c - a)]
2 23 Sqrt[2 b^2 + 2 c^2 - a^2]
3 (none) 1
4 186 |cos A|
5 2070 Sqrt[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]
6 187 b c Sqrt[(-a^2+2 b^2+2 c^2)]
7 32624 (b+c-a) Sqrt[a (a-b-c) (a^2+a b-2 b^2+a c+4 b c-2 c^2)]
8 17100 Sqrt[a (a^2-a b-2 b^2-a c+4 b c-2 c^2)]
9 32625 Sqrt[b c (a^4-2 a^2 b^2+b^4-4 b^3 c-2 a^2 c^2+6 b^2 c^2-4 b c^3+c^4)]
10 1324 Sqrt[a^3-2 a b^2-b^3+a b c-2 a c^2-c^3]
11 14667 (See X(11).)
12 332626 (See X(12).)
13 6104 (See X(13).)
14 6105 (See X(14).)
15 16 b c
17 32627 (See X(17).)
18 32628 (See X(18).)
19 32756 (See X(19).)
20 2071 (See X(20).)
34 32757 (See X(34).)
37 32758 (See X(37).)
42 32759 (See X(42).)
46 32760 (See X(46).)
50 32761 (See X(50).)
52 32762 (See X(52).)
265 5961 a^2((a^2 - b^2 - c^2)^2 - b^2 c^2)
1687 1688 b c Sqrt[b^2 + b^2]
3513 3514 b + c - a
5000 5001 Sqrt[SA]
5002 5003 a
5004 5005 Sqrt[b^2 + c^2]
5980 5981 a Sqrt[b^4 + b^2 c^2 + c^4]
32622 32623 Sqrt[b c]
32753 32754 Sqrt[b + c - a]
32757 32770 (pending)
32763 32764 Sqrt[a]
32765 32766 Sqrt[a^2 + b c]

If X has tripolars x: y : z, then barycentrics for X are

a^2 (D SA + T S) : : and a^2( D SA - T S ) : : , where

SA = b c cos A, S = 2 area(ABC), T = b^2 y^2 + c^2 z^2 - a^2 x^2, and

D = Sqrt[(a x + b y + c z)(- a x + b y + c z)(a x - b y + c z)(a x + b y - c z)];

For details, see X(5002). Further developments are given at

Antreas P. Hatzipolakis, Floor van Lamoen, Barry Wolk, and Paul Yiu, Concurrency of Four Euler Lines

Albrecht Hess, Transforming Tripolar into Barycentric Coordinates


X(32751) = X(3)X(76)∩X(83)X(1688)

Barycentrics    a^2 (-a^2 + b^2 + c^2) Sqrt[b^2 c^2 + c^2 a^2 + a^2 b^2] - (a^4 - b^2 c^2 - c^2 a^2 - a^2 b^2) S : :
Tripolars    sin(A + ω) : :
X(32751) = 4 (1 + Sin[w]) X[3] + Csc[w] X[76]

X(32751) lies on these lines: {3,76}, {83,1688}, {1690,7760}

X(32751) = circumcircle-inverse of X(32752)
X(32751) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {3, 1078, 32752}, {76, 12203, 32752}, {98, 99, 32752}


X(32752) = X(3)X(76)∩X(83)X(1687)

Barycentrics    a^2 (-a^2 + b^2 + c^2) Sqrt[b^2 c^2 + c^2 a^2 + a^2 b^2] + (a^4 - b^2 c^2 - c^2 a^2 - a^2 b^2) S : :
Tripolars    sin(A + ω) : :
X(32752) = 4 (1 - Sin[w]) X[3] - Csc[w] X[76]

X(32752) lies on these lines: {3,76}, {83,1687}, {1689,7760}

X(32752) = circumcircle-inverse of X(32751)
X(32752) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {3, 1078, 32751}, {76, 12203, 32751}, {98, 99, 32751}


X(32753) = (name pending)

Barycentrics    a^2 ((-a^2+b^2+c^2) Sqrt[-a^6+2 a^5 b-3 a^4 b^2+4 a^3 b^3-3 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-3 a^4 c^2+6 a^2 b^2 c^2-3 b^4 c^2+4 a^3 c^3+4 b^3 c^3-3 a^2 c^4-2 a b c^4-3 b^2 c^4+2 a c^5+2 b c^5-c^6]+2 (a^3-a^2 b+a b^2-b^3-a^2 c+b^2 c+a c^2+b c^2-c^3) S) : :
Tripolars    Sqrt[b+c-a] : :

X(32753) lies on the Stevanovic circle and this line: {3,142}

X(32753) = reflection of X(32754) in the Gergonne line
X(32753) = circumcircle-inverse of X(32754)
X(32753) = {X(3),X(1486)}-harmonic conjugate of X(32754)


X(32754) = (name pending)

Barycentrics    a^2 ((-a^2+b^2+c^2) Sqrt[-a^6+2 a^5 b-3 a^4 b^2+4 a^3 b^3-3 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-3 a^4 c^2+6 a^2 b^2 c^2-3 b^4 c^2+4 a^3 c^3+4 b^3 c^3-3 a^2 c^4-2 a b c^4-3 b^2 c^4+2 a c^5+2 b c^5-c^6]-2 (a^3-a^2 b+a b^2-b^3-a^2 c+b^2 c+a c^2+b c^2-c^3) S) : :
Tripolars    Sqrt[b+c-a] : :

X(32754) lies on the Stevanovic circle and this line: {3,142}

X(32754) = reflection of X(32753) in the Gergonne line
X(32754) = circumcircle-inverse of X(32753)
X(32754) = {X(3),X(1486)}-harmonic conjugate of X(32753)


X(32755) = (name pending)

Barycentrics    a^2*((-a^2 + b^2 + c^2)*Sqrt[-a^8 + 2*a^4*b^4 - b^8 - 4*a^6*b*c + 4*a^5*b^2*c + 4*a^2*b^5*c - 4*a*b^6*c + 4*a^5*b*c^2 - 4*a^4*b^2*c^2 + 8*a^3*b^3*c^2 - 4*a^2*b^4*c^2 + 4*a*b^5*c^2 + 8*a^3*b^2*c^3 + 8*a^2*b^3*c^3 + 2*a^4*c^4 - 4*a^2*b^2*c^4 + 2*b^4*c^4 + 4*a^2*b*c^5 + 4*a*b^2*c^5 - 4*a*b*c^6 - c^8] + 2*(a^4 - b^4 + 2*a^2*b*c - 2*a*b^2*c - 2*a*b*c^2 - c^4)*S) : :
Tripolars    (pending) : :

X(32755) lies on this line: {3, 8}

X(32755) = {X(100),X(104)}-harmonic conjugate of X(32770)
X(32755) = circumcircle-inverse of X(32770)


X(32756) = CIRCUMCIRCLE-INVERSE OF X(19)

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

X(32756) lies on these lines: {3, 19}, {650, 1946}, {5089, 5172}

X(32756) = circumcircle-inverse of X(19)


X(32757) = CIRCUMCIRCLE-INVERSE OF X(34)

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

X(32757) lies on these lines: {3, 34}, {1785, 10058}, {1870, 18861}, {1946, 6129}

X(32757) = circumcircle-inverse of X(34)
X(32757) = circumperp conjugate of X(36986)


X(32758) = CIRCUMCIRCLE-INVERSE OF X(37)

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

X(32758) lies on these 3, 37}, {36, 3290}, {172, 2915}, {187, 20872}, {502, 3444}, {650, 667}, {1325, 17737}, {3230, 5078}, {5251, 19309}, {18447, 21861}

X(32758) = circumcircle-inverse of X(37)
X(32758) = Stevanovic circle inverse of X(20989)


X(32759) = CIRCUMCIRCLE-INVERSE OF X(42)

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

X(32759) lies on these lines: {3, 42}, {649, 4079}, {3011, 17729}, {5196, 17734}, {5264, 17019}

X(32759) = circumcircle-inverse of X(42)


X(32760) = CIRCUMCIRCLE-INVERSE OF X(46)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + a^3*b*c + a^2*b^2*c - a*b^3*c - 2*a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + b^3*c^2 + 2*a^2*c^3 - a*b*c^3 + b^2*c^3 + a*c^4 - c^5) : :
Tripolars   
X(32760) = (R - r) R X[1] - 2 r^2 X[3], X[36] + 2 X[55], 2 X[1319] + X[5119], X[3434] - 4 X[6681], 8 X[6690] - 5 X[31263], X[10087] + 2 X[17010], X[10679] + 2 X[23961], 4 X[25405] - X[25415]

X(32760) lies on these lines: {1, 3}, {21, 5176}, {90, 17857}, {100, 1737}, {186, 15500}, {405, 5123}, {497, 6880}, {498, 2478}, {499, 3434}, {515, 10057}, {519, 10087}, {528, 3582}, {535, 10056}, {611, 9037}, {855, 1283}, {902, 22350}, {906, 8608}, {912, 1727}, {915, 1785}, {920, 3811}, {954, 28534}, {993, 12647}, {1399, 5399}, {1478, 6938}, {1479, 6796}, {1532, 3583}, {1698, 25875}, {1725, 5497}, {1728, 2900}, {1772, 30117}, {1837, 32141}, {1878, 11398}, {1914, 13006}, {2886, 13747}, {3085, 5080}, {3086, 20075}, {3149, 22835}, {3419, 18395}, {3476, 6950}, {3488, 10051}, {3560, 10827}, {3584, 11113}, {3585, 7680}, {3651, 16153}, {4187, 5259}, {4294, 6838}, {4302, 6925}, {4309, 6962}, {4881, 17100}, {5180, 5703}, {5218, 6947}, {5252, 6914}, {5281, 6992}, {5312, 16472}, {5433, 10948}, {6149, 19624}, {6284, 10523}, {6905, 30384}, {6909, 21578}, {6911, 23708}, {6924, 11376}, {6929, 7951}, {6936, 31452}, {6959, 7741}, {8715, 10573}, {10090, 21630}, {10572, 11491}, {10826, 11499}, {10896, 18499}, {11813, 13411}, {12739, 14988}, {13405, 16152}

X(32760) = midpoint of X(55) and X(5172)
X(32760) = reflection of X(36) and X(5172)
X(32760) = circumcircle-inverse of X(46)
X(32760) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5010, 14793}, {3, 55, 5119}, {3, 1319, 36}, {3, 3295, 10966}, {3, 11508, 1}, {35, 36, 2077}, {35, 14795, 10902}, {35, 14798, 3}, {35, 15931, 5010}, {36, 5537, 484}, {55, 56, 10679}, {55, 8069, 1}, {55, 24929, 3746}, {55, 32613, 35}, {56, 10679, 25415}, {56, 23961, 36}, {1381, 1382, 46}, {2077, 2078, 36}, {3295, 22765, 5048}, {3295, 22766, 1}, {3560, 11501, 10827}, {11249, 26358, 30323}, {14796, 14797, 5697}, {23961, 25405, 56}


X(32761) = CIRCUMCIRCLE-INVERSE OF X(50)

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

X(32761) lies on these lines: {2, 249}, {3, 6}, {4, 14591}, {30, 19627}, {49, 18321}, {110, 3016}, {112, 9161}, {115, 17702}, {184, 512}, {246, 20976}, {477, 2549}, {691, 10560}, {842, 3431}, {868, 5475}, {1147, 31848}, {1511, 2493}, {1625, 9696}, {1915, 14537}, {2871, 3455}, {3269, 32607}, {5012, 9218}, {5477, 15357}, {6785, 15033}, {6792, 21843}, {7748, 14585}, {7749, 10413}, {14355, 18333}, {18334, 32662}

X(32761) = circumcircle-inverse of X(50)
X(32761) = Brocard-circle-inverse of X(2088)
X(32761) = second-Lemoine-circle-inverse of X(18449)
X(32761) = Moses-circle-inverse of X(3284)
X(32761) = X(1577)-isoconjugate of X(9160)
X(32761) = crosssum of X(31862) and X(31863)
X(32761) = crossdifference of every pair of points on line {523, 3580}
X(32761) = barycentric quotient X(1576)/X(9160)
X(32761) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 2088}, {6, 2420, 32}, {371, 372, 18114}, {1379, 1380, 50}, {1666, 1667, 18449}, {2028, 2029, 3284}


X(32762) = CIRCUMCIRCLE-INVERSE OF X(52)

Barycentrics    a^2*(a^10 - 4*a^8*b^2 + 7*a^6*b^4 - 7*a^4*b^6 + 4*a^2*b^8 - b^10 - 4*a^8*c^2 + 7*a^6*b^2*c^2 - 2*a^4*b^4*c^2 - 3*a^2*b^6*c^2 + 2*b^8*c^2 + 7*a^6*c^4 - 2*a^4*b^2*c^4 + 2*a^2*b^4*c^4 - b^6*c^4 - 7*a^4*c^6 - 3*a^2*b^2*c^6 - b^4*c^6 + 4*a^2*c^8 + 2*b^2*c^8 - c^10) : :
Barycentrics    Sin[A] (Cos[A + w] - (2 Cos[2 w] - 1) Csc[w] Sin[2 A] Sin[B] Sin[C]) : :
Tripolars   

X(32762) lies on these lines: {3, 6}, {5, 2934}, {24, 5963}, {26, 14693}, {249, 14587}, {316, 7509}, {625, 7393}, {691, 2383}, {7395, 13449}, {16188, 21284}

X(32762) = circumcircle-inverse of X(52)
X(32762) = {X(1379),X(1380)}-harmonic conjugate of X(52)


X(32763) = (name pending)

Barycentrics    a^2*(a^6 - 2*a^3*b^3 + b^6 - 2*a^3*c^3 - 2*b^3*c^3 + c^6)*((a^2 - b^2 - c^2)*Sqrt[-a^6 + 2*a^3*b^3 - b^6 + 2*a^3*c^3 + 2*b^3*c^3 - c^6] + 2*(a^3 - b^3 - c^3)*S) : :
Tripolars    Sqrt[a] : :

The barycentrics are real-valued only when ABC is acute.

X(32763) lies on this line: {3, 142}

X(32763) = circumcircle-inverse of X(32764)


X(32764) = (name pending)

Barycentrics    a^2*(a^6 - 2*a^3*b^3 + b^6 - 2*a^3*c^3 - 2*b^3*c^3 + c^6)*((a^2 - b^2 - c^2)*Sqrt[-a^6 + 2*a^3*b^3 - b^6 + 2*a^3*c^3 + 2*b^3*c^3 - c^6] - 2*(a^3 - b^3 - c^3)*S) : :
Tripolars    Sqrt[a] : :

The barycentrics are real-valued only when ABC is acute.

X(32764) lies on this line: {3, 142}

X(32764) = circumcircle-inverse of X(32763)


X(32765) = (name pending)

Barycentrics    a^2*((a^2 - b^2 - c^2)*Sqrt[-a^8 + 2*a^4*b^4 - b^8 - 2*a^6*b*c + 2*a^5*b^2*c + 2*a^2*b^5*c - 2*a*b^6*c + 2*a^5*b*c^2 - a^4*b^2*c^2 + 2*a^3*b^3*c^2 - a^2*b^4*c^2 + 2*a*b^5*c^2 + 2*a^3*b^2*c^3 + 2*a^2*b^3*c^3 + 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*b*c^5 + 2*a*b^2*c^5 - 2*a*b*c^6 - c^8] + (2*a^4 - 2*b^4 + 2*a^2*b*c - 2*a*b^2*c - 2*a*b*c^2 - 2*c^4)*S) : :
Tripolars    Sqrt[a^2 + b c] : :

The barycentrics are real-valued only when ABC is acute.

X(32765) lies on this line: {3, 10}

X(32765) = circumcircle-inverse of X(32766)


X(32766) = (name pending)

Barycentrics    a^2*((a^2 - b^2 - c^2)*Sqrt[-a^8 + 2*a^4*b^4 - b^8 - 2*a^6*b*c + 2*a^5*b^2*c + 2*a^2*b^5*c - 2*a*b^6*c + 2*a^5*b*c^2 - a^4*b^2*c^2 + 2*a^3*b^3*c^2 - a^2*b^4*c^2 + 2*a*b^5*c^2 + 2*a^3*b^2*c^3 + 2*a^2*b^3*c^3 + 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*b*c^5 + 2*a*b^2*c^5 - 2*a*b*c^6 - c^8] - (2*a^4 - 2*b^4 + 2*a^2*b*c - 2*a*b^2*c - 2*a*b*c^2 - 2*c^4)*S) : :
Tripolars    Sqrt[a^2 + b c] : :

The barycentrics are real-valued only when ABC is acute.

X(32766) lies on this line: {3, 10}

X(32766) = circumcircle-inverse of X(32765)


X(32767) = COMPLEMENT OF X(10282)

Barycentrics    a^8*b^2 - a^6*b^4 - 3*a^4*b^6 + 5*a^2*b^8 - 2*b^10 + a^8*c^2 - 4*a^6*b^2*c^2 + 3*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 6*b^8*c^2 - a^6*c^4 + 3*a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 4*b^6*c^4 - 3*a^4*c^6 - 6*a^2*b^2*c^6 - 4*b^4*c^6 + 5*a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :
X(32767) = 9 X[2] - X[9833],3 X[2] + X[18381],5 X[3] + 3 X[18405],X[3] + 3 X[23325],X[4] + 3 X[23329],5 X[5] - X[2883],3 X[5] + X[6247],X[5] + 3 X[23332],X[20] + 3 X[18376],X[64] + 7 X[3851],3 X[154] - 11 X[5070],3 X[381] + X[3357],9 X[381] - X[5895],X[382] + 3 X[11204],3 X[547] - X[16252],X[550] - 3 X[10193],X[550] + 3 X[23324],5 X[632] - 3 X[10182],X[1147] - 5 X[31283],X[1498] - 9 X[5055],5 X[1656] + 3 X[1853],5 X[1656] - X[6759],5 X[1656] + X[14864],3 X[1853] + X[6759],3 X[1853] - X[14864],3 X[2883] + 5 X[6247],X[2883] + 5 X[20299],X[2883] + 15 X[23332],7 X[3090] + X[14216],15 X[3091] + X[12250],5 X[3091] - X[22802],3 X[3357] + X[5895],7 X[3526] - 3 X[11202],9 X[3545] - X[5878],X[3627] + 3 X[23328],3 X[3830] + 5 X[8567],7 X[3832] + X[20427],5 X[3843] + 3 X[10606],3 X[3845] + X[5894],9 X[5054] - X[17845],3 X[5066] - X[5893],13 X[5067] + 3 X[32064],15 X[5071] + X[12324],3 X[5656] - 19 X[15022],X[6247] - 3 X[20299],X[6247] - 9 X[23332],X[8549] + 3 X[11178],X[9833] - 3 X[10282],X[9833] + 3 X[18381],X[9927] + 3 X[18281],3 X[10250] + X[15069],X[12250] + 3 X[22802],X[13093] + 15 X[19709],X[13289] - 5 X[15059],X[13293] + 3 X[14644],X[13346] + 3 X[14852],3 X[14076] - X[21230],5 X[14530] - 21 X[15703],5 X[15027] + 3 X[15131],7 X[15057] - 3 X[16219],3 X[15061] + X[19506],5 X[18383] - 3 X[18405],X[18383] - 3 X[23325],X[18405] - 5 X[23325],X[20299] - 3 X[23332],X[21230] + 3 X[32351]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29094.

X(32767) lies on these lines: {2, 9833}, {3, 18383}, {4, 11270}, {5, 2883}, {20, 18376}, {30, 20191}, {51, 26917}, {64, 3851}, {125, 389}, {140, 13470}, {154, 5070}, {185, 7577}, {186, 11572}, {343, 15606}, {381, 3357}, {382, 11204}, {403, 13474}, {427, 10110}, {468, 13419}, {511, 5449}, {542, 9820}, {546, 2777}, {547, 16252}, {550, 10193}, {575, 18952}, {578, 5094}, {632, 10182}, {858, 15644}, {1092, 30744}, {1147, 31283}, {1204, 7547}, {1209, 3819}, {1216, 14076}, {1493, 11232}, {1495, 14940}, {1498, 5055}, {1503, 3628}, {1531, 11440}, {1656, 1853}, {1885, 7687}, {2072, 5907}, {2781, 10095}, {3090, 14216}, {3091, 7703}, {3520, 13851}, {3526, 11202}, {3541, 18390}, {3545, 5878}, {3581, 32395}, {3627, 23328}, {3830, 8567}, {3832, 20427}, {3843, 10606}, {3845, 5894}, {3850, 15311}, {5020, 32321}, {5054, 17845}, {5066, 5893}, {5067, 32064}, {5071, 12324}, {5498, 30522}, {5562, 23293}, {5576, 5943}, {5651, 31282}, {5656, 15022}, {5663, 32184}, {5972, 12134}, {6143, 12254}, {6640, 18474}, {6723, 16238}, {7505, 11550}, {7507, 11438}, {7553, 32223}, {7574, 32365}, {7603, 32445}, {8549, 11178}, {8681, 23307}, {9927, 15123}, {10113, 25564}, {10117, 18369}, {10224, 13561}, {10226, 18379}, {10250, 15069}, {10254, 10575}, {10255, 12162}, {10274, 13353}, {11245, 12242}, {11264, 32376}, {11381, 16868}, {11585, 11793}, {12006, 13413}, {12370, 15113}, {13093, 19709}, {13154, 15577}, {13160, 16836}, {13289, 15059}, {13293, 14644}, {13346, 14852}, {13382, 18388}, {13383, 29012}, {13406, 14915}, {14530, 15703}, {14627, 17847}, {14810, 18382}, {15027, 15131}, {15037, 17824}, {15057, 16219}, {15061, 19506}, {15116, 20301}, {15578, 17714}, {17702, 23336}, {17712, 25337}, {18488, 23515}, {18567, 32210}, {23300, 24206}, {31724, 32110}

X(32767) = complement of X(10282)
X(32767) = complement of the isogonal of X(15319)
X(32767) = X(15319)-complementary conjugate of X(10)
X(32767) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 18383}, {5, 20299}, {125, 32743}, {546, 6696}, {5449, 13371}, {6697, 20300}, {6759, 14864}, {10113, 25564}, {10193, 23324}, {10224, 13561}, {10226, 18379}, {10282, 18381}, {14076, 32351}, {14810, 18382}, {15116, 20301}, {18567, 32210}, {23300, 24206}
X(32767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18381, 10282}, {3, 23325, 18383}, {5, 23332, 20299}, {125, 1594, 389}, {125, 3574, 26879}, {1594, 26879, 3574}, {1656, 1853, 6759}, {1853, 6759, 14864}, {3574, 26879, 389}, {6143, 25739, 13367}, {7577, 23294, 185}, {11585, 21243, 11793}, {13353, 15139, 10274}


X(32768) = COMPLEMENT OF X(32769)

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

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29097.

X(32768) lies on this line: {2, 32769}

X(32768) = complement of X(32769)

X(32769) = ANTICOMPLEMENT OF X(32768)

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

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29097.

X(32769) lies on these lines: {2, 32768}, {10625, 15331}

X(32769) = anticomplement of X(32768)

X(32770) = (name pending)

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

X(32770) lies on this line: {3, 8}

X(32770) = {X(100),X(104)}-harmonic conjugate of X(32755)
X(32770) = circumcircle inverse of X(32755)

leftri

Centers of degree 3 with coefficients in {-1,0,1}: X(32771)-X(32784)

rightri

Centers X(32771)-X(32784) were contributed by Peter Moses, June 20, 2019:

Each center in this section has barycentrics of the form p(a,b,c) : : , where p(a,b,c) is a polynomial homogeneous of degree 3 in a,b,c, with coefficents in the set {-1, 0 , 1}. For more of these, see also X(32842)-X(32866), X(32911)-X(32950), and X(33064)-X(33175).


X(32771) = X(1)X(321)∩X(2)X(38)

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

X(32771) lies on these lines: {1, 321}, {2, 38}, {7, 26034}, {8, 2650}, {10, 3681}, {31, 894}, {37, 17157}, {42, 75}, {43, 4359}, {51, 17049}, {55, 4363}, {56, 7211}, {57, 29828}, {72, 31339}, {81, 4362}, {86, 5311}, {100, 3980}, {142, 25961}, {171, 26227}, {192, 1962}, {200, 25590}, {210, 3739}, {226, 25760}, {238, 26223}, {274, 869}, {312, 3720}, {354, 30942}, {518, 30969}, {551, 4135}, {561, 1909}, {611, 26000}, {612, 3263}, {726, 28606}, {740, 17018}, {748, 16823}, {750, 7081}, {870, 3112}, {873, 7033}, {899, 19804}, {908, 25960}, {940, 17763}, {968, 3729}, {976, 1010}, {977, 1220}, {986, 26115}, {1125, 3971}, {1278, 21806}, {1621, 3923}, {1757, 5278}, {1911, 18895}, {2177, 17116}, {2308, 3758}, {2345, 3475}, {2887, 29667}, {3009, 31997}, {3120, 29685}, {3159, 27785}, {3175, 15569}, {3187, 4649}, {3190, 18698}, {3293, 28612}, {3315, 29668}, {3474, 7222}, {3589, 29852}, {3616, 3994}, {3666, 17155}, {3677, 29826}, {3683, 17351}, {3703, 17056}, {3705, 31120}, {3715, 17259}, {3736, 30599}, {3741, 3873}, {3742, 30818}, {3745, 4670}, {3751, 5271}, {3772, 29631}, {3782, 4026}, {3797, 17032}, {3836, 27186}, {3846, 31053}, {3869, 30076}, {3874, 10479}, {3896, 4980}, {3932, 29854}, {3938, 5263}, {3961, 24342}, {3974, 4648}, {4011, 5284}, {4037, 16777}, {4046, 4665}, {4054, 24210}, {4082, 29571}, {4088, 24353}, {4358, 26102}, {4388, 24725}, {4446, 20966}, {4519, 4891}, {4655, 17483}, {4660, 20292}, {4661, 27798}, {4671, 29814}, {4672, 17127}, {4683, 5905}, {4688, 4849}, {4692, 30116}, {4697, 17126}, {4699, 21805}, {4703, 17484}, {4739, 21870}, {4850, 6685}, {4892, 25958}, {4972, 17889}, {5205, 17124}, {5220, 19732}, {5293, 16454}, {5550, 25079}, {5718, 29849}, {5750, 21101}, {5835, 15888}, {6057, 17243}, {6382, 18059}, {6533, 17749}, {6535, 17233}, {6679, 29681}, {6703, 17602}, {7191, 25496}, {7229, 10578}, {10434, 29069}, {11680, 25385}, {12263, 17397}, {13476, 14973}, {13740, 28082}, {15523, 18134}, {16569, 24589}, {16706, 29663}, {16720, 21010}, {16915, 18266}, {17030, 20456}, {17061, 29636}, {17122, 26627}, {17135, 31025}, {17147, 17592}, {17150, 19717}, {17163, 20011}, {17234, 29687}, {17279, 29851}, {17289, 24943}, {17369, 29638}, {17449, 31241}, {17591, 29825}, {17716, 20045}, {17718, 29846}, {17720, 29845}, {17724, 29848}, {17874, 20237}, {18139, 29674}, {18743, 30950}, {19784, 24159}, {19786, 29647}, {19869, 26728}, {20711, 26107}, {20909, 23655}, {21350, 24674}, {24174, 26030}, {24295, 29672}, {24321, 24333}, {24330, 24357}, {24456, 26976}, {24709, 26105}, {24789, 29850}, {24924, 30584}, {25525, 29857}, {25526, 30142}, {25959, 28595}, {27475, 30821}

X(32771) =


X(32772) = X(1)X(321)∩X(2)X(31)

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

X(32772) lies on these lines: {1, 321}, {2, 31}, {6, 4042}, {10, 1203}, {11, 6703}, {21, 36}, {38, 894}, {42, 3996}, {55, 16405}, {57, 29826}, {58, 19863}, {75, 17017}, {81, 3741}, {86, 310}, {100, 6685}, {142, 4224}, {190, 3989}, {239, 21020}, {244, 1281}, {274, 21415}, {312, 5311}, {333, 2308}, {354, 4670}, {474, 27639}, {497, 2268}, {561, 870}, {614, 10436}, {740, 17011}, {756, 16830}, {940, 30942}, {975, 25591}, {978, 16454}, {984, 26223}, {1001, 1011}, {1010, 1193}, {1100, 3706}, {1215, 3920}, {1220, 10459}, {1386, 31993}, {1449, 17156}, {1471, 27339}, {1621, 4203}, {1699, 19645}, {1724, 19858}, {1757, 4981}, {1836, 4657}, {1848, 4206}, {1909, 18064}, {1961, 4358}, {1962, 3685}, {2049, 16466}, {2298, 4071}, {2344, 32664}, {2886, 29631}, {2895, 3775}, {2975, 30076}, {3112, 18091}, {3120, 14012}, {3218, 4697}, {3219, 4672}, {3550, 29825}, {3589, 3925}, {3616, 4195}, {3624, 16342}, {3666, 4418}, {3703, 17369}, {3745, 17763}, {3750, 29822}, {3757, 17469}, {3772, 29636}, {3821, 20292}, {3842, 27065}, {3873, 29652}, {3914, 17023}, {3923, 28606}, {3966, 17303}, {3980, 4850}, {4038, 8025}, {4046, 14459}, {4357, 4683}, {4359, 24342}, {4360, 4365}, {4363, 17155}, {4383, 26037}, {4387, 16777}, {4423, 15668}, {4429, 29663}, {4432, 10180}, {4438, 29664}, {4514, 29685}, {4649, 17135}, {4682, 30818}, {4693, 27804}, {4716, 17163}, {4722, 17120}, {4854, 17045}, {4865, 29667}, {4886, 8013}, {4972, 29633}, {4974, 27798}, {5014, 29659}, {5248, 16452}, {5255, 26115}, {5269, 29828}, {5271, 16475}, {5278, 16468}, {5695, 20182}, {5718, 29846}, {6536, 17322}, {6686, 9342}, {7081, 31264}, {7083, 16352}, {7191, 24325}, {8053, 19339}, {8692, 19749}, {9313, 30909}, {9347, 29649}, {10453, 17379}, {10582, 24179}, {10886, 13478}, {11680, 29635}, {13733, 28628}, {14006, 17923}, {14829, 31241}, {15523, 17289}, {15988, 24997}, {16445, 25498}, {16477, 19742}, {16480, 29576}, {16484, 19740}, {16706, 29684}, {16827, 16926}, {17056, 29632}, {17061, 29834}, {17063, 26627}, {17140, 17598}, {17147, 17600}, {17150, 31025}, {17234, 29677}, {17279, 29854}, {17368, 26061}, {17381, 29647}, {17686, 23682}, {17716, 26227}, {17718, 29848}, {17720, 29847}, {17723, 29849}, {17889, 19271}, {18134, 24943}, {18139, 29637}, {19738, 28650}, {20132, 31027}, {20148, 27035}, {24295, 29653}, {24725, 27184}, {24789, 29852}, {25385, 29645}, {25441, 25639}, {25524, 28348}, {25525, 29855}, {26102, 31005}, {26105, 30943}, {26128, 29648}, {27186, 29666}, {29860, 30588}

X(32772) = complement of X(33083)


X(32773) = X(1)X(977)∩X(2)X(11)

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

X(32773) lies on these lines: {1, 977}, {2, 11}, {4, 1220}, {6, 4388}, {8, 1211}, {10, 312}, {31, 29631}, {33, 5174}, {37, 29641}, {38, 1227}, {42, 4417}, {43, 3846}, {56, 4201}, {63, 24723}, {75, 305}, {76, 18057}, {81, 6327}, {141, 10453}, {171, 4660}, {192, 3703}, {209, 3869}, {238, 25453}, {239, 3966}, {319, 17156}, {321, 29667}, {350, 5224}, {354, 3662}, {495, 16052}, {518, 27184}, {595, 20083}, {614, 16706}, {748, 17352}, {750, 29845}, {846, 4438}, {894, 1836}, {899, 25960}, {902, 29863}, {940, 4645}, {958, 26117}, {962, 5799}, {968, 29857}, {982, 3821}, {984, 4425}, {999, 11359}, {1213, 23918}, {1215, 3944}, {1233, 3673}, {1478, 17677}, {1479, 13740}, {1486, 25494}, {1654, 4042}, {1738, 19804}, {1757, 4703}, {1818, 24550}, {1848, 1869}, {1962, 29643}, {1999, 3416}, {2049, 19865}, {2177, 29846}, {2345, 21956}, {2476, 26115}, {2975, 17676}, {3006, 28606}, {3120, 29685}, {3136, 27042}, {3175, 3790}, {3240, 5741}, {3314, 17302}, {3475, 26132}, {3616, 4202}, {3617, 3974}, {3661, 3706}, {3666, 3705}, {3677, 17304}, {3681, 26580}, {3687, 3755}, {3717, 4656}, {3720, 17234}, {3722, 29848}, {3739, 21949}, {3743, 30172}, {3744, 29634}, {3745, 29841}, {3750, 3771}, {3757, 3772}, {3782, 24349}, {3836, 26102}, {3840, 24217}, {3873, 17184}, {3886, 19815}, {3920, 5014}, {3936, 17018}, {3959, 21954}, {3980, 24715}, {3995, 31079}, {3996, 30832}, {4030, 17602}, {4073, 4357}, {4193, 26030}, {4195, 6284}, {4205, 19853}, {4234, 4302}, {4358, 29679}, {4387, 17280}, {4398, 17155}, {4442, 28605}, {4450, 17126}, {4657, 20541}, {4676, 5294}, {4683, 17347}, {4872, 10436}, {4884, 17246}, {4891, 17231}, {4999, 19278}, {5016, 17016}, {5057, 26223}, {5241, 26038}, {5259, 19846}, {5264, 25441}, {5484, 12513}, {5550, 17674}, {5698, 26065}, {5749, 9812}, {6679, 8616}, {6682, 17774}, {6685, 17717}, {7069, 25024}, {7081, 17720}, {8543, 28776}, {9664, 24275}, {9668, 11354}, {10582, 17282}, {11109, 11393}, {11110, 19854}, {11269, 14829}, {13725, 19843}, {13728, 24390}, {15171, 17698}, {15523, 17233}, {15985, 21299}, {16060, 27309}, {16484, 29642}, {16823, 24789}, {17017, 17380}, {17063, 24169}, {17127, 29868}, {17235, 21342}, {17306, 24392}, {17354, 26061}, {17378, 31134}, {17381, 29647}, {17469, 29636}, {17522, 20988}, {17550, 26965}, {17592, 29671}, {17598, 29844}, {17671, 30107}, {17715, 29656}, {17716, 17766}, {17719, 29670}, {17722, 29650}, {17792, 21334}, {17889, 24325}, {18139, 25959}, {19270, 26363}, {19273, 31493}, {19823, 19993}, {20011, 31037}, {20173, 25006}, {21020, 23928}, {21026, 29854}, {22267, 26686}, {23682, 31997}, {24357, 25345}, {24551, 24678}, {24703, 27064}, {24752, 25978}, {25496, 29633}, {25914, 26093}, {25961, 30950}, {27047, 27313}, {28595, 29674}, {29632, 31237}, {29839, 30811}

X(32773) =


X(32774) = X(1)X(4202)∩X(2)X(37)

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

X(32774) lies on these lines: {1, 4202}, {2, 37}, {6, 17184}, {10, 3891}, {31, 3821}, {38, 25453}, {42, 26128}, {55, 26230}, {57, 21376}, {63, 17304}, {81, 3662}, {86, 17173}, {100, 29634}, {141, 3187}, {142, 20268}, {171, 29636}, {226, 7225}, {238, 29852}, {244, 29635}, {306, 3946}, {333, 17305}, {354, 29829}, {379, 2140}, {443, 1058}, {693, 25603}, {726, 26061}, {740, 24943}, {748, 4425}, {750, 24169}, {940, 17290}, {942, 4463}, {964, 23537}, {968, 24542}, {975, 17674}, {982, 29631}, {984, 29850}, {1104, 17676}, {1125, 3914}, {1211, 17366}, {1215, 29663}, {1255, 17244}, {1386, 6327}, {1824, 5439}, {1961, 25961}, {1962, 29642}, {1999, 17291}, {2177, 29656}, {2275, 16717}, {2308, 4655}, {2887, 17017}, {2895, 3759}, {2999, 5741}, {3006, 17599}, {3120, 25496}, {3219, 4389}, {3315, 29843}, {3416, 17150}, {3578, 17272}, {3589, 3782}, {3618, 5905}, {3624, 4442}, {3663, 5294}, {3670, 20083}, {3702, 19836}, {3744, 29831}, {3750, 29638}, {3758, 17483}, {3765, 26965}, {3836, 5311}, {3875, 3969}, {3920, 4429}, {3936, 5256}, {3938, 4085}, {3948, 30107}, {4357, 5278}, {4383, 26580}, {4392, 29868}, {4414, 6679}, {4417, 17012}, {4438, 29867}, {4514, 17024}, {4641, 17235}, {4643, 19742}, {4656, 31191}, {4660, 17469}, {4675, 8025}, {4683, 16468}, {4852, 20017}, {4865, 29819}, {4968, 19784}, {5016, 5262}, {5222, 5739}, {5233, 17020}, {5263, 29648}, {5268, 24988}, {5271, 17306}, {5287, 17282}, {5333, 17397}, {5745, 31229}, {5826, 14557}, {6682, 24892}, {6703, 26627}, {7490, 9776}, {10453, 26150}, {12610, 19645}, {16484, 29853}, {17011, 17380}, {17019, 17234}, {17025, 25958}, {17027, 30965}, {17061, 26227}, {17063, 29845}, {17064, 29826}, {17122, 29847}, {17127, 24723}, {17253, 19723}, {17325, 19732}, {17352, 27065}, {17361, 20086}, {17367, 27184}, {17372, 20046}, {17394, 20553}, {17591, 29856}, {17592, 29632}, {17594, 29855}, {17596, 29859}, {17597, 29835}, {17600, 29643}, {17715, 29836}, {17716, 29834}, {17750, 18098}, {17861, 20886}, {17889, 19271}, {18044, 28654}, {23292, 26651}, {23681, 29598}, {24046, 25441}, {24175, 24594}, {24325, 29647}, {25581, 25598}, {25760, 29821}, {27064, 29630}, {29671, 31237}

X(32774) =


X(32775) = X(1)X(3454)∩X(2)X(38)

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

X(32775) lies on these lines: {1, 3454}, {2, 38}, {6, 29636}, {9, 29855}, {31, 4683}, {37, 29632}, {42, 19786}, {55, 29848}, {81, 29645}, {100, 3821}, {141, 17602}, {171, 17184}, {210, 29850}, {238, 26230}, {312, 24943}, {321, 23689}, {354, 29845}, {518, 29631}, {612, 25527}, {614, 25960}, {750, 3662}, {896, 6646}, {899, 16706}, {902, 24723}, {908, 1125}, {940, 29847}, {976, 16062}, {1001, 20999}, {1150, 29658}, {1155, 17235}, {1211, 17061}, {1279, 29836}, {1283, 1621}, {1386, 29834}, {1757, 29859}, {1961, 18139}, {1962, 29839}, {2239, 31004}, {2887, 3920}, {2895, 3791}, {3011, 4357}, {3120, 5263}, {3219, 6679}, {3616, 5484}, {3666, 29846}, {3681, 25453}, {3712, 17246}, {3717, 30768}, {3771, 28606}, {3772, 31330}, {3782, 4418}, {3836, 5297}, {3846, 7191}, {3873, 29635}, {3874, 25441}, {3935, 4085}, {3944, 24552}, {3961, 4972}, {3989, 29865}, {3994, 17280}, {4009, 17357}, {4023, 17366}, {4026, 17724}, {4062, 4360}, {4104, 26723}, {4202, 5293}, {4204, 30961}, {4358, 29637}, {4364, 9318}, {4383, 29852}, {4388, 17469}, {4389, 4414}, {4413, 17290}, {4417, 17017}, {4423, 29853}, {4430, 29864}, {4649, 29833}, {4655, 17126}, {4657, 17718}, {4661, 29868}, {4672, 17484}, {4696, 19879}, {4697, 17483}, {4703, 17127}, {4766, 16826}, {4852, 14459}, {4865, 25958}, {5205, 17291}, {5219, 29826}, {5268, 25961}, {5284, 29672}, {5311, 18134}, {5363, 31019}, {5741, 29821}, {5904, 20083}, {6327, 17716}, {6536, 29689}, {6693, 6763}, {7018, 18064}, {7174, 29857}, {11375, 28386}, {11680, 29652}, {14829, 29683}, {17150, 31037}, {17305, 25374}, {17306, 29828}, {17599, 29849}, {17720, 30942}, {17722, 29823}, {17725, 26227}, {18743, 29677}, {19812, 29647}, {19836, 25591}, {19863, 24160}, {21093, 24295}, {24412, 24450}, {24542, 29860}, {24709, 29660}, {24789, 26037}, {25466, 27687}, {25496, 29648}, {27065, 29871}, {27131, 29666}, {29641, 31237}, {29643, 30811}, {29657, 30834}, {29671, 30831}

X(32775) =


X(32776) = X(1)X(6327)∩X(2)X(846)

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

X(32776) lies on these lines: {1, 6327}, {2, 846}, {6, 4683}, {9, 29850}, {10, 28605}, {31, 19786}, {37, 25957}, {38, 1227}, {42, 27184}, {43, 26580}, {55, 29848}, {57, 29845}, {63, 29631}, {81, 4655}, {141, 4854}, {149, 29652}, {171, 29847}, {190, 26061}, {191, 20083}, {192, 15523}, {238, 29852}, {354, 17235}, {614, 17304}, {726, 29667}, {748, 16706}, {756, 4429}, {894, 29647}, {902, 29634}, {964, 24851}, {968, 25527}, {984, 4972}, {986, 5051}, {1001, 16064}, {1125, 1770}, {1621, 26128}, {1699, 29826}, {1738, 26037}, {1836, 4657}, {1962, 18134}, {2292, 16062}, {2887, 28606}, {3175, 3844}, {3218, 29635}, {3219, 25453}, {3661, 4365}, {3662, 3720}, {3663, 17155}, {3666, 25760}, {3681, 4085}, {3685, 24943}, {3703, 17246}, {3706, 17237}, {3735, 20859}, {3752, 25960}, {3763, 4387}, {3782, 4026}, {3816, 25378}, {3846, 4850}, {3914, 4357}, {3920, 4660}, {3924, 26117}, {3925, 4364}, {3936, 17592}, {3966, 17301}, {3971, 29679}, {3989, 17247}, {3995, 29674}, {4042, 17253}, {4388, 17017}, {4392, 29655}, {4423, 17290}, {4450, 17716}, {4512, 29855}, {4645, 5311}, {4722, 17347}, {5057, 25496}, {5224, 21020}, {5249, 16778}, {5278, 24697}, {6682, 11680}, {6685, 31053}, {6703, 11246}, {7018, 30964}, {7226, 29673}, {8616, 26230}, {10453, 17236}, {12514, 27661}, {12579, 16865}, {16342, 24161}, {16705, 16891}, {17126, 29645}, {17127, 29654}, {17156, 17272}, {17165, 29659}, {17187, 17202}, {17291, 29677}, {17320, 31134}, {17323, 17599}, {17383, 29684}, {17449, 29843}, {17491, 19717}, {17594, 29846}, {17763, 26034}, {17766, 29815}, {21241, 29664}, {23537, 31339}, {24210, 30942}, {24349, 29685}, {24551, 26573}, {24627, 29662}, {25058, 30984}, {25958, 29671}, {25959, 29653}, {26223, 29633}, {26840, 29837}, {27064, 29663}, {27804, 31017}, {30632, 31008}

X(32776) =


X(32777) = X(1)X(3695)∩X(2)X(37)

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

X(32777) lies on these lines: {1, 3695}, {2, 37}, {3, 23847}, {6, 306}, {8, 1104}, {9, 440}, {10, 55}, {25, 1376}, {31, 3416}, {38, 24943}, {42, 26061}, {44, 5739}, {57, 7198}, {63, 141}, {69, 4641}, {81, 4851}, {100, 9078}, {171, 29674}, {190, 27184}, {209, 10477}, {226, 17355}, {238, 3966}, {239, 16974}, {244, 29677}, {318, 18679}, {333, 3661}, {355, 1746}, {406, 9371}, {429, 1329}, {474, 27802}, {553, 21255}, {594, 5271}, {599, 4001}, {612, 3932}, {726, 26128}, {740, 25453}, {750, 29687}, {894, 18134}, {936, 1040}, {940, 3912}, {958, 8192}, {968, 4026}, {982, 29637}, {1009, 2352}, {1125, 17599}, {1214, 14376}, {1215, 3771}, {1403, 3831}, {1427, 28739}, {1441, 28776}, {1621, 29667}, {1698, 3712}, {1708, 26942}, {1714, 5295}, {1722, 25992}, {1724, 5814}, {1766, 19542}, {1836, 2887}, {1914, 5278}, {1962, 29647}, {1999, 17233}, {2161, 2339}, {2325, 4656}, {2886, 29857}, {2901, 20083}, {2915, 25440}, {3006, 24552}, {3120, 31237}, {3187, 3969}, {3219, 4376}, {3452, 21062}, {3501, 24310}, {3589, 5256}, {3679, 3749}, {3686, 19723}, {3687, 3713}, {3705, 17721}, {3714, 5230}, {3715, 4104}, {3719, 26543}, {3729, 3782}, {3741, 4438}, {3750, 29659}, {3758, 17778}, {3763, 3977}, {3773, 4362}, {3790, 29634}, {3836, 3980}, {3840, 17728}, {3844, 4640}, {3846, 4011}, {3891, 26230}, {3914, 5695}, {3929, 17272}, {3931, 19784}, {3936, 26223}, {3961, 30615}, {3965, 23600}, {4024, 25684}, {4195, 7270}, {4204, 26037}, {4361, 26723}, {4363, 5249}, {4365, 29867}, {4387, 24210}, {4388, 4676}, {4415, 17340}, {4417, 17354}, {4418, 5880}, {4647, 19846}, {4659, 23681}, {4660, 28595}, {4675, 18139}, {4689, 9780}, {4760, 21221}, {4798, 5333}, {4863, 29673}, {4886, 17349}, {5014, 31079}, {5016, 11319}, {5057, 25958}, {5090, 17520}, {5226, 30823}, {5241, 7308}, {5247, 10371}, {5263, 29641}, {5273, 14021}, {5287, 6703}, {5328, 28656}, {5332, 19742}, {5336, 11679}, {5712, 5749}, {5737, 17293}, {5745, 21483}, {5750, 19701}, {5772, 10578}, {5791, 10479}, {5793, 24987}, {5794, 13733}, {5835, 19860}, {5905, 17351}, {6057, 17602}, {6541, 29645}, {6690, 29828}, {7283, 16062}, {7580, 12618}, {7795, 25083}, {8299, 31330}, {11374, 25645}, {11680, 29872}, {14555, 26685}, {14829, 17285}, {15985, 22370}, {16577, 25078}, {16594, 20196}, {16844, 19857}, {17023, 20182}, {17056, 17369}, {17061, 29855}, {17080, 28780}, {17184, 17276}, {17227, 26840}, {17229, 24597}, {17242, 29841}, {17334, 25734}, {17339, 30832}, {17345, 20078}, {17592, 29633}, {17595, 29596}, {17598, 29660}, {17600, 29646}, {17723, 24295}, {18141, 29579}, {18235, 26066}, {19744, 31477}, {20292, 25959}, {21245, 27052}, {21376, 24335}, {24325, 29642}, {24330, 30985}, {24691, 30965}, {24703, 25760}, {24954, 25079}, {25019, 26958}, {25591, 25681}, {27272, 31997}, {29678, 31264}, {30831, 31053}

X(32777) =


X(32778) = X(1)X(2)∩X(57)X(12588)

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

X(32778) lies on these lines: {1, 2}, {57, 12588}, {75, 2887}, {141, 982}, {171, 3416}, {190, 4703}, {192, 4425}, {238, 3966}, {305, 1930}, {312, 3773}, {321, 3944}, {333, 4438}, {345, 846}, {573, 5282}, {584, 3684}, {594, 2886}, {726, 27184}, {984, 1211}, {1215, 4417}, {1376, 5096}, {1757, 5739}, {2321, 24210}, {2345, 4071}, {3120, 25958}, {3210, 3821}, {3509, 5227}, {3596, 6382}, {3662, 24165}, {3686, 5037}, {3690, 5692}, {3717, 4104}, {3742, 17231}, {3744, 4914}, {3752, 3844}, {3790, 3971}, {3836, 19804}, {3883, 8616}, {3923, 4388}, {3932, 5743}, {3980, 4645}, {4011, 17280}, {4026, 17592}, {4038, 4851}, {4358, 25960}, {4359, 25957}, {4418, 6327}, {4429, 28595}, {4657, 17600}, {4671, 6535}, {4680, 14012}, {4865, 5263}, {5247, 5814}, {5278, 8300}, {5294, 16468}, {5300, 19271}, {5515, 20551}, {5846, 17716}, {5904, 10974}, {7281, 27542}, {8167, 17267}, {10009, 30631}, {16478, 17698}, {17123, 17279}, {17140, 31017}, {17155, 17184}, {17165, 31037}, {17229, 24217}, {17281, 24703}, {17289, 25496}, {17293, 17722}, {17490, 24169}, {17596, 17740}, {18134, 24325}, {18203, 20911}, {18788, 26118}, {19822, 24342}, {20292, 31134}, {21024, 23918}, {21241, 21829}, {21726, 31003}, {21920, 31245}, {21962, 25666}, {24589, 25961}, {26590, 27474}, {30599, 30984}, {31327, 31419}

X(32778) =


X(32779) = X(2)X(37)∩X(8)X(5266)

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

X(32779) lies on these lines: {2, 37}, {8, 5266}, {9, 21368}, {10, 21}, {22, 1376}, {43, 26061}, {55, 29667}, {63, 17272}, {81, 306}, {88, 24170}, {141, 3218}, {171, 15523}, {190, 26580}, {226, 30831}, {244, 29637}, {319, 16704}, {320, 31017}, {333, 32025}, {464, 5273}, {740, 29631}, {750, 29674}, {894, 3936}, {908, 17355}, {940, 17311}, {982, 24943}, {1150, 3661}, {1155, 3844}, {1211, 3219}, {1214, 18632}, {1215, 29846}, {1332, 26637}, {1465, 28780}, {1698, 21935}, {1738, 30768}, {1836, 25958}, {1861, 7466}, {1999, 3969}, {2064, 20896}, {2177, 29659}, {2886, 29872}, {2887, 4418}, {2895, 4641}, {2901, 25441}, {3006, 5263}, {3306, 5525}, {3416, 17126}, {3589, 17012}, {3687, 5294}, {3703, 3920}, {3704, 17016}, {3705, 24552}, {3712, 4026}, {3750, 29685}, {3758, 31034}, {3763, 17595}, {3773, 17763}, {3891, 29634}, {3912, 16785}, {3923, 5057}, {3925, 29873}, {3932, 5297}, {3966, 17127}, {3977, 4357}, {3980, 25957}, {4011, 25960}, {4062, 4649}, {4195, 5016}, {4256, 19867}, {4360, 29833}, {4363, 30811}, {4365, 29863}, {4370, 27776}, {4416, 31143}, {4417, 26223}, {4422, 5241}, {4427, 24723}, {4438, 31330}, {4642, 19879}, {4851, 14996}, {4886, 19742}, {4933, 21806}, {5051, 7283}, {5233, 17354}, {5247, 20653}, {5249, 20106}, {5262, 17698}, {5295, 24883}, {5333, 17189}, {5718, 17369}, {5739, 26065}, {5741, 27064}, {5743, 27065}, {5744, 29611}, {5791, 13726}, {5880, 25959}, {5955, 9780}, {6292, 17292}, {6350, 24635}, {6535, 29683}, {6703, 17019}, {7270, 11115}, {9709, 13730}, {16729, 25280}, {16823, 24542}, {17021, 17243}, {17061, 29874}, {17063, 29677}, {17122, 29687}, {17155, 26128}, {17234, 26627}, {17256, 27081}, {17293, 21488}, {17351, 17484}, {17360, 31303}, {17367, 24277}, {17521, 19842}, {17557, 19857}, {17592, 29647}, {17598, 29686}, {17599, 29648}, {17889, 31237}, {19262, 26446}, {19846, 28612}, {21857, 27320}, {24160, 25669}, {24325, 29632}, {24342, 29862}, {24593, 29587}, {24594, 29629}, {25496, 29849}, {26064, 31445}, {26070, 29591}, {26685, 30479}, {26738, 30828}, {30566, 30867}

X(32779) =


X(32780) = X(1)X(3695)∩X(2)X(38)

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

X(32780) lies on these lines: {1, 3695}, {2, 38}, {8, 3791}, {10, 58}, {12, 57}, {31, 29667}, {36, 19867}, {55, 29659}, {65, 19879}, {75, 25453}, {81, 15523}, {86, 29653}, {190, 4425}, {238, 5294}, {292, 16587}, {306, 4649}, {312, 29635}, {321, 29631}, {334, 8033}, {345, 17592}, {354, 29637}, {409, 5260}, {583, 17303}, {726, 19786}, {750, 29679}, {846, 4026}, {894, 2887}, {940, 29674}, {958, 5329}, {985, 5278}, {986, 19784}, {1089, 25441}, {1125, 17598}, {1126, 21081}, {1211, 1757}, {1213, 3509}, {1376, 4265}, {1460, 9708}, {1621, 29685}, {1723, 5831}, {1762, 3925}, {1961, 3932}, {1999, 3773}, {2161, 2886}, {2895, 4722}, {3219, 24697}, {3329, 3705}, {3339, 19880}, {3589, 29821}, {3624, 3677}, {3634, 18201}, {3666, 29633}, {3678, 24931}, {3679, 5269}, {3741, 17289}, {3742, 17357}, {3757, 6679}, {3772, 29856}, {3790, 29841}, {3846, 27064}, {3873, 24943}, {3891, 29636}, {3912, 4038}, {3953, 19881}, {3966, 16468}, {3976, 19836}, {3980, 4429}, {4011, 17354}, {4284, 5750}, {4358, 29845}, {4359, 29850}, {4363, 17889}, {4385, 19806}, {4388, 4672}, {4418, 4972}, {4645, 4697}, {4650, 26034}, {4671, 29864}, {4703, 17350}, {4850, 29663}, {5143, 18235}, {5249, 30768}, {5251, 5285}, {5263, 29673}, {5749, 26098}, {5955, 6048}, {7186, 17792}, {7262, 26065}, {16706, 24165}, {17023, 17600}, {17056, 29862}, {17061, 29859}, {17123, 17353}, {17263, 25501}, {17279, 26102}, {17280, 29837}, {17355, 24210}, {17381, 29644}, {17597, 29660}, {17599, 29646}, {18165, 22279}, {19684, 29643}, {19792, 20083}, {20368, 26446}, {24295, 29655}, {24586, 29576}, {24725, 25958}, {24746, 28653}, {25760, 26223}, {25961, 26627}, {26040, 26929}, {27798, 28604}, {28605, 29868}, {28606, 29647}, {31019, 31237}

X(32780) =


X(32781) = X(2)X(31)∩X(6)X(29663)

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

X(32781) lies on these lines: {2, 31}, {6, 29663}, {10, 38}, {37, 29687}, {42, 141}, {55, 3763}, {63, 1698}, {81, 29633}, {210, 17237}, {226, 31264}, {321, 3821}, {333, 29850}, {354, 29685}, {536, 6535}, {595, 19881}, {612, 17306}, {672, 1213}, {756, 3263}, {758, 19867}, {896, 3634}, {899, 1211}, {940, 29647}, {968, 17284}, {982, 29667}, {984, 29679}, {1001, 29677}, {1125, 17469}, {1150, 25453}, {1215, 17184}, {1386, 29684}, {1468, 19784}, {1621, 29637}, {1737, 11031}, {1738, 21020}, {1962, 3912}, {2177, 3619}, {2223, 6292}, {2228, 20966}, {2308, 3589}, {2886, 31241}, {2975, 19879}, {3006, 6682}, {3416, 17017}, {3666, 3844}, {3683, 17357}, {3715, 17253}, {3720, 4026}, {3741, 4972}, {3744, 29686}, {3745, 17384}, {3757, 17291}, {3769, 29636}, {3773, 17147}, {3775, 4651}, {3812, 27714}, {3831, 5051}, {3873, 29659}, {3915, 19836}, {3925, 30970}, {3932, 3989}, {3936, 6685}, {3969, 4970}, {4001, 4722}, {4085, 17135}, {4358, 4425}, {4413, 7085}, {4418, 17289}, {4429, 31330}, {4655, 26223}, {4657, 5311}, {4660, 24552}, {4683, 27064}, {4698, 8040}, {4987, 5750}, {5014, 29652}, {5224, 26037}, {5251, 7293}, {5282, 17303}, {5314, 24931}, {5372, 29868}, {5745, 30768}, {5846, 29819}, {6057, 17246}, {6690, 29865}, {8013, 17239}, {8620, 16587}, {8728, 28274}, {9342, 31247}, {9345, 18141}, {11246, 17369}, {11680, 29827}, {14829, 29631}, {16062, 19810}, {16570, 19876}, {16707, 16887}, {16818, 20985}, {17283, 29851}, {17370, 29852}, {17398, 21764}, {17674, 28269}, {17716, 25539}, {17763, 19786}, {19812, 29847}, {19877, 26065}, {24697, 27065}, {25351, 27798}, {25527, 29828}, {25914, 28352}, {26128, 26227}, {28599, 29823}, {28606, 29674}, {29678, 30811}

X(32781) =


X(32782) = X(2)X(6)∩X(7)X(19822)

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

X(32782) lies on these lines: {2, 6}, {7, 19822}, {8, 3891}, {9, 21367}, {10, 3681}, {63, 17272}, {75, 17184}, {76, 321}, {100, 26034}, {192, 3969}, {210, 3844}, {238, 24943}, {305, 16703}, {306, 4357}, {308, 18096}, {312, 17228}, {319, 3187}, {320, 19808}, {329, 29611}, {405, 26064}, {464, 18642}, {518, 29667}, {594, 3782}, {748, 29637}, {756, 29674}, {956, 19258}, {961, 10372}, {964, 1330}, {980, 7794}, {984, 15523}, {986, 20653}, {997, 6505}, {1008, 4388}, {1043, 17676}, {1255, 17316}, {1257, 15474}, {1352, 4220}, {1386, 29648}, {1757, 26061}, {1999, 17287}, {2049, 26131}, {2345, 5905}, {2476, 3454}, {2886, 25958}, {2887, 3775}, {3175, 17229}, {3210, 17236}, {3219, 4376}, {3305, 17284}, {3416, 3920}, {3662, 4359}, {3666, 17237}, {3679, 23681}, {3686, 26723}, {3687, 4850}, {3703, 7226}, {3739, 27186}, {3741, 11680}, {3791, 29636}, {3821, 21085}, {3836, 26037}, {3840, 25960}, {3842, 29854}, {3846, 30942}, {3923, 4683}, {3925, 25959}, {3948, 17550}, {3966, 7191}, {3995, 17233}, {4026, 17018}, {4062, 17592}, {4193, 17182}, {4202, 9534}, {4360, 20017}, {4363, 17483}, {4384, 26724}, {4389, 17147}, {4415, 4671}, {4416, 5294}, {4418, 4655}, {4429, 4651}, {4469, 8024}, {4641, 17344}, {4649, 29647}, {4656, 29594}, {4657, 17011}, {4851, 17019}, {4886, 16706}, {4966, 29814}, {4974, 29852}, {4981, 29641}, {5044, 18732}, {5051, 10449}, {5256, 17306}, {5262, 5814}, {5263, 6327}, {5271, 17270}, {5273, 26932}, {5287, 17296}, {5337, 7854}, {5564, 19796}, {5793, 20060}, {5846, 29815}, {6682, 29849}, {6989, 12359}, {7232, 26842}, {7321, 19797}, {7465, 11442}, {7761, 24271}, {7789, 21508}, {7795, 21511}, {7800, 21495}, {10371, 17016}, {10519, 26118}, {13728, 19767}, {14907, 16046}, {16342, 25650}, {16585, 25078}, {16887, 18601}, {17123, 29677}, {17227, 19804}, {17239, 31019}, {17257, 17776}, {17275, 24789}, {17279, 27065}, {17289, 26223}, {17292, 27064}, {17293, 17484}, {17325, 20182}, {17355, 17781}, {17360, 19812}, {17361, 19827}, {17717, 31241}, {17889, 21020}, {18135, 26601}, {18200, 24921}, {18229, 31266}, {18747, 31018}, {19819, 32087}, {20173, 26593}, {20208, 21482}, {20929, 20955}, {21024, 31060}, {21240, 29576}, {24988, 26038}, {25539, 29684}, {25914, 27625}, {26747, 27641}, {27038, 27096}, {27047, 27263}, {27131, 30818}, {27476, 27495}, {28654, 30473}

X(32782) = complement of X(37685)


X(32783) = X(1)X(2)∩X(75)X(26128)

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

X(32783) lies on these lines: {1, 2}, {75, 26128}, {141, 171}, {238, 1211}, {242, 1848}, {261, 7305}, {319, 3791}, {320, 4697}, {321, 23689}, {333, 3775}, {350, 18697}, {594, 17061}, {740, 19786}, {846, 4357}, {1011, 23850}, {1213, 3684}, {1215, 17289}, {1283, 4199}, {1376, 3763}, {1707, 17272}, {1757, 5294}, {1891, 4212}, {2238, 16470}, {2308, 2895}, {2309, 27270}, {2345, 21101}, {2887, 5263}, {3416, 17716}, {3550, 26034}, {3662, 3980}, {3681, 26061}, {3683, 24697}, {3685, 4425}, {3740, 17357}, {3750, 4026}, {3769, 17228}, {3846, 30832}, {3923, 27184}, {3967, 17359}, {3971, 17280}, {3996, 4085}, {4038, 4966}, {4046, 4716}, {4104, 17353}, {4204, 5259}, {4279, 28242}, {4417, 25496}, {4418, 17184}, {4640, 17237}, {4643, 4797}, {4647, 19787}, {4657, 17592}, {4676, 4703}, {4682, 17231}, {4693, 4854}, {4734, 17383}, {4886, 4974}, {4970, 17302}, {5227, 17754}, {5247, 17698}, {5249, 24342}, {5284, 31247}, {5285, 16056}, {5329, 11358}, {5739, 16468}, {5743, 17123}, {5814, 16478}, {5955, 24174}, {7110, 14844}, {8300, 24542}, {10180, 17322}, {16800, 17277}, {17291, 24169}, {17293, 17725}, {17306, 17594}, {17358, 27538}, {17490, 26150}, {17591, 17740}, {17889, 25527}, {18491, 19540}, {19808, 24325}, {24259, 31004}, {24295, 27064}, {24552, 25760}

X(32783) =


X(32784) = X(1)X(141)∩X(2)X(31)

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

X(32784) lies on these lines: {1, 141}, {2, 31}, {3, 29020}, {5, 6210}, {6, 29633}, {8, 3775}, {9, 46}, {10, 75}, {11, 29827}, {12, 1423}, {37, 3844}, {38, 29667}, {43, 1211}, {69, 4649}, {81, 29647}, {165, 19542}, {192, 3773}, {242, 5117}, {256, 5051}, {306, 17592}, {312, 4425}, {333, 25453}, {405, 7295}, {451, 2212}, {516, 7377}, {518, 17237}, {519, 17399}, {524, 28650}, {545, 19875}, {740, 3661}, {756, 29679}, {894, 4655}, {958, 19879}, {960, 25144}, {982, 24163}, {1001, 3763}, {1125, 3883}, {1150, 29631}, {1215, 27184}, {1279, 29660}, {1386, 17384}, {1429, 12588}, {1621, 24943}, {1716, 4205}, {1757, 4643}, {1861, 24341}, {2209, 27270}, {2214, 16470}, {2345, 24248}, {2354, 5142}, {3097, 25349}, {3219, 26061}, {3220, 5251}, {3454, 27042}, {3589, 16468}, {3616, 17232}, {3618, 16477}, {3619, 16484}, {3624, 7290}, {3634, 17353}, {3662, 24325}, {3670, 4446}, {3679, 7174}, {3685, 17292}, {3696, 17239}, {3705, 6682}, {3751, 17272}, {3755, 4923}, {3757, 26128}, {3758, 17770}, {3769, 19812}, {3790, 17247}, {3823, 4708}, {3831, 21257}, {3842, 4019}, {3873, 29685}, {3915, 21289}, {3923, 17289}, {3925, 24310}, {3932, 4364}, {3966, 29821}, {3980, 19808}, {3993, 17233}, {4073, 6734}, {4197, 28287}, {4202, 31339}, {4356, 29594}, {4362, 19786}, {4393, 17772}, {4417, 6685}, {4432, 29613}, {4488, 7229}, {4514, 29652}, {4660, 5263}, {4663, 17344}, {4664, 6541}, {4672, 17368}, {4676, 17371}, {4683, 26223}, {4687, 25354}, {4693, 29611}, {4703, 27064}, {4710, 30473}, {4741, 17771}, {4972, 31330}, {4974, 17367}, {5047, 7301}, {5220, 17253}, {5234, 19880}, {5247, 19784}, {5271, 19834}, {5278, 29850}, {5284, 29677}, {5294, 7262}, {5361, 29868}, {5372, 29864}, {5625, 17391}, {5692, 19867}, {5695, 17293}, {5718, 29825}, {5743, 16569}, {5749, 24695}, {5847, 17023}, {5904, 22277}, {6211, 26446}, {6536, 29687}, {7083, 11108}, {8728, 27626}, {9791, 17280}, {11680, 31241}, {12587, 18162}, {14829, 29635}, {15254, 17357}, {15523, 28606}, {15569, 17231}, {15601, 19872}, {16475, 29598}, {16476, 16818}, {16706, 16825}, {16739, 18057}, {16823, 17291}, {16830, 17326}, {16927, 30174}, {17064, 18229}, {17236, 24349}, {17308, 17738}, {17327, 19856}, {17350, 26083}, {17469, 29648}, {17593, 17740}, {17719, 29828}, {17722, 29826}, {17725, 26227}, {17755, 25351}, {17889, 31993}, {19717, 20290}, {19804, 24169}, {19855, 27509}, {19877, 26685}, {20994, 24273}, {21912, 26040}, {24206, 31394}, {24217, 30942}, {24231, 31178}, {24693, 29610}, {24931, 25440}, {25005, 25024}, {26030, 26772}, {26064, 27320}, {26251, 26580}, {28595, 29641}, {29640, 30811}, {29678, 30831}, {29822, 31017}, {30940, 30966}, {31053, 31264}

X(32784) =

leftri

Points with first barycentric of type h f(a,b,c) + k S: X(32785)-X(32841)

rightri

Centers X(32785)-X(32841) were contributed by Clark Kimberling, June 20, 2019:

Centers X(32785) - X(32790) . . . . . . . of form h a^2 + k S : :
Centers X(32791) - X(32804) . . . . . . . of form h b c + k S : :
Centers X(32804) - X(32841) . . . . . . . of form h SA^2 + k S : :


X(32785) = (name pending)

Barycentrics    a^2 + 3 S : :

X(32785) lies on these lines: {2, 6}, {3, 18538}, {4, 5418}, {5, 6221}, {10, 13902}, {20, 6411}, {30, 6451}, {125, 18923}, {140, 1587}, {187, 11292}, {239, 32795}, {371, 3090}, {372, 3525}, {376, 6564}, {381, 6445}, {485, 631}, {486, 5067}, {488, 8376}, {546, 6449}, {547, 13785}, {549, 6452}, {550, 23253}, {574, 11291}, {605, 17123}, {606, 17122}, {632, 3312}, {638, 33364}, {641, 13651}, {642, 7376}, {894, 32796}, {1030, 21565}, {1125, 13893}, {1131, 15717}, {1151, 3091}, {1267, 17117}, {1327, 19708}, {1588, 1656}, {1589, 22052}, {1590, 10979}, {1600, 8939}, {1698, 8983}, {2045, 5335}, {2046, 5334}, {2066, 10589}, {2067, 10588}, {3035, 31413}, {3070, 3523}, {3071, 5056}, {3085, 9661}, {3086, 9646}, {3146, 6409}, {3247, 5393}, {3311, 3628}, {3317, 6435}, {3366, 18581}, {3391, 18582}, {3522, 23251}, {3524, 6560}, {3526, 6395}, {3533, 5420}, {3545, 6480}, {3590, 6434}, {3616, 13911}, {3624, 13883}, {3627, 6455}, {3634, 18991}, {3731, 6351}, {3817, 9616}, {3832, 6433}, {3851, 9690}, {3855, 9680}, {4254, 21546}, {4294, 31499}, {4361, 32799}, {4363, 32800}, {4413, 13887}, {5054, 6446}, {5068, 6468}, {5070, 7584}, {5071, 6565}, {5072, 6407}, {5094, 13884}, {5120, 21549}, {5124, 21568}, {5326, 19037}, {5391, 17116}, {5412, 8889}, {5432, 13898}, {5433, 13897}, {5550, 7968}, {6118, 13834}, {6119, 13770}, {6419, 13939}, {6424, 31404}, {6425, 15022}, {6427, 13993}, {6439, 9543}, {6447, 12812}, {6450, 14869}, {6456, 12108}, {6481, 15702}, {6496, 15704}, {6519, 12811}, {6622, 11473}, {6667, 19113}, {6683, 19090}, {6721, 19056}, {6722, 19109}, {6723, 19111}, {7288, 31472}, {7294, 18995}, {7389, 9600}, {7484, 13889}, {7486, 31454}, {7509, 8276}, {7582, 10577}, {7749, 31411}, {7786, 8992}, {7808, 13885}, {7914, 13892}, {7969, 9780}, {8167, 18999}, {8227, 13912}, {8993, 31268}, {8997, 14061}, {8998, 15059}, {9582, 18483}, {9583, 10175}, {9602, 18584}, {9615, 19925}, {9675, 31415}, {9679, 31418}, {10299, 23269}, {10533, 32064}, {10819, 15081}, {11444, 12239}, {11513, 16051}, {12240, 15028}, {12257, 26951}, {12900, 19060}, {13888, 13936}, {13894, 15184}, {13896, 24953}, {13906, 26364}, {13907, 26363}, {13922, 31272}, {13924, 19102}, {13973, 19877}, {14241, 15719}, {15492, 30412}, {15694, 18512}, {15703, 18510}, {16239, 19117}, {16419, 19006}, {16814, 30413}, {17538, 22644}, {17819, 23332}, {18755, 21991}, {18992, 19862}, {19004, 19872}, {19058, 22247}, {19089, 31239}, {19108, 31274}, {19112, 31235}, {19116, 31487}, {19355, 23291}, {24842, 27191}}

X(32785) = {X(2),X(6)}-harmonic conjugate of X(32786)


X(32786) = (name pending)

Barycentrics    a^2 - 3 S : :

X(32786) lies on these lines: {2, 6}, {3, 18762}, {4, 5420}, {5, 6398}, {10, 13959}, {20, 6412}, {30, 6452}, {125, 18924}, {140, 1588}, {187, 11291}, {239, 32796}, {371, 3525}, {372, 3090}, {376, 6565}, {381, 6446}, {485, 5067}, {486, 631}, {546, 6450}, {547, 13665}, {549, 6451}, {550, 23263}, {574, 11292}, {605, 17122}, {606, 17123}, {632, 3311}, {637, 9675}, {641, 7375}, {642, 13770}, {894, 32795}, {1030, 21568}, {1125, 13947}, {1132, 15717}, {1151, 10303}, {1152, 3091}, {1267, 17116}, {1328, 19708}, {1587, 1656}, {1589, 10979}, {1590, 22052}, {1599, 8943}, {1698, 13971}, {2045, 5334}, {2046, 5335}, {3070, 5056}, {3071, 3523}, {3146, 6410}, {3247, 5405}, {3312, 3628}, {3316, 6436}, {3367, 18581}, {3392, 18582}, {3522, 23261}, {3524, 6561}, {3526, 6199}, {3533, 5418}, {3545, 6481}, {3591, 6433}, {3616, 13973}, {3624, 13902}, {3627, 6456}, {3634, 18992}, {3731, 6352}, {3832, 6434}, {3851, 23253}, {4254, 21549}, {4361, 32800}, {4363, 32799}, {4413, 13940}, {5054, 6445}, {5068, 6469}, {5070, 7583}, {5071, 6564}, {5072, 6408}, {5094, 13937}, {5120, 21546}, {5124, 21565}, {5326, 19038}, {5391, 17117}, {5413, 8889}, {5414, 10589}, {5432, 13955}, {5433, 13954}, {5550, 7969}, {6118, 13651}, {6119, 13711}, {6420, 13886}, {6423, 31404}, {6426, 15022}, {6428, 13925}, {6448, 12812}, {6449, 14869}, {6455, 12108}, {6480, 15702}, {6490, 9692}, {6497, 15704}, {6502, 10588}, {6522, 12811}, {6622, 11474}, {6667, 19112}, {6683, 19089}, {6721, 19055}, {6722, 19108}, {6723, 19110}, {7294, 18996}, {7388, 13934}, {7484, 13943}, {7486, 31414}, {7509, 8277}, {7581, 10576}, {7786, 13983}, {7808, 13938}, {7914, 13946}, {7968, 9780}, {8167, 19000}, {8227, 13975}, {9602, 12221}, {10299, 23275}, {10534, 32064}, {10820, 15081}, {11444, 12240}, {11514, 16051}, {12239, 15028}, {12900, 19059}, {13883, 13942}, {13911, 19877}, {13948, 15184}, {13953, 24953}, {13964, 26364}, {13965, 26363}, {13989, 14061}, {13991, 31272}, {14226, 15719}, {15492, 30413}, {15694, 18510}, {15703, 18512}, {16239, 19116}, {16419, 19005}, {16814, 30412}, {17538, 22615}, {17820, 23332}, {17851, 19709}, {18966, 31408}, {18991, 19862}, {19003, 19872}, {19057, 22247}, {19090, 31239}, {19105, 32209}, {19109, 31274}, {19113, 31235}, {19356, 23291}, {24843, 27191}}

X(32786) = {X(2),X(6)}-harmonic conjugate of X(32785)


X(32787) = (name pending)

Barycentrics    3 a^2 + 2 S : :

X(32787) lies on these lines: {2, 6}, {3, 9680}, {4, 3592}, {5, 6419}, {16, 15764}, {20, 6425}, {30, 371}, {32, 32421}, {39, 13821}, {44, 5393}, {61, 18585}, {62, 15765}, {99, 19058}, {115, 13703}, {140, 6420}, {239, 32801}, {372, 549}, {376, 1151}, {381, 485}, {397, 2043}, {398, 2044}, {428, 5412}, {486, 5055}, {519, 7969}, {547, 7584}, {550, 6453}, {551, 7968}, {588, 1989}, {589, 30537}, {631, 3594}, {671, 19109}, {894, 32802}, {903, 24819}, {1124, 10072}, {3524, 7581}, {1327, 3830}, {1335, 10056}, {1384, 13712}, {1503, 11241}, {1504, 5309}, {1506, 13921}, {1585, 1990}, {1586, 6749}, {1588, 3545}, {1656, 6427}, {1657, 6447}, {1702, 31162}, {2066, 3058}, {2067, 5434}, {2482, 8997}, {2549, 13644}, {2965, 26912}, {3003, 8962}, {3094, 22722}, {3146, 31414}, {3163, 8968}, {3167, 11209}, {3241, 19066}, {3299, 3582}, {3301, 3584}, {3304, 31475}, {3312, 5054}, {3365, 16962}, {3390, 16963}, {3523, 6426}, {3526, 6428}, {3530, 6454}, {3534, 6221}, {3543, 6459}, {3590, 15022}, {3679, 13911}, {3828, 13936}, {3839, 6470}, {3845, 6564}, {4254, 21558}, {4361, 32797}, {4363, 32798}, {4370, 24842}, {4428, 13887}, {4995, 5414}, {5058, 7753}, {5064, 5410}, {5066, 6565}, {5070, 10195}, {5071, 7582}, {5120, 21561}, {5254, 12962}, {5286, 26289}, {5298, 6502}, {5319, 11313}, {5405, 16666}, {5413, 13884}, {5415, 19024}, {5420, 6418}, {5421, 8963}, {5459, 13917}, {5460, 13916}, {5463, 19074}, {5464, 19076}, {5642, 8998}, {6054, 19056}, {6055, 8980}, {6174, 13922}, {6200, 8703}, {6351, 16885}, {6352, 16884}, {6395, 15701}, {6396, 12100}, {6398, 15693}, {6407, 15689}, {6408, 15718}, {6409, 6460}, {6410, 15692}, {6411, 19708}, {6412, 15698}, {6415, 10262}, {6422, 7739}, {6424, 31411}, {6432, 13935}, {6433, 9542}, {6435, 10109}, {6437, 9541}, {6438, 15719}, {6441, 23273}, {6445, 15695}, {6449, 15688}, {6450, 15700}, {6452, 15716}, {6455, 14093}, {6456, 15706}, {6468, 15697}, {6471, 15721}, {6480, 15690}, {6481, 19711}, {6500, 13951}, {6519, 15696}, {6772, 13646}, {6775, 13645}, {6811, 8550}, {7392, 20197}, {7576, 10880}, {7615, 12158}, {7737, 8375}, {7755, 32491}, {7757, 19090}, {7772, 31483}, {7865, 19012}, {7991, 31440}, {8376, 21843}, {8573, 8939}, {8909, 19062}, {8992, 9466}, {9140, 19111}, {9166, 19057}, {9167, 13989}, {9605, 19105}, {9607, 11293}, {9692, 10147}, {10128, 10961}, {10192, 11242}, {10577, 15699}, {10691, 11513}, {10706, 19060}, {10707, 19113}, {10711, 19082}, {10718, 19115}, {10819, 19052}, {11157, 12159}, {11179, 19145}, {11237, 18996}, {11238, 19038}, {11291, 31465}, {11539, 13966}, {11646, 13640}, {12239, 14831}, {12240, 16226}, {13651, 22485}, {13674, 13749}, {13701, 13720}, {13711, 13932}, {13785, 19709}, {13832, 33457}, {13833, 13835}, {13882, 19103}, {13888, 18992}, {13893, 13973}, {13947, 19876}, {13961, 15723}, {13968, 14971}, {15682, 23249}, {15684, 22644}, {16777, 30413}, {17120, 32792}, {17121, 32791}, {19064, 22712}, {19073, 22489}, {19075, 22490}, {19092, 31168}, {28198, 31439}}

X(32787) = complement of X(32808)
X(32787) = {X(2),X(6)}-harmonic conjugate of X(32788)


X(32788) = (name pending)

Barycentrics    3 a^2 - 2 S : :

X(32788) lies on these lines: {2, 6}, {3, 9681}, {4, 3594}, {5, 6420}, {15, 15764}, {20, 6426}, {30, 372}, {32, 32419}, {39, 13701}, {44, 5405}, {61, 15765}, {62, 18585}, {99, 19057}, {115, 13823}, {140, 6419}, {239, 32802}, {371, 549}, {376, 1152}, {381, 486}, {397, 2044}, {398, 2043}, {428, 5413}, {485, 5055}, {519, 7968}, {547, 7583}, {550, 6454}, {551, 7969}, {588, 30537}, {589, 1989}, {631, 3592}, {671, 19108}, {894, 32801}, {903, 24818}, {1124, 10056}, {1151, 3524}, {1328, 3830}, {1335, 10072}, {1384, 13835}, {1503, 11242}, {1505, 5309}, {1506, 13880}, {1585, 6749}, {1586, 1990}, {1587, 3545}, {1656, 6428}, {1657, 6448}, {1703, 31162}, {2066, 4995}, {2067, 5298}, {2482, 13989}, {2549, 13763}, {3058, 5414}, {3094, 22723}, {3167, 11210}, {3241, 19065}, {3299, 3584}, {3301, 3582}, {3311, 5054}, {3364, 16962}, {3389, 16963}, {3523, 6425}, {3526, 6427}, {3530, 6453}, {3534, 6398}, {3543, 6460}, {3591, 15022}, {3628, 8960}, {3679, 13973}, {3828, 13883}, {3839, 6471}, {3845, 6565}, {4254, 21561}, {4361, 32798}, {4363, 32797}, {4370, 24843}, {4428, 13940}, {5062, 7753}, {5064, 5411}, {5066, 6564}, {5068, 31414}, {5070, 10194}, {5071, 7581}, {5120, 21558}, {5254, 12969}, {5286, 26288}, {5319, 11314}, {5393, 16666}, {5412, 13937}, {5416, 19023}, {5418, 6417}, {5434, 6502}, {5459, 13982}, {5460, 13981}, {5463, 19073}, {5464, 19075}, {5642, 13990}, {6054, 19055}, {6055, 13967}, {6174, 13991}, {6199, 15701}, {6200, 12100}, {6221, 15693}, {6351, 16884}, {6352, 16885}, {6396, 8703}, {6407, 15718}, {6408, 15689}, {6409, 15692}, {6410, 6459}, {6411, 15698}, {6412, 9541}, {6416, 10261}, {6421, 7739}, {6431, 9540}, {6436, 10109}, {6437, 15719}, {6438, 11001}, {6442, 23267}, {6446, 15695}, {6449, 15700}, {6450, 15688}, {6451, 15716}, {6455, 15706}, {6456, 14093}, {6469, 15697}, {6470, 15721}, {6480, 19711}, {6481, 15690}, {6488, 9693}, {6501, 8976}, {6522, 15696}, {6772, 13765}, {6775, 13764}, {6813, 8550}, {7494, 20197}, {7576, 10881}, {7615, 12159}, {7737, 8376}, {7755, 32490}, {7757, 19089}, {7865, 19011}, {8375, 21843}, {8573, 8943}, {8981, 11539}, {8983, 19883}, {8997, 9167}, {9140, 19110}, {9166, 19058}, {9466, 13983}, {9605, 19102}, {9607, 11294}, {9680, 15720}, {10128, 10963}, {10192, 11241}, {10576, 15699}, {10691, 11514}, {10706, 19059}, {10707, 19112}, {10711, 19081}, {10718, 19114}, {11158, 12158}, {11179, 19146}, {11237, 18995}, {11238, 19037}, {11646, 13760}, {12239, 16226}, {12240, 14831}, {13665, 19709}, {13712, 13769}, {13748, 13794}, {13821, 13843}, {13831, 33456}, {13834, 13850}, {13893, 19876}, {13903, 15723}, {13908, 14971}, {13911, 13947}, {13942, 18991}, {13954, 31472}, {15682, 23259}, {15684, 22615}, {16777, 30412}, {17120, 32791}, {17121, 32792}, {19063, 22712}, {19074, 22489}, {19076, 22490}, {19091, 31168}

X(32788) = complement of X(32809)
X(32788) = {X(2),X(6)}-harmonic conjugate of X(32787)


X(32789) = (name pending)

Barycentrics    a^2 + 6 S : :

X(32789) lies on these lines: {2, 6}, {3, 22644}, {4, 6411}, {5, 6200}, {140, 3070}, {187, 32432}, {371, 3628}, {372, 632}, {381, 6451}, {485, 3526}, {486, 5070}, {547, 6480}, {549, 6564}, {574, 6118}, {631, 6412}, {641, 11614}, {642, 32491}, {1030, 21553}, {1151, 3090}, {3525, 23267}, {1327, 15701}, {1587, 3533}, {1656, 3071}, {2045, 5318}, {2046, 5321}, {3091, 6409}, {3316, 13935}, {3366, 33416}, {3391, 33417}, {3523, 23251}, {3594, 13886}, {3624, 13911}, {3634, 7969}, {3723, 5393}, {4361, 32795}, {4363, 32796}, {5024, 13711}, {5054, 6452}, {5055, 6445}, {5056, 6433}, {5067, 6437}, {5071, 9541}, {5072, 6455}, {5079, 6449}, {5124, 21492}, {5159, 11513}, {5210, 11292}, {5326, 5414}, {5420, 6395}, {6351, 16677}, {6352, 16674}, {6410, 10303}, {6420, 13925}, {6431, 13939}, {6434, 6460}, {6436, 19117}, {6440, 31414}, {6441, 7582}, {6446, 13665}, {6459, 6468}, {6481, 11539}, {6502, 7294}, {7583, 16239}, {7741, 31499}, {7968, 19862}, {8960, 13966}, {8981, 10577}, {9600, 11313}, {9675, 32490}, {9680, 9690}, {10299, 23253}, {10533, 23332}, {10645, 18585}, {10646, 15765}, {11314, 31415}, {13785, 15703}, {13834, 13882}, {13883, 19878}, {13902, 19877}, {13924, 31483}, {13936, 31253}, {14813, 16967}, {14814, 16966}, {15723, 18512}, {17116, 32792}, {17117, 32791}, {17118, 32800}, {17119, 32799}, {18991, 19872}

X(32789) = complement of X(32807)
X(32789) = {X(2),X(6)}-harmonic conjugate of X(32790)


X(32790) = (name pending)

Barycentrics    a^2 - 6 S : :

X(32790) lies on these

X(32790) lies on these lines: {2, 6}, {3, 22615}, {4, 6412}, {5, 6396}, {140, 3071}, {187, 32435}, {371, 632}, {372, 3628}, {381, 6452}, {485, 5070}, {486, 3526}, {547, 6481}, {549, 6565}, {574, 6119}, {631, 6411}, {639, 9675}, {641, 32490}, {642, 11614}, {1030, 21492}, {1151, 3525}, {3090, 23249}, {1328, 15701}, {1588, 3533}, {1656, 3070}, {2045, 5321}, {2046, 5318}, {2066, 5326}, {2067, 7294}, {3091, 6410}, {3317, 9540}, {3367, 33416}, {3392, 33417}, {3523, 23261}, {3592, 13939}, {3624, 13973}, {3634, 7968}, {3723, 5405}, {4361, 32796}, {4363, 32795}, {5024, 13834}, {5054, 6451}, {5055, 6446}, {5056, 6434}, {5067, 6438}, {5072, 6456}, {5079, 6450}, {5124, 21553}, {5159, 11514}, {5210, 11291}, {5418, 6199}, {6351, 16674}, {6352, 16677}, {6409, 10303}, {6419, 13993}, {6426, 31412}, {6432, 13886}, {6433, 6459}, {6435, 19116}, {6436, 8960}, {6442, 7581}, {6445, 13785}, {6460, 6469}, {6480, 11539}, {7584, 16239}, {7969, 19862}, {9541, 15702}, {9600, 11315}, {10299, 23263}, {10534, 23332}, {10576, 13966}, {10645, 15765}, {10646, 18585}, {11313, 31415}, {13665, 15703}, {13883, 31253}, {13936, 19878}, {13959, 19877}, {14813, 16966}, {14814, 16967}, {15723, 18510}, {17116, 32791}, {17117, 32792}, {17118, 32799}, {17119, 32800}, {18992, 19872}

X(32790) = complement of isotomic conjugate of X(10194)
X(32790) = {X(2),X(6)}-harmonic conjugate of X(32789)


X(32791) = (name pending)

Barycentrics    b c + 2 S : :

X(32791) lies on these

X(32791) = lines: {2, 37}, {7, 32805}, {8, 32806}, {86, 5405}, {239, 590}, {274, 3302}, {319, 491}, {320, 492}, {591, 17364}, {615, 894}, {1270, 17361}, {1271, 17360}, {1991, 17363}, {3068, 3759}, {3069, 3758}, {4360, 5393}, {4361, 8253}, {4363, 8252}, {5590, 17227}, {5591, 17228}, {7321, 32807}, {10436, 16513}, {17116, 32790}, {17117, 32789}, {17120, 32788}, {17121, 32787}, {17335, 30413}, {17336, 30412}, {21296, 32810}, {32099, 32811}

X(32791) = {X(2),X(75)}-harmonic conjugate of X(32792)


X(32792) = (name pending)

Barycentrics    b c - 2 S : :

X(32792) lies on these

X(32792) = lines: {2, 37}, {7, 32806}, {8, 32805}, {86, 5393}, {239, 615}, {274, 3300}, {319, 492}, {320, 491}, {590, 894}, {591, 17363}, {1270, 17360}, {1271, 17361}, {1991, 17364}, {3068, 3758}, {3069, 3759}, {4360, 5405}, {4361, 8252}, {4363, 8253}, {5564, 32807}, {5590, 17228}, {5591, 17227}, {10436, 16512}, {17116, 32789}, {17117, 32790}, {17120, 32787}, {17121, 32788}, {17335, 30412}, {17336, 30413}, {21296, 32811}, {32099, 32810}

X(32792) = {X(2),X(75)}-harmonic conjugate of X(32791)


X(32793) = (name pending)

Barycentrics    2 b c + S : :

X(32793) lies on these

X(32793) = lines: {2, 37}, {7, 1270}, {8, 176}, {239, 7585}, {320, 32814}, {590, 17119}, {594, 5591}, {615, 17118}, {894, 7586}, {1086, 5590}, {1991, 4399}, {3068, 4361}, {3069, 4363}, {3593, 31995}, {3595, 32087}, {3729, 30412}, {4384, 30413}, {4969, 26339}, {5393, 17151}, {5405, 25590}, {5860, 17365}, {5861, 17362}, {7277, 26340}, {8972, 17117}, {13941, 17116}

X(32793) = anticomplement of X(6351)
X(32793) = {X(2),X(75)}-harmonic conjugate of X(32794)


X(32794) = (name pending)

Barycentrics    2 b c - S : :

X(32794) lies on these lines: {2, 37}, {7, 1271}, {8, 175}, {239, 7586}, {319, 32814}, {590, 17118}, {591, 4399}, {594, 5590}, {615, 17119}, {894, 7585}, {1086, 5591}, {3068, 4363}, {3069, 4361}, {3593, 32087}, {3595, 31995}, {3729, 30413}, {4384, 30412}, {4969, 26340}, {5393, 25590}, {5405, 17151}, {5860, 17362}, {5861, 17365}, {7277, 26339}, {8972, 17116}, {13941, 17117}

X(32794) = anticomplement of X(6352)
X(32794) = {X(2),X(75)}-harmonic conjugate of X(32793)


X(32795) = (name pending)

Barycentrics    b c + 3 S : :

X(32795) lies on these lines: {2, 37}, {7, 32807}, {239, 32785}, {319, 3595}, {320, 3593}, {491, 32099}, {492, 21296}, {894, 32786}, {3068, 17121}, {3069, 17120}, {3661, 26362}, {3662, 26361}, {3758, 13941}, {3759, 8972}, {4361, 32789}, {4363, 32790}

X(32795) =


X(32796) = (name pending)

Barycentrics    b c - 3 S : :

X(32796) lies on these

X(32796) = lines: {2, 37}, {8, 32807}, {239, 32786}, {319, 3593}, {320, 3595}, {491, 21296}, {492, 32099}, {894, 32785}, {3068, 17120}, {3069, 17121}, {3661, 26361}, {3662, 26362}, {3758, 8972}, {3759, 13941}, {4361, 32790}, {4363, 32789}


X(32797) = (name pending)

Barycentrics    3 b c + S : :

X(32797) lies on these

X(32797) = lines: {2, 37}, {7, 32808}, {8, 10910}, {239, 19054}, {491, 32087}, {492, 31995}, {894, 19053}, {1270, 7321}, {1271, 5564}, {3068, 17117}, {3069, 17116}, {4361, 32787}, {4363, 32788}, {5861, 29617}, {13846, 17119}


X(32798) = (name pending)

Barycentrics    3 b c - S : :

X(32798) lies on these lines: {2, 37}, {7, 32809}, {8, 10911}, {239, 19053}, {491, 31995}, {492, 32087}, {894, 19054}, {1270, 5564}, {1271, 7321}, {3068, 17116}, {3069, 17117}, {4361, 32788}, {4363, 32787}, {5860, 29617}, {13846, 17118}, {13847, 17119}

X(32798) =


X(32799) = (name pending)

Barycentrics    2 b c + 3 S : :

X(32799) lies on these lines: {2, 37}, {7, 3593}, {8, 3595}, {239, 8972}, {594, 26362}, {894, 13941}, {1086, 26361}, {1270, 21296}, {1271, 32099}, {4361, 32785}, {4363, 32786}, {7585, 17121}, {7586, 17120}, {17118, 32790}, {17119, 32789}, {25728, 30412}

X(32799) =


X(32800) = (name pending)

Barycentrics    2 b c - 3 S : :

X(32800) lies on these lines: {2, 37}, {7, 3595}, {8, 3593}, {239, 13941}, {594, 26361}, {894, 8972}, {1086, 26362}, {1270, 32099}, {1271, 21296}, {4361, 32786}, {4363, 32785}, {7585, 17120}, {7586, 17121}, {17118, 32789}, {17119, 32790}, {25728, 30413}

X(32800) =


X(32801) = (name pending)

Barycentrics    3 b c + 2 S : :

X(32801) lies on these lines: {2, 37}, {7, 32810}, {8, 32811}, {239, 32787}, {319, 32809}, {320, 32808}, {491, 5564}, {492, 7321}, {590, 17117}, {615, 17116}, {894, 32788}, {1991, 29617}, {3758, 19053}, {3759, 19054}, {4361, 13846}, {4363, 13847}, {5393, 17160}, {31995, 32805}, {32087, 32806}

X(32801) =


X(32802) = (name pending)

Barycentrics    3 b c - 2 S : :

X(32802) lies on these

X(32802) = lines: {2, 37}, {7, 32811}, {8, 32810}, {239, 32788}, {319, 32808}, {320, 32809}, {491, 7321}, {492, 5564}, {590, 17116}, {591, 29617}, {615, 17117}, {894, 32787}, {3758, 19054}, {3759, 19053}, {4361, 13847}, {4363, 13846}, {5405, 17160}, {31995, 32806}, {32087, 32805}


X(32803) = (name pending)

Barycentrics    b c + 4 S : :

X(32803) lies on these lines: {2, 37}, {7, 32812}, {8, 32813}, {239, 8253}, {319, 32806}, {320, 32805}, {491, 17360}, {492, 17361}, {590, 3759}, {615, 3758}, {894, 8252}, {5393, 17393}, {5405, 17394}, {13846, 17121}, {13847, 17120}

X(32803) =


X(32804) = (name pending)

Barycentrics    b c - 4 S : :

X(32804) lies on these lines: {2, 37}, {7, 32813}, {8, 32812}, {239, 8252}, {319, 32805}, {320, 32806}, {491, 17361}, {492, 17360}, {590, 3758}, {615, 3759}, {894, 8253}, {5393, 17394}, {5405, 17393}, {13846, 17120}, {13847, 17121}

X(32804) =


X(32805) = (name pending)

Barycentrics    SA + 2 S : :

X(32805) lies on these lines: {2, 6}, {3, 12322}, {4, 9739}, {5, 488}, {7, 32791}, {8, 32792}, {20, 14233}, {76, 3317}, {99, 26619}, {140, 487}, {264, 3536}, {315, 7376}, {317, 3535}, {319, 32804}, {320, 32803}, {486, 641}, {489, 3523}, {490, 3091}, {631, 637}, {638, 3090}, {639, 5420}, {1151, 12221}, {1328, 13701}, {1444, 16433}, {1505, 32969}, {1583, 9723}, {1588, 15883}, {3311, 32839}, {3312, 32491}, {3591, 32820}, {3845, 13678}, {3926, 13951}, {5058, 32977}, {5405, 17321}, {5408, 10963}, {5491, 6119}, {6292, 13829}, {6340, 8281}, {6398, 32827}, {6412, 26618}, {6460, 32489}, {6776, 10846}, {7389, 13935}, {7582, 7769}, {7584, 11315}, {7763, 13939}, {7782, 23275}, {8797, 11090}, {11294, 33364}, {11313, 13966}, {11314, 32828}, {12100, 13798}, {13654, 25320}, {13676, 14971}, {14907, 26620}, {18762, 32815}, {31995, 32801}, {32087, 32802}, {32490, 32838}

X(32805) =


X(32806) = (name pending)

Barycentrics    SA - 2 S : :

X(32806) lies on these

X(32806) = lines: {2, 6}, {3, 12323}, {4, 9738}, {5, 487}, {7, 32792}, {8, 32791}, {20, 14230}, {76, 3316}, {99, 26620}, {140, 488}, {264, 3535}, {315, 7375}, {317, 3536}, {319, 32803}, {320, 32804}, {485, 642}, {489, 3091}, {490, 3523}, {631, 638}, {637, 3090}, {640, 5418}, {1151, 23312}, {1327, 13821}, {1444, 16432}, {1504, 32969}, {1584, 9723}, {1587, 15884}, {3311, 32490}, {3312, 32839}, {3590, 32820}, {3845, 13798}, {3926, 8976}, {5062, 32977}, {5391, 8243}, {5393, 17321}, {5409, 10961}, {5490, 6118}, {6221, 32827}, {6290, 21736}, {6292, 13709}, {6340, 8280}, {6411, 26617}, {6459, 32488}, {6462, 13881}, {6776, 10845}, {7388, 9540}, {7581, 7769}, {7583, 11316}, {7763, 13886}, {7782, 23269}, {8797, 11091}, {8968, 13430}, {8981, 11314}, {9674, 33238}, {11293, 31412}, {11313, 32828}, {12100, 13678}, {13774, 25320}, {13796, 14971}, {14001, 31481}, {14907, 26619}, {18538, 32815}, {31411, 32970}, {31995, 32802}, {32087, 32801}, {32491, 32838}, {32497, 32990}


X(32807) = (name pending)

Barycentrics    SA + 3 S : :

X(32807) lies on these lines: {2, 6}, {5, 490}, {7, 32795}, {8, 32796}, {76, 10194}, {140, 637}, {316, 2459}, {487, 3525}, {488, 3090}, {489, 631}, {621, 2045}, {622, 2046}, {638, 1656}, {641, 7388}, {1267, 31995}, {1444, 21553}, {1585, 32002}, {3317, 5490}, {3523, 12322}, {3818, 6813}, {5056, 12323}, {5391, 32087}, {5564, 32792}, {6118, 6420}, {6119, 32832}, {6811, 31670}, {7321, 32791}, {11293, 23311}, {11315, 13951}, {13798, 15719}, {13966, 32491}

X(32807) = isotomic conjugate of X(10195)
X(32807) = anticomplement of X(32789)


X(32808) = (name pending)

Barycentrics    3 SA + S : :

X(32808) lies on these lines: {2, 6}, {7, 32797}, {8, 10911}, {30, 490}, {76, 1328}, {99, 13712}, {315, 32421}, {319, 32802}, {320, 32801}, {340, 1585}, {376, 488}, {381, 638}, {633, 2043}, {634, 2044}, {1267, 21296}, {1494, 11090}, {3543, 12322}, {3839, 12323}, {3926, 26289}, {5391, 32099}, {5490, 14241}, {6200, 13701}, {7389, 7768}, {9166, 13927}, {9732, 13692}, {11001, 13678}, {11128, 33442}, {11129, 33440}, {13850, 33228}, {23259, 32892}, {26615, 32817}, {32419, 32833}

X(32808) = anticomplement of X(32787)
X(32808) = {X(2),X(69)}-harmonic conjugate of X(32809)


X(32809) = (name pending)

Barycentrics    3 SA - S : :

X(32809) lies on these lines: {2, 6}, {7, 32798}, {8, 10910}, {30, 489}, {76, 1327}, {99, 13835}, {315, 32419}, {319, 32801}, {320, 32802}, {340, 1586}, {376, 487}, {381, 637}, {488, 3524}, {633, 2044}, {634, 2043}, {1267, 32099}, {1494, 11091}, {3543, 12323}, {3839, 12322}, {3926, 26288}, {5391, 21296}, {6396, 13821}, {7388, 7768}, {9166, 13874}, {9733, 13812}, {11001, 13798}, {11128, 33443}, {11129, 33441}, {13674, 21737}, {13932, 33228}, {23249, 32892}, {26616, 32817}, {32421, 32833}

X(32809) = anticomplement of X(32788)
X(32809) = {X(2),X(69)}-harmonic conjugate of X(32808)


X(32810) = (name pending)

Barycentrics    3 SA + 2 S : :

X(32810) lies on these lines: {2, 6}, {7, 32801}, {8, 32802}, {30, 488}, {76, 14226}, {99, 26615}, {340, 3535}, {376, 637}, {381, 12323}, {487, 549}, {489, 10304}, {490, 3543}, {519, 31582}, {542, 33341}, {638, 3545}, {1327, 5490}, {1444, 21559}, {6231, 13172}, {6289, 22806}, {6337, 13701}, {7376, 7768}, {7811, 26620}, {8703, 13798}, {11315, 32825}, {12222, 23311}, {13651, 13920}, {13692, 21736}, {13785, 32892}, {13834, 13988}, {14907, 26616}, {21296, 32791}, {26288, 32006}, {26619, 32833}, {32099, 32792}, {32815, 33457}

X(32810) =


X(32811) = (name pending)

Barycentrics    3 SA - 2 S : :

X(32811) lies on these lines: {2, 6}, {7, 32802}, {8, 32801}, {76, 14241}, {99, 26616}, {340, 3536}, {376, 638}, {381, 12322}, {488, 549}, {489, 3543}, {490, 10304}, {519, 31583}, {637, 3545}, {1444, 21560}, {6230, 13172}, {7375, 7768}, {7811, 26619}, {8703, 13678}, {11316, 32825}, {13665, 32892}, {14907, 26615}, {21296, 32792}, {26289, 32006}, {26620, 32833}, {32099, 32791}, {32815, 33456}

X(32811) =


X(32812) = (name pending)

Barycentrics    SA + 4 S : :

X(32812) lies on these lines: {2, 6}, {7, 32803}, {8, 32804}, {20, 14239}, {488, 1656}, {489, 10303}, {490, 5056}, {631, 12322}, {637, 3525}, {638, 5067}, {1444, 21547}, {3090, 12323}, {5490, 10194}, {7376, 32006}, {10577, 11292}, {13678, 19709}, {32488, 33364}

X(32812) = isotomic conjugate of X(34089)


X(32813) = (name pending)

Barycentrics    SA - 4 S : :

X(32813) lies on these lines: {2, 6}, {7, 32804}, {8, 32803}, {20, 14235}, {488, 3526}, {489, 5056}, {490, 10303}, {631, 12323}, {637, 5067}, {638, 3525}, {1444, 21548}, {3090, 12322}, {7375, 32006}, {10576, 11291}, {13678, 15701}, {32489, 33365}

X(32813) = isotomic conjugate of X(34091)


X(32814) = (name pending)

Barycentrics    4 SA + S : :

X(32814) lies on these

X(32814) = lines: {2, 6}, {8, 481}, {20, 14227}, {319, 32794}, {320, 32793}, {487, 15717}, {488, 3522}, {490, 5059}, {637, 3146}, {638, 3832}, {1267, 17361}, {3933, 9543}, {5391, 17360}, {6351, 17374}, {6352, 17344}, {12322, 17578}, {17296, 30412}, {26617, 32817}


X(32815) = (name pending)

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

X(32815) lies on these lines: {2, 99}, {3, 32828}, {4, 325}, {5, 6337}, {6, 14033}, {20, 76}, {30, 69}, {32, 6392}, {39, 32971}, {140, 32867}, {141, 32986}, {183, 376}, {193, 538}, {194, 14035}, {230, 32985}, {253, 22468}, {264, 18850}, {274, 452}, {305, 6995}, {315, 3146}, {316, 3543}, {350, 4293}, {381, 1007}, {382, 3933}, {384, 5286}, {385, 33007}, {393, 15014}, {489, 5871}, {490, 5870}, {491, 23249}, {492, 23259}, {550, 32868}, {598, 11148}, {626, 32982}, {631, 32838}, {668, 17784}, {736, 6658}, {754, 20080}, {1003, 7735}, {1078, 3522}, {1285, 14614}, {1352, 10008}, {1506, 32991}, {1597, 3964}, {1657, 7767}, {1909, 4294}, {1992, 11159}, {2386, 12272}, {2548, 7781}, {2782, 6776}, {2794, 5921}, {2795, 24280}, {2896, 32997}, {2996, 3767}, {3053, 33239}, {3090, 32839}, {3091, 7763}, {3096, 33025}, {3314, 33017}, {3363, 11165}, {3523, 7782}, {3524, 32885}, {3525, 32883}, {3528, 32886}, {3529, 7750}, {3618, 11286}, {3619, 11287}, {3620, 7761}, {3627, 7776}, {3760, 4299}, {3761, 4302}, {3788, 32972}, {3815, 8716}, {3832, 7752}, {3839, 7799}, {3843, 32876}, {3849, 11160}, {3858, 32891}, {3934, 32990}, {3972, 5304}, {4190, 18135}, {5013, 15491}, {5020, 19583}, {5056, 7769}, {5059, 7802}, {5067, 32884}, {5068, 15031}, {5073, 32890}, {5077, 21356}, {5210, 13468}, {5254, 14001}, {5395, 32450}, {5485, 11164}, {5866, 6644}, {5939, 12243}, {5976, 13172}, {6214, 12296}, {6215, 12297}, {6340, 6677}, {6462, 31411}, {6525, 6528}, {6781, 17131}, {6787, 15631}, {6904, 18140}, {7487, 28706}, {7500, 8024}, {7519, 9464}, {7694, 14981}, {7736, 8370}, {7738, 7770}, {7739, 7804}, {7746, 32989}, {7747, 7758}, {7748, 7795}, {7754, 19687}, {7756, 7800}, {7766, 19686}, {7771, 10304}, {7774, 11361}, {7775, 14148}, {7777, 33016}, {7778, 16041}, {7783, 16924}, {7784, 33238}, {7785, 14068}, {7787, 14031}, {7788, 15682}, {7789, 14064}, {7791, 16986}, {7792, 14039}, {7793, 33244}, {7796, 17578}, {7797, 14037}, {7803, 33198}, {7806, 33255}, {7811, 15683}, {7823, 33280}, {7828, 33181}, {7832, 33180}, {7833, 16990}, {7836, 14063}, {7839, 14034}, {7840, 23334}, {7847, 33202}, {7848, 32479}, {7850, 15640}, {7851, 14069}, {7857, 33205}, {7863, 32980}, {7864, 16898}, {7868, 33190}, {7879, 19695}, {7881, 33229}, {7885, 33279}, {7891, 32961}, {7893, 19696}, {7898, 33192}, {7904, 33253}, {7906, 14042}, {7912, 32996}, {7925, 33006}, {7929, 19691}, {7930, 33182}, {7931, 33251}, {7941, 14066}, {7942, 33183}, {7945, 33283}, {7947, 14062}, {9723, 9818}, {9741, 11163}, {9744, 23235}, {9770, 11317}, {10723, 32458}, {11001, 32892}, {11111, 16992}, {11147, 16509}, {11179, 14928}, {11336, 16317}, {11352, 24597}, {11355, 30962}, {12082, 15574}, {12215, 14853}, {13586, 17008}, {13881, 32970}, {14712, 22564}, {15075, 28406}, {15271, 33215}, {15301, 31415}, {15815, 32978}, {16044, 31404}, {16589, 33039}, {17005, 33005}, {17129, 33257}, {17538, 32888}, {17738, 24247}, {18354, 18420}, {18534, 22241}, {18538, 32806}, {18762, 32805}, {19570, 33187}, {20088, 20105}, {21734, 32872}, {21843, 32456}, {23055, 27088}, {24248, 24291}, {27269, 33058}, {31276, 32965}, {31401, 32987}, {32459, 33216}, {32810, 33457}

X(32815) =


X(32816) = (name pending)

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

X(32816) lies on these lines: {2, 32}, {3, 1007}, {4, 325}, {5, 69}, {6, 14064}, {20, 316}, {39, 32974}, {75, 31418}, {76, 3091}, {99, 3146}, {115, 6392}, {127, 28406}, {141, 32968}, {148, 32996}, {183, 3090}, {187, 32989}, {193, 625}, {194, 14063}, {230, 32969}, {232, 28710}, {264, 18855}, {274, 5177}, {305, 7378}, {317, 3089}, {350, 10591}, {381, 3933}, {382, 6390}, {385, 32961}, {439, 620}, {491, 1588}, {492, 1587}, {511, 10008}, {524, 13881}, {538, 2996}, {574, 33023}, {631, 7750}, {637, 26468}, {638, 26469}, {1285, 33189}, {1502, 8801}, {1598, 3964}, {1656, 7767}, {1909, 10590}, {1992, 5305}, {2456, 5207}, {2549, 7764}, {2794, 8781}, {3053, 32970}, {3266, 31099}, {3314, 16924}, {3522, 7802}, {3523, 7769}, {3525, 32884}, {3528, 32887}, {3543, 7799}, {3545, 7788}, {3589, 33221}, {3618, 7866}, {3620, 3934}, {3627, 32876}, {3628, 14929}, {3631, 18584}, {3734, 32979}, {3788, 7737}, {3815, 7784}, {3832, 7796}, {3839, 7871}, {3843, 32875}, {3850, 32878}, {3851, 32868}, {3854, 15031}, {3858, 32890}, {3972, 33181}, {5013, 32986}, {5024, 8357}, {5025, 5286}, {5032, 7817}, {5056, 7768}, {5067, 32883}, {5068, 7917}, {5071, 32885}, {5073, 32891}, {5187, 18135}, {5254, 9766}, {5304, 7828}, {5319, 7838}, {5395, 7804}, {5475, 7795}, {5490, 23311}, {5552, 20553}, {5866, 12084}, {6526, 6528}, {6622, 32001}, {6656, 7736}, {6856, 16992}, {6919, 18140}, {7387, 9723}, {7408, 16276}, {7486, 7850}, {7509, 15574}, {7603, 7854}, {7694, 30270}, {7735, 7762}, {7738, 7841}, {7739, 7861}, {7745, 7778}, {7746, 7845}, {7747, 7888}, {7748, 31173}, {7751, 20080}, {7754, 33228}, {7761, 31401}, {7771, 10303}, {7777, 7791}, {7779, 32966}, {7783, 33017}, {7786, 33202}, {7789, 14033}, {7790, 33200}, {7792, 32951}, {7794, 32991}, {7797, 33283}, {7803, 7858}, {7806, 33248}, {7819, 15484}, {7823, 7925}, {7832, 33198}, {7835, 33201}, {7836, 14035}, {7840, 33006}, {7842, 33272}, {7847, 33210}, {7849, 31417}, {7851, 33285}, {7864, 33251}, {7868, 16045}, {7873, 31455}, {7876, 31407}, {7877, 14061}, {7878, 33182}, {7879, 32992}, {7881, 8370}, {7882, 11160}, {7891, 23334}, {7893, 17008}, {7897, 16044}, {7898, 32965}, {7901, 7921}, {7904, 17005}, {7906, 14041}, {7911, 33025}, {7919, 14930}, {7920, 14046}, {7931, 16898}, {7935, 9698}, {7939, 16921}, {7940, 33203}, {7945, 14037}, {7946, 32963}, {7947, 11361}, {7949, 14568}, {8359, 31467}, {8361, 30435}, {8981, 11314}, {9300, 33223}, {9605, 33184}, {11057, 15692}, {11163, 33190}, {11174, 32956}, {11184, 33215}, {11287, 31406}, {11313, 32805}, {11324, 15437}, {13571, 33290}, {14712, 32964}, {14881, 18906}, {15271, 32975}, {15815, 33226}, {16589, 33038}, {16999, 33053}, {17004, 32998}, {17128, 33016}, {17538, 32889}, {17578, 32841}, {18907, 32954}, {19569, 33266}, {20081, 32993}, {21531, 23291}, {21734, 32873}, {22110, 32985}, {26558, 31405}, {26590, 31402}, {27269, 33057}, {31276, 32962}, {31489, 32978}, {31859, 33229}

X(32816) = isotomic conjugate of X(34285)


X(32817) = (name pending)

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

X(32817) lies on these lines: {2, 2418}, {3, 15589}, {4, 325}, {5, 32831}, {6, 14039}, {20, 3933}, {22, 22241}, {39, 16045}, {69, 74}, {76, 631}, {140, 32834}, {141, 8716}, {148, 16041}, {183, 3524}, {193, 1003}, {194, 10336}, {264, 18852}, {274, 16845}, {305, 6353}, {315, 3529}, {316, 15682}, {345, 5088}, {348, 7283}, {378, 3964}, {385, 32985}, {394, 13509}, {488, 10784}, {489, 14227}, {490, 14242}, {491, 23267}, {492, 23273}, {538, 7735}, {543, 7908}, {549, 32869}, {632, 32870}, {1007, 3545}, {1078, 10299}, {1656, 32835}, {1992, 3972}, {2394, 3265}, {2482, 17131}, {2549, 7801}, {2896, 33226}, {3053, 15480}, {3090, 7763}, {3091, 32841}, {3146, 7776}, {3147, 28706}, {3314, 32986}, {3522, 7767}, {3525, 32828}, {3528, 3785}, {3533, 32832}, {3534, 14929}, {3618, 7757}, {3620, 8356}, {3712, 7223}, {3734, 7736}, {3760, 7288}, {3761, 5218}, {3767, 7863}, {3788, 32457}, {3855, 7752}, {3945, 4234}, {4045, 7738}, {4121, 32064}, {4175, 31383}, {4387, 7181}, {5013, 32960}, {5054, 32874}, {5067, 32829}, {5070, 32871}, {5071, 32837}, {5254, 32951}, {5286, 7789}, {5304, 8369}, {5305, 33181}, {5475, 9770}, {5971, 26255}, {6392, 7807}, {6527, 21312}, {7493, 9464}, {7494, 8024}, {7620, 22110}, {7710, 14981}, {7714, 16276}, {7737, 7813}, {7739, 7820}, {7750, 17538}, {7754, 32973}, {7758, 7816}, {7761, 15301}, {7762, 32981}, {7766, 33255}, {7771, 15698}, {7774, 14033}, {7777, 32983}, {7778, 33285}, {7779, 33007}, {7782, 21735}, {7783, 16043}, {7788, 11001}, {7790, 33196}, {7796, 32006}, {7806, 33224}, {7828, 33195}, {7831, 21356}, {7832, 33194}, {7835, 33197}, {7836, 14064}, {7839, 14037}, {7851, 32953}, {7864, 33221}, {7868, 33230}, {7879, 33023}, {7881, 32974}, {7891, 32970}, {7893, 33244}, {7897, 20094}, {7898, 8591}, {7900, 33280}, {7906, 14035}, {7921, 14031}, {7925, 32984}, {7929, 33253}, {7931, 33223}, {7939, 32997}, {7941, 14068}, {7947, 14063}, {8598, 11160}, {8667, 32459}, {9605, 33198}, {9740, 27088}, {12215, 14912}, {13172, 32458}, {13881, 32958}, {15022, 32881}, {15491, 31400}, {15694, 32893}, {15717, 32880}, {16898, 18841}, {16925, 20081}, {16990, 33215}, {17008, 33216}, {17128, 32968}, {17129, 32964}, {17130, 31401}, {17526, 18600}, {17567, 18135}, {18533, 32001}, {20065, 33239}, {20105, 33225}, {20888, 30478}, {26615, 32808}, {26616, 32809}, {26617, 32814}, {27269, 33043}, {30435, 33201}, {31239, 31450}, {31276, 32978}

X(32817) =


X(32818) = (name pending)

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

X(32818) lies on these lines: {2, 3933}, {3, 14929}, {4, 325}, {5, 32830}, {6, 14069}, {8, 27187}, {20, 6390}, {24, 3964}, {32, 33191}, {39, 32956}, {54, 69}, {76, 1007}, {99, 3529}, {140, 15589}, {141, 31400}, {183, 3525}, {193, 7807}, {194, 14064}, {230, 32959}, {264, 18853}, {305, 1235}, {315, 376}, {345, 17181}, {385, 32970}, {487, 10784}, {488, 10783}, {491, 7581}, {492, 7582}, {547, 32874}, {620, 7916}, {626, 7738}, {632, 32871}, {1285, 7762}, {1384, 33205}, {1656, 32834}, {1909, 8164}, {1992, 7870}, {2548, 7801}, {2549, 7821}, {2896, 33215}, {3091, 32840}, {3266, 16051}, {3314, 16043}, {3329, 18841}, {3523, 7767}, {3524, 3785}, {3528, 7750}, {3533, 7769}, {3541, 32000}, {3545, 7752}, {3618, 7832}, {3619, 7786}, {3620, 11285}, {3760, 10589}, {3761, 10588}, {3763, 9606}, {3767, 7813}, {3788, 7735}, {3815, 32957}, {3832, 32879}, {3855, 7814}, {4121, 11433}, {5024, 33202}, {5032, 8366}, {5055, 32869}, {5067, 32828}, {5070, 32870}, {5071, 32836}, {5254, 33285}, {5286, 7778}, {5304, 32954}, {5319, 7874}, {5485, 32984}, {6179, 11008}, {6392, 7887}, {7494, 26233}, {7503, 22241}, {7512, 9723}, {7710, 30270}, {7736, 7764}, {7737, 7863}, {7739, 7867}, {7757, 33196}, {7760, 33195}, {7768, 10299}, {7774, 7787}, {7777, 32968}, {7779, 10351}, {7783, 32986}, {7785, 14033}, {7789, 9766}, {7791, 7897}, {7792, 32952}, {7793, 33216}, {7794, 31401}, {7800, 7895}, {7803, 7909}, {7806, 33222}, {7809, 15682}, {7811, 15698}, {7823, 33239}, {7825, 14148}, {7826, 21843}, {7837, 33224}, {7840, 7891}, {7841, 9741}, {7864, 33223}, {7879, 32990}, {7885, 33238}, {7893, 32964}, {7898, 33247}, {7900, 33007}, {7912, 16041}, {7917, 14907}, {7921, 14037}, {7925, 32969}, {7929, 33008}, {7931, 33221}, {7939, 32965}, {7941, 14035}, {7945, 13571}, {8361, 22253}, {8781, 14651}, {13219, 30552}, {13881, 22110}, {14548, 25650}, {14614, 33231}, {15022, 32880}, {15048, 33180}, {15699, 32893}, {15717, 32881}, {16990, 32978}, {16999, 33049}, {17008, 32977}, {17128, 32983}, {17130, 31415}, {17170, 32851}, {17538, 32876}, {18907, 33201}, {20080, 32989}, {20081, 32961}, {20088, 33255}, {20094, 33279}, {25583, 29641}, {25592, 31091}, {27269, 33042}, {30435, 33181}, {31276, 32975}, {31859, 32974}

X(32818) = {X(76),X(1007)}-harmonic conjugate of X(3090)


X(32819) = (name pending)

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

X(32819) lies on these lines: {2, 15815}, {3, 11185}, {4, 325}, {5, 99}, {6, 14035}, {20, 183}, {30, 76}, {32, 19687}, {39, 543}, {69, 3146}, {83, 15048}, {115, 7807}, {140, 7782}, {141, 6655}, {148, 384}, {187, 33250}, {194, 7745}, {230, 3552}, {264, 1885}, {274, 11113}, {305, 428}, {311, 12225}, {315, 382}, {316, 3627}, {317, 12173}, {338, 26179}, {350, 7354}, {376, 32828}, {381, 7763}, {385, 6658}, {395, 11121}, {396, 11122}, {427, 16276}, {489, 13749}, {490, 13748}, {491, 23251}, {492, 23261}, {524, 7823}, {528, 24524}, {529, 17144}, {538, 7747}, {546, 6390}, {548, 7771}, {550, 1078}, {574, 32992}, {575, 14928}, {597, 8596}, {599, 33192}, {620, 33249}, {625, 7863}, {626, 33229}, {631, 32867}, {671, 7828}, {682, 9149}, {1003, 3767}, {1007, 3832}, {1235, 18560}, {1503, 18906}, {1657, 14907}, {1909, 6284}, {2548, 31859}, {2549, 7770}, {2896, 33256}, {7735, 32981}, {3053, 22329}, {3054, 33259}, {3055, 33002}, {3058, 25303}, {3091, 6337}, {3096, 8357}, {3314, 33019}, {3329, 9607}, {3524, 32838}, {3529, 3785}, {3543, 7788}, {3545, 32829}, {3589, 7864}, {3619, 33025}, {3629, 20088}, {3631, 7929}, {3734, 6656}, {3760, 10483}, {3788, 33228}, {3815, 7783}, {3818, 6393}, {3830, 7776}, {3839, 32831}, {3845, 7799}, {3849, 7826}, {3853, 7796}, {3861, 7814}, {3934, 7756}, {3964, 11403}, {3972, 5305}, {5013, 16924}, {5023, 17008}, {5025, 7789}, {5059, 15589}, {5071, 32839}, {5206, 8598}, {5210, 33254}, {5286, 14033}, {5306, 19686}, {5475, 7781}, {5480, 12215}, {5939, 13335}, {5976, 6248}, {6392, 14614}, {6661, 7834}, {6781, 7780}, {6872, 16992}, {7398, 19583}, {7576, 28706}, {7610, 33208}, {7620, 11164}, {7736, 32979}, {7737, 7754}, {7738, 11174}, {7746, 18546}, {7749, 32456}, {7753, 32450}, {7755, 32457}, {7760, 18907}, {7761, 17130}, {7765, 7804}, {7774, 14068}, {7777, 33018}, {7778, 14063}, {7784, 33017}, {7785, 14042}, {7787, 14034}, {7790, 7819}, {7793, 33257}, {7794, 7842}, {7795, 7841}, {7800, 33234}, {7801, 7825}, {7803, 11286}, {7809, 15687}, {7810, 32479}, {7813, 7843}, {7820, 7861}, {7830, 8353}, {7832, 33184}, {7833, 31276}, {7835, 8361}, {7836, 14041}, {7837, 20105}, {7838, 14537}, {7846, 19697}, {7847, 8362}, {7851, 14001}, {7862, 18424}, {7868, 32974}, {7871, 12102}, {7891, 32966}, {7904, 33264}, {7906, 14066}, {7907, 32459}, {7912, 14062}, {7918, 8364}, {7919, 33185}, {7920, 14032}, {7923, 19689}, {7925, 32993}, {7930, 8360}, {7932, 14036}, {7939, 8597}, {7942, 8368}, {7947, 14044}, {8556, 33207}, {8591, 33013}, {8667, 33193}, {8716, 33016}, {10330, 14389}, {11112, 18140}, {11159, 30435}, {11742, 33243}, {13468, 33265}, {13881, 16925}, {14031, 16989}, {14360, 16042}, {14712, 17129}, {14994, 29317}, {15014, 27376}, {15075, 28695}, {15271, 32965}, {15491, 33020}, {15640, 32869}, {15682, 32836}, {15692, 32870}, {15697, 32893}, {15702, 32883}, {16990, 32997}, {17004, 33014}, {17005, 33024}, {17537, 18600}, {17579, 18135}, {19708, 32885}, {20065, 33280}, {24291, 24851}, {31400, 32983}, {31489, 32962}

X(32819) =


X(32820) = (name pending)

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

X(32820) lies on these lines: {2, 9607}, {3, 32833}, {4, 325}, {5, 7799}, {6, 14037}, {20, 7788}, {30, 7796}, {39, 6704}, {69, 3522}, {76, 140}, {99, 550}, {141, 7783}, {148, 7947}, {183, 3523}, {194, 7789}, {230, 7891}, {305, 468}, {315, 1657}, {384, 13571}, {524, 3552}, {538, 7755}, {543, 7821}, {546, 7814}, {548, 7811}, {597, 19689}, {599, 32965}, {631, 32836}, {754, 33250}, {1003, 7758}, {1007, 5068}, {1078, 15712}, {1656, 7763}, {1992, 33201}, {2396, 15000}, {2482, 7780}, {2549, 7881}, {3035, 20943}, {3090, 32837}, {3516, 3964}, {3533, 32828}, {3590, 32806}, {3591, 32805}, {3627, 7809}, {3631, 7904}, {3785, 21735}, {3815, 17128}, {3850, 7752}, {3851, 11185}, {5056, 32831}, {5059, 32879}, {5073, 7776}, {5254, 7836}, {5305, 7835}, {5306, 33225}, {5319, 33220}, {5485, 32958}, {6310, 6786}, {6656, 7781}, {6658, 7840}, {6661, 7772}, {6781, 7882}, {7495, 8024}, {7610, 33206}, {7738, 7868}, {7739, 33217}, {7745, 7906}, {7748, 7908}, {7756, 7895}, {7757, 7819}, {7759, 19687}, {7760, 8369}, {7762, 7813}, {7764, 8370}, {7765, 7880}, {7767, 7782}, {7774, 14031}, {7778, 33283}, {7787, 14040}, {7791, 8716}, {7793, 32459}, {7794, 8356}, {7795, 31859}, {7806, 20105}, {7818, 19695}, {7820, 32450}, {7826, 32456}, {7827, 33185}, {7832, 15048}, {7856, 8368}, {7870, 8361}, {7873, 8353}, {7878, 19697}, {7885, 20094}, {7888, 33228}, {7905, 18907}, {7909, 33184}, {7922, 8357}, {7936, 8354}, {7946, 33257}, {8362, 10159}, {8550, 12215}, {8556, 33012}, {8591, 33256}, {8667, 32964}, {9741, 32956}, {9766, 14035}, {9770, 32979}, {9939, 33268}, {10018, 28706}, {10301, 16276}, {10303, 32869}, {10992, 32458}, {11057, 12103}, {11148, 33182}, {11163, 32971}, {11184, 32962}, {13468, 33259}, {13747, 18145}, {14023, 33235}, {14614, 32973}, {15533, 33208}, {15702, 32892}, {15815, 16990}, {16712, 17698}, {16772, 30471}, {16773, 30472}, {16925, 22329}, {17130, 32992}, {19570, 33245}, {20576, 32520}, {22110, 32966}

X(32820) =


X(32821) = (name pending)

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

X(32821) lies on these lines: {2, 9606}, {3, 7768}, {4, 325}, {5, 32833}, {6, 7836}, {39, 7868}, {69, 3523}, {76, 1656}, {99, 1657}, {140, 183}, {187, 7916}, {194, 7778}, {298, 22236}, {299, 22238}, {305, 5094}, {315, 550}, {316, 5073}, {340, 3515}, {381, 7814}, {382, 7809}, {384, 9766}, {524, 16925}, {538, 7887}, {574, 7879}, {599, 7824}, {620, 7855}, {626, 31859}, {631, 32837}, {754, 33235}, {1003, 7759}, {1007, 5056}, {1078, 15720}, {1273, 17928}, {1384, 7877}, {1992, 33181}, {2896, 15815}, {3053, 7779}, {3090, 32836}, {3096, 5024}, {3314, 5013}, {3522, 6337}, {3533, 32829}, {3552, 7840}, {3763, 32449}, {3785, 10299}, {3788, 7754}, {3850, 11185}, {3851, 7752}, {3854, 32879}, {4352, 30761}, {5007, 33220}, {5023, 7893}, {5059, 32006}, {5068, 32840}, {5206, 7882}, {5254, 33283}, {5309, 33218}, {6179, 11288}, {6655, 8716}, {6658, 11164}, {7486, 32869}, {7610, 16923}, {7739, 8363}, {7745, 14031}, {7748, 14148}, {7751, 33233}, {7757, 7866}, {7758, 7807}, {7760, 7870}, {7764, 7770}, {7765, 33219}, {7767, 15712}, {7772, 7880}, {7774, 7789}, {7777, 33020}, {7781, 7821}, {7782, 7917}, {7783, 7784}, {7785, 14034}, {7786, 10159}, {7793, 13196}, {7794, 11285}, {7795, 11174}, {7798, 7874}, {7816, 7903}, {7818, 33234}, {7828, 22253}, {7832, 9605}, {7835, 7905}, {7837, 33225}, {7839, 7945}, {7848, 15515}, {7858, 11286}, {7865, 31652}, {7867, 32450}, {7876, 22332}, {7878, 33237}, {7883, 11165}, {7907, 8667}, {7912, 14045}, {7921, 14040}, {7922, 11287}, {7925, 13881}, {7946, 13586}, {8556, 33015}, {9300, 16898}, {9770, 32971}, {9939, 33276}, {11055, 33240}, {11057, 15696}, {11168, 33003}, {11184, 16921}, {12150, 33242}, {13468, 33000}, {15533, 33274}, {21735, 32876}, {22110, 32961}, {22329, 32970}, {22331, 33246}, {31276, 31489}

X(32821) =


X(32822) = (name pending)

Barycentrics    2 SA^2 + 3 SB SC : :
Barycentrics    5*a^4 - 4*a^2*b^2 - b^4 - 4*a^2*c^2 + 10*b^2*c^2 - c^4 : :

X(32822) lies on these lines: {3, 32834}, {4, 325}, {5, 32835}, {20, 7767}, {30, 32830}, {69, 3529}, {76, 376}, {83, 14482}, {99, 631}, {115, 32955}, {148, 7945}, {183, 3528}, {193, 19687}, {194, 14033}, {264, 18851}, {305, 7714}, {381, 32831}, {385, 33239}, {489, 14242}, {490, 14227}, {491, 23269}, {492, 23275}, {543, 7795}, {547, 32871}, {550, 15589}, {1003, 6392}, {1007, 3855}, {1078, 21735}, {1285, 7754}, {2549, 7822}, {2896, 33247}, {2996, 7807}, {3090, 6337}, {3091, 6390}, {3146, 3933}, {3314, 33238}, {3524, 32828}, {3525, 32867}, {3534, 32869}, {3543, 7776}, {3545, 7763}, {3619, 7847}, {3620, 33234}, {3734, 6704}, {3767, 33191}, {3785, 17538}, {3839, 32841}, {4217, 18600}, {5013, 32957}, {5054, 32870}, {5071, 32829}, {5254, 14069}, {5286, 14039}, {5305, 33201}, {5485, 8859}, {6240, 32001}, {6353, 16276}, {7735, 7816}, {7736, 7781}, {7737, 7890}, {7750, 11001}, {7778, 33292}, {7779, 33280}, {7782, 10299}, {7783, 32968}, {7789, 32951}, {7790, 33194}, {7791, 11606}, {7797, 14001}, {7828, 33197}, {7832, 33196}, {7835, 33195}, {7836, 16041}, {7839, 14031}, {7851, 32952}, {7868, 33232}, {7879, 33272}, {7881, 32982}, {7886, 33189}, {7891, 32969}, {7893, 33193}, {7897, 33279}, {7906, 14068}, {7917, 15682}, {7921, 14035}, {7928, 32986}, {7929, 33271}, {7939, 33192}, {7947, 32996}, {8370, 9741}, {8591, 31276}, {8703, 32874}, {8716, 31400}, {12100, 32893}, {13881, 32959}, {14912, 18906}, {14929, 17800}, {15048, 33198}, {15300, 15515}, {15683, 32880}, {15692, 32872}, {15702, 32838}, {15715, 32886}, {16043, 17128}, {16990, 33226}, {17129, 33244}, {19686, 20105}, {20081, 33007}, {31859, 32971}

X(32822) = {X(4),X(3926)}-harmonic conjugate of X(32823)


X(32823) = (name pending)

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

X(32823) lies on these lines: {2, 7762}, {3, 32835}, {4, 325}, {5, 32834}, {6, 32951}, {30, 32831}, {32, 33189}, {39, 9770}, {69, 576}, {76, 3545}, {141, 31404}, {183, 5067}, {193, 7887}, {194, 16041}, {230, 32958}, {264, 18854}, {315, 631}, {316, 3529}, {376, 7763}, {381, 32830}, {385, 32969}, {491, 7582}, {492, 7581}, {547, 32870}, {625, 7758}, {626, 7736}, {1078, 3533}, {1285, 7807}, {1384, 33203}, {1594, 32000}, {1656, 15589}, {1992, 7828}, {2548, 7821}, {2896, 32978}, {3053, 22110}, {3091, 3933}, {3146, 6390}, {3314, 18840}, {3329, 33221}, {3524, 7750}, {3525, 3785}, {3526, 14929}, {3542, 32001}, {3543, 32841}, {3618, 7858}, {3619, 7922}, {3620, 32992}, {3767, 7890}, {3788, 33191}, {3815, 32960}, {3839, 32840}, {3855, 7796}, {3964, 10594}, {5024, 33025}, {5054, 32871}, {5056, 10513}, {5066, 32869}, {5071, 7788}, {5254, 33292}, {5286, 9766}, {5304, 8361}, {5305, 33199}, {5395, 6661}, {5485, 20081}, {6392, 33228}, {7735, 7759}, {7737, 7888}, {7738, 7764}, {7745, 14039}, {7754, 32972}, {7766, 33248}, {7774, 7797}, {7775, 7795}, {7777, 7928}, {7778, 14069}, {7779, 32961}, {7783, 33238}, {7784, 31400}, {7785, 7945}, {7792, 32953}, {7793, 32977}, {7794, 31415}, {7799, 15682}, {7803, 33196}, {7811, 15709}, {7812, 33197}, {7818, 31401}, {7823, 32985}, {7836, 14033}, {7839, 33283}, {7840, 32984}, {7860, 21735}, {7862, 14023}, {7871, 11185}, {7881, 32971}, {7885, 32986}, {7891, 33239}, {7897, 16924}, {7898, 33226}, {7900, 16925}, {7906, 14063}, {7925, 20065}, {7926, 33195}, {7929, 33001}, {7934, 14482}, {7946, 17008}, {7947, 14035}, {7949, 11008}, {8781, 9862}, {9605, 33180}, {9723, 12088}, {10299, 14907}, {11001, 32837}, {11057, 15710}, {11163, 33230}, {14930, 33182}, {15048, 33200}, {15484, 33198}, {15683, 32881}, {15692, 32873}, {15702, 32839}, {15715, 32887}, {16990, 32975}, {16999, 33048}, {17129, 32963}, {18907, 33181}, {19709, 32874}, {20080, 32988}, {31406, 33202}, {31859, 32982}

X(32823) = {X(4),X(3926)}-harmonic conjugate of X(32822)


X(32824) = (name pending)

Barycentrics    3 SA^2 + 2 SB SC : :
Barycentrics    5*a^4 - 6*a^2*b^2 + b^4 - 6*a^2*c^2 + 10*b^2*c^2 + c^4 : :

X(32824) lies on these lines: {2, 7765}, {3, 32836}, {4, 325}, {5, 32837}, {20, 7768}, {69, 550}, {76, 3523}, {99, 3522}, {140, 6337}, {148, 33290}, {183, 10299}, {193, 7816}, {194, 14037}, {305, 4232}, {315, 5059}, {439, 7751}, {524, 33239}, {538, 32973}, {543, 32982}, {599, 33226}, {1007, 3851}, {1656, 6390}, {1657, 3933}, {2548, 14148}, {2549, 7869}, {3091, 7799}, {3146, 7796}, {3524, 32892}, {3525, 32885}, {3529, 7788}, {3533, 32838}, {3620, 15301}, {3839, 7814}, {3850, 32876}, {3854, 7752}, {5056, 7763}, {5068, 11185}, {5073, 32006}, {5286, 7892}, {5485, 32959}, {6392, 7755}, {7620, 32966}, {7757, 33198}, {7758, 32981}, {7760, 33201}, {7764, 32979}, {7774, 14034}, {7782, 15589}, {7794, 33023}, {7801, 32974}, {7802, 10513}, {7809, 17578}, {7827, 11148}, {7836, 33283}, {7839, 14040}, {7840, 33280}, {7870, 33199}, {7888, 32980}, {7909, 33200}, {7922, 33210}, {7946, 33193}, {8591, 32997}, {8716, 16043}, {8859, 16925}, {9741, 16045}, {9939, 33214}, {13571, 14031}, {14568, 33203}, {15712, 32878}, {15717, 32869}, {15720, 32868}, {17128, 31400}, {21735, 32877}

X(32824) = {X(4),X(3926)}-harmonic conjugate of X(32825)


X(32825) = (name pending)

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

X(32825) lies on these lines: {2, 3108}, {3, 32837}, {4, 325}, {5, 32836}, {20, 7799}, {69, 140}, {76, 5056}, {99, 5059}, {183, 3533}, {193, 3788}, {194, 33283}, {315, 3522}, {439, 754}, {524, 32970}, {538, 32972}, {550, 6337}, {599, 32978}, {625, 2996}, {631, 7788}, {1007, 1656}, {1078, 10513}, {1273, 3546}, {1657, 6390}, {1992, 32954}, {2548, 7908}, {3091, 7814}, {3146, 7809}, {3314, 31400}, {3517, 3964}, {3523, 3785}, {3619, 31406}, {3620, 7895}, {3850, 32875}, {3854, 11185}, {5067, 32885}, {5068, 7752}, {5071, 32892}, {5286, 7901}, {5304, 7905}, {5306, 33222}, {6179, 33203}, {6392, 7813}, {7620, 32993}, {7736, 7881}, {7750, 21735}, {7757, 33180}, {7759, 32973}, {7767, 15720}, {7769, 15589}, {7770, 9770}, {7774, 7892}, {7775, 32979}, {7780, 11160}, {7781, 32982}, {7785, 14031}, {7801, 32971}, {7811, 15717}, {7812, 33201}, {7818, 33023}, {7821, 32974}, {7827, 33182}, {7836, 14037}, {7840, 16925}, {7846, 14930}, {7858, 33198}, {7863, 32981}, {7865, 31450}, {7870, 33181}, {7882, 21843}, {7897, 33021}, {7912, 33290}, {7916, 20080}, {7922, 33202}, {7941, 14034}, {7946, 32964}, {8667, 32977}, {8716, 33238}, {9607, 33223}, {9766, 14001}, {11163, 16045}, {11184, 32975}, {11315, 32810}, {11316, 32811}, {12815, 17131}, {14023, 32989}, {14614, 33189}, {14976, 33252}, {15022, 32869}, {17130, 32991}, {19570, 33277}, {22110, 32969}, {22329, 32959}, {23334, 33280}, {31404, 33020}

X(32825) = {X(4),X(3926)}-harmonic conjugate of X(32824)


X(32826) = (name pending)

Barycentrics    SA^2 + 4 SB SC : :
Barycentrics    5*a^4 - 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 10*b^2*c^2 - 3*c^4 : :

X(32826) lies on these lines: {2, 7748}, {3, 32838}, {4, 325}, {5, 32839}, {20, 1078}, {30, 3785}, {32, 2996}, {39, 32979}, {69, 382}, {76, 3146}, {99, 3091}, {115, 32973}, {141, 33238}, {148, 4027}, {183, 3529}, {193, 7747}, {194, 14068}, {230, 33239}, {264, 18846}, {305, 7408}, {315, 3543}, {316, 17578}, {376, 32885}, {381, 6337}, {385, 33280}, {439, 7746}, {491, 23253}, {492, 23263}, {543, 2548}, {546, 1007}, {574, 32987}, {620, 32988}, {631, 32883}, {2549, 7808}, {2896, 33192}, {3090, 32884}, {3096, 33210}, {3314, 33279}, {3363, 31467}, {3522, 32832}, {3523, 32867}, {3619, 8357}, {3620, 17130}, {3627, 32006}, {3734, 32974}, {3767, 32981}, {3788, 32980}, {3830, 3933}, {3832, 7763}, {3839, 7752}, {3843, 6390}, {3853, 7776}, {3854, 32835}, {3855, 32887}, {3934, 33023}, {5013, 32983}, {5056, 15031}, {5059, 14907}, {5068, 7769}, {5073, 7767}, {5254, 14033}, {5305, 11159}, {5395, 7772}, {5866, 7506}, {6392, 7737}, {7378, 16276}, {7500, 26233}, {7615, 7749}, {7620, 8859}, {7735, 19687}, {7738, 8370}, {7750, 32888}, {7756, 32990}, {7774, 14042}, {7783, 31404}, {7789, 16041}, {7790, 33198}, {7793, 33193}, {7795, 32982}, {7796, 32875}, {7797, 14031}, {7800, 33272}, {7802, 15589}, {7811, 15640}, {7814, 32841}, {7828, 33201}, {7832, 33200}, {7835, 33199}, {7836, 32996}, {7839, 11361}, {7851, 14039}, {7860, 10513}, {7881, 8352}, {7891, 33006}, {7900, 23334}, {7904, 33271}, {7938, 33278}, {7945, 33290}, {11057, 32874}, {13881, 32985}, {14034, 16989}, {14061, 33203}, {14853, 18502}, {15271, 33226}, {15682, 32892}, {15815, 32975}, {16044, 31400}, {16990, 33256}, {17004, 33254}, {17008, 33257}, {17128, 33017}, {18135, 31295}, {20094, 33018}, {21734, 32870}, {31276, 32997}, {31401, 32991}, {32459, 32977}

X(32826) = {X(4),X(3926)}-harmonic conjugate of X(32827)


X(32827) = (name pending)

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

X(32827) lies on these lines: {2, 187}, {3, 32839}, {4, 325}, {5, 3785}, {6, 16041}, {20, 7694}, {30, 1007}, {32, 32972}, {39, 32982}, {69, 381}, {76, 3832}, {83, 33180}, {99, 3543}, {115, 193}, {141, 32983}, {183, 3545}, {194, 32996}, {230, 32984}, {305, 7409}, {315, 3091}, {317, 6623}, {382, 6337}, {385, 33006}, {491, 23259}, {492, 23249}, {532, 16634}, {533, 16635}, {546, 7776}, {574, 33272}, {626, 32971}, {631, 32884}, {1078, 5056}, {1160, 12323}, {1161, 12322}, {1506, 32990}, {2548, 4045}, {2549, 7775}, {2896, 32962}, {3053, 32969}, {3090, 7750}, {3146, 7763}, {3199, 28710}, {3314, 33016}, {3329, 33251}, {3363, 21356}, {3522, 7769}, {3523, 7802}, {3529, 32887}, {3589, 33223}, {3618, 15484}, {3620, 7818}, {3767, 7843}, {3788, 32981}, {3815, 32986}, {3830, 6390}, {3839, 7809}, {3843, 3933}, {3851, 7767}, {3854, 7768}, {3855, 32886}, {3934, 32991}, {3964, 18535}, {5013, 33238}, {5023, 32977}, {5025, 16989}, {5032, 5355}, {5059, 7782}, {5066, 14929}, {5068, 7860}, {5207, 14853}, {5286, 7785}, {5304, 7812}, {5971, 31105}, {6221, 32806}, {6392, 7759}, {6398, 32805}, {6655, 31400}, {6683, 31417}, {6776, 15980}, {7615, 11160}, {7620, 7840}, {7735, 33228}, {7736, 7841}, {7738, 33229}, {7745, 14064}, {7747, 32973}, {7774, 14041}, {7777, 33017}, {7778, 14033}, {7783, 33279}, {7784, 32968}, {7786, 33025}, {7787, 33283}, {7788, 32892}, {7791, 31404}, {7792, 33285}, {7793, 32963}, {7795, 32979}, {7797, 33290}, {7800, 32987}, {7803, 33200}, {7814, 17578}, {7823, 32961}, {7827, 14930}, {7836, 14068}, {7842, 31401}, {7845, 18424}, {7846, 33182}, {7851, 33292}, {7862, 32989}, {7871, 32840}, {7885, 16924}, {7891, 33280}, {7899, 33181}, {7900, 32993}, {7904, 32999}, {7906, 14044}, {7911, 33202}, {7912, 14035}, {7917, 32878}, {7920, 33289}, {7921, 14045}, {7925, 33007}, {7929, 33024}, {7932, 33287}, {7938, 33269}, {7940, 33205}, {7941, 14062}, {7945, 14031}, {7947, 14066}, {8352, 9770}, {9723, 18534}, {11174, 33190}, {11318, 18907}, {13512, 31723}, {15031, 32868}, {15491, 16043}, {15533, 20112}, {15815, 33247}, {16589, 33050}, {16990, 33013}, {17005, 33008}, {20065, 32966}, {21734, 32871}, {21908, 21969}, {21970, 21973}, {25303, 31410}, {31276, 32995}, {31489, 33215}

X(32827) = {X(4),X(3926)}-harmonic conjugate of X(32826)


X(32828) = (name pending)

Barycentrics    SA^2 + 2 S2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 6*b^2*c^2 + c^4 : :

X(32828) lies on these lines: {2, 39}, {3, 32815}, {4, 183}, {5, 69}, {6, 32968}, {20, 1078}, {32, 32971}, {83, 5304}, {99, 3523}, {115, 7800}, {140, 6337}, {141, 5490}, {148, 32965}, {187, 32981}, {193, 2548}, {230, 14001}, {264, 3089}, {304, 28808}, {308, 393}, {311, 3547}, {315, 3091}, {316, 3832}, {325, 3090}, {339, 3549}, {348, 20925}, {350, 3085}, {376, 32819}, {381, 7767}, {384, 17008}, {385, 16924}, {439, 7816}, {498, 3760}, {499, 3761}, {599, 32984}, {626, 3620}, {631, 1975}, {1007, 1656}, {1217, 9291}, {1235, 3542}, {1506, 7758}, {1799, 6995}, {1909, 3086}, {2549, 2996}, {2896, 14063}, {3053, 13468}, {3054, 32977}, {3096, 33180}, {3146, 14907}, {3314, 32961}, {3522, 7771}, {3524, 32822}, {3525, 32817}, {3526, 6390}, {3533, 32820}, {3543, 7802}, {3545, 7773}, {3618, 5305}, {3619, 6393}, {3630, 18584}, {3734, 32973}, {3763, 33221}, {3815, 32975}, {3839, 7811}, {3850, 14929}, {3854, 7860}, {4396, 9596}, {4400, 9599}, {4441, 5552}, {5013, 32978}, {5023, 33239}, {5025, 16990}, {5056, 7752}, {5067, 32818}, {5068, 7768}, {5071, 7788}, {5084, 16992}, {5254, 15271}, {5319, 7808}, {5475, 14023}, {5976, 14651}, {6376, 19843}, {6381, 26363}, {6622, 32000}, {6722, 7869}, {7080, 17143}, {7393, 9723}, {7409, 16275}, {7486, 7796}, {7603, 7855}, {7610, 32985}, {7615, 7810}, {7617, 7896}, {7620, 7833}, {7697, 9752}, {7735, 7770}, {7736, 7754}, {7737, 7780}, {7738, 11285}, {7745, 8667}, {7748, 33023}, {7749, 17130}, {7759, 20080}, {7761, 32982}, {7766, 33020}, {7774, 16921}, {7775, 11160}, {7777, 32999}, {7778, 32969}, {7779, 33002}, {7782, 15717}, {7783, 33001}, {7784, 16041}, {7785, 32962}, {7787, 33269}, {7789, 32970}, {7790, 33202}, {7792, 16045}, {7793, 14035}, {7794, 32988}, {7806, 16898}, {7812, 9740}, {7823, 33016}, {7830, 18546}, {7831, 33025}, {7835, 33203}, {7851, 32956}, {7854, 32980}, {7857, 33181}, {7868, 18840}, {7873, 18424}, {7879, 33228}, {7881, 33249}, {7885, 33006}, {7891, 17006}, {7893, 33013}, {7894, 14930}, {7898, 32996}, {7900, 33024}, {7904, 33017}, {7906, 16922}, {7912, 32963}, {7925, 32998}, {7928, 33251}, {7929, 32993}, {7931, 33248}, {7938, 33283}, {7944, 33182}, {8369, 23055}, {8556, 32986}, {9939, 23334}, {10311, 28724}, {10513, 15022}, {10519, 18906}, {10594, 15574}, {11168, 33215}, {11174, 32957}, {11313, 32806}, {11314, 32805}, {11318, 16509}, {14061, 32458}, {14068, 14712}, {14561, 14994}, {16044, 20065}, {16419, 19583}, {16925, 17004}, {16999, 33028}, {20094, 33022}, {20888, 26364}, {22253, 31406}

X(32828) = anticomplement of X(31401)
X(32828) = {X(2),X(3926)}-harmonic conjugate of X(32829)


X(32829) = (name pending)

Barycentrics    SA^2 - 2 S2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 - 2*b^2*c^2 + 3*c^4 : :

X(32829) lies on these

X(32829) = lines: {2, 39}, {3, 1007}, {5, 6337}, {6, 10008}, {20, 7694}, {32, 32989}, {69, 140}, {83, 33181}, {99, 3091}, {115, 32988}, {141, 32978}, {148, 32963}, {183, 3525}, {193, 7764}, {230, 32977}, {315, 3523}, {316, 3522}, {325, 631}, {376, 7773}, {384, 31404}, {385, 33000}, {439, 7737}, {491, 13935}, {492, 9540}, {549, 7776}, {574, 32974}, {620, 2548}, {625, 32982}, {626, 32990}, {1078, 10303}, {1444, 19547}, {1506, 32971}, {1656, 6390}, {1975, 3090}, {2549, 7862}, {2896, 33012}, {3053, 33216}, {3055, 32975}, {3085, 25303}, {3095, 9752}, {3146, 7782}, {3260, 3546}, {3314, 33001}, {3524, 7750}, {3526, 3933}, {3533, 32821}, {3545, 32819}, {3618, 6393}, {3620, 7815}, {3734, 32987}, {3815, 14001}, {3972, 33205}, {4045, 31450}, {5013, 14064}, {5024, 8361}, {5054, 7767}, {5056, 11185}, {5067, 32817}, {5071, 32822}, {5254, 32969}, {5304, 7857}, {5475, 32981}, {5552, 25278}, {5866, 7526}, {6642, 9723}, {7583, 11316}, {7584, 11315}, {7603, 32991}, {7618, 7756}, {7622, 7830}, {7735, 33233}, {7736, 7807}, {7738, 7887}, {7745, 11184}, {7748, 32980}, {7749, 7758}, {7759, 21843}, {7762, 9770}, {7772, 31274}, {7774, 7907}, {7777, 16925}, {7778, 16043}, {7780, 20080}, {7783, 32961}, {7784, 22110}, {7785, 32964}, {7788, 15702}, {7789, 31489}, {7790, 33199}, {7791, 7925}, {7792, 33189}, {7793, 33206}, {7796, 15589}, {7800, 7888}, {7802, 10304}, {7809, 15692}, {7811, 15708}, {7814, 14907}, {7816, 31415}, {7819, 31467}, {7825, 33272}, {7835, 33198}, {7846, 33183}, {7847, 33200}, {7851, 32955}, {7853, 31457}, {7864, 33248}, {7868, 32960}, {7871, 10513}, {7885, 33008}, {7891, 16924}, {7899, 33180}, {7906, 16923}, {7912, 32965}, {7916, 11160}, {7917, 15721}, {7934, 33025}, {7938, 33258}, {7941, 33274}, {7947, 16990}, {9606, 33222}, {10011, 10983}, {11057, 15705}, {11174, 14069}, {11272, 18906}, {11318, 12040}, {12108, 14929}, {13881, 32976}, {15561, 19910}, {15815, 32986}, {16989, 33245}, {17095, 21605}, {17128, 32999}, {20065, 33259}, {20094, 33011}, {23334, 33208}, {26686, 31402}, {31407, 33225}, {31492, 33221}, {31859, 33249}, {32458, 33203}, {32459, 33239}

X(32829) = {X(2),X(3926)}-harmonic conjugate of X(32828)


X(32830) = (name pending)

Barycentrics    2 SA^2 + S2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 6*b^2*c^2 + c^4 : :
Barycentrics    2 csc^2 A - 1 : :
Barycentrics    2 cot^2 A + 1 : :

X(32830) lies on these lines: {2, 39}, {3, 15589}, {4, 3933}, {5, 32818}, {6, 33198}, {20, 64}, {24, 22241}, {30, 32822}, {32, 33201}, {83, 14930}, {85, 345}, {99, 3522}, {141, 7738}, {148, 32458}, {183, 3523}, {193, 384}, {230, 33203}, {279, 304}, {312, 348}, {315, 3146}, {316, 17578}, {325, 3091}, {339, 3546}, {350, 14986}, {376, 7767}, {381, 32823}, {385, 32973}, {391, 17691}, {439, 7793}, {543, 7896}, {626, 33200}, {631, 6390}, {1007, 5056}, {1078, 15717}, {1219, 3672}, {1235, 3088}, {1238, 7544}, {1270, 11294}, {1271, 11293}, {1434, 18141}, {1593, 32000}, {1657, 14929}, {2548, 7813}, {2549, 7794}, {2896, 10008}, {2996, 5025}, {2998, 6339}, {3085, 3761}, {3086, 3760}, {3314, 32974}, {3543, 7788}, {3575, 32001}, {3620, 6393}, {3674, 3729}, {3734, 7758}, {3763, 9607}, {3832, 7796}, {3839, 7773}, {3854, 7871}, {3879, 4339}, {3945, 4195}, {3964, 7503}, {4201, 5232}, {5024, 32960}, {5059, 7768}, {5065, 26224}, {5068, 7752}, {5254, 33180}, {5304, 7754}, {5305, 14069}, {5319, 7820}, {5395, 7921}, {5485, 11318}, {7283, 17170}, {7735, 7789}, {7737, 7855}, {7751, 33205}, {7762, 14033}, {7764, 31404}, {7766, 14037}, {7774, 17128}, {7777, 32987}, {7778, 33199}, {7779, 14035}, {7781, 7800}, {7782, 21734}, {7783, 16990}, {7784, 33210}, {7785, 32979}, {7802, 15683}, {7815, 14148}, {7816, 14023}, {7819, 22253}, {7839, 16898}, {7851, 33182}, {7863, 17131}, {7879, 32986}, {7881, 14064}, {7891, 17008}, {7893, 11160}, {7897, 14063}, {7900, 14068}, {7906, 16924}, {7912, 32980}, {7925, 32988}, {7929, 20094}, {7939, 33017}, {7941, 33016}, {7947, 32961}, {8359, 9741}, {8362, 18840}, {9605, 16045}, {9740, 32985}, {9748, 32515}, {9873, 11180}, {10519, 11257}, {11148, 21356}, {14031, 20088}, {14039, 30435}, {14376, 28425}, {15048, 32956}, {15480, 22331}, {16043, 31859}, {16925, 17129}, {16992, 17558}, {17079, 21605}, {17095, 28808}, {17740, 26563}, {19843, 20888}, {19855, 32092}, {20065, 20080}, {23115, 28717}, {31406, 32957}

X(32830) = anticomplement of X(5286)
X(32830) = {X(2),X(3926)}-harmonic conjugate of X(32831)


X(32831) = (name pending)

Barycentrics    2 SA^2 - S2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 + 2*b^2*c^2 + 3*c^4 : :
Barycentrics    2 cot^2 A - 1 : :

X(32831) lies on these

X(32831) = lines: {2, 39}, {3, 14929}, {4, 6390}, {5, 32817}, {6, 33181}, {20, 325}, {30, 32823}, {32, 33205}, {69, 3523}, {99, 3146}, {148, 8781}, {183, 10303}, {193, 6393}, {315, 3522}, {316, 5059}, {345, 17095}, {348, 21605}, {376, 7776}, {381, 32822}, {384, 5395}, {385, 32989}, {439, 20065}, {620, 7758}, {626, 33025}, {631, 3933}, {668, 27525}, {1007, 1975}, {1434, 30828}, {2482, 7903}, {2548, 7863}, {2549, 7888}, {3095, 9748}, {3260, 6527}, {3314, 32990}, {3515, 32001}, {3524, 7767}, {3543, 7773}, {3620, 7824}, {3734, 31404}, {3785, 7796}, {3832, 7752}, {3839, 32819}, {3964, 17928}, {5013, 33202}, {5024, 32956}, {5033, 7793}, {5056, 32820}, {5068, 11185}, {5254, 33199}, {5304, 7807}, {5305, 33189}, {5921, 12215}, {6292, 31450}, {7080, 25278}, {7488, 9723}, {7509, 22241}, {7618, 7830}, {7735, 33203}, {7736, 7789}, {7738, 7778}, {7745, 9770}, {7750, 10304}, {7754, 32970}, {7762, 32985}, {7764, 33201}, {7774, 7891}, {7777, 32971}, {7779, 32964}, {7783, 32974}, {7785, 32981}, {7788, 15692}, {7791, 7947}, {7792, 33183}, {7800, 7908}, {7809, 15683}, {7811, 15705}, {7814, 17578}, {7819, 18841}, {7835, 14930}, {7855, 21843}, {7862, 14148}, {7871, 14907}, {7879, 33215}, {7881, 16043}, {7885, 33272}, {7897, 32965}, {7900, 33244}, {7912, 32982}, {7921, 33255}, {7925, 32972}, {7939, 33008}, {7941, 33007}, {9605, 14069}, {9741, 11318}, {11160, 33274}, {11165, 33190}, {14064, 31859}, {14482, 32952}, {14961, 28425}, {14981, 22664}, {15048, 32951}, {16045, 31406}, {17128, 32987}, {17129, 33000}, {17740, 27187}, {20094, 32996}, {25592, 31130}, {30435, 33191}, {31467, 32957}

X(32831) = isotomic conjugate of polar conjugate of X(32001)
X(32831) = isotomic conjugate of isogonal conjugate of X(37672)
X(32831) = {X(2),X(3926)}-harmonic conjugate of X(32830)


X(32832) = (name pending)

Barycentrics    SA^2 + 3 S2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 4*b^2*c^2 + c^4 : :

X(32832) lies on these lines: {2, 39}, {3, 11185}, {4, 1078}, {5, 183}, {6, 32992}, {20, 7771}, {32, 16924}, {69, 576}, {75, 26364}, {83, 7735}, {99, 631}, {115, 7791}, {140, 1975}, {141, 7887}, {148, 33004}, {187, 14035}, {193, 7858}, {230, 7770}, {264, 3542}, {308, 2165}, {311, 7558}, {316, 3091}, {317, 1594}, {325, 1656}, {339, 6639}, {350, 498}, {381, 7750}, {384, 17004}, {385, 2548}, {491, 639}, {492, 640}, {499, 1909}, {543, 15515}, {547, 7788}, {574, 33001}, {620, 17130}, {625, 7854}, {626, 16990}, {632, 6390}, {668, 10527}, {671, 33215}, {754, 33005}, {1007, 5067}, {1235, 7505}, {1506, 7751}, {1799, 6997}, {2549, 7824}, {2896, 32966}, {3053, 7610}, {3054, 7789}, {3096, 14061}, {3314, 32967}, {3329, 5319}, {3522, 32826}, {3523, 7782}, {3525, 6337}, {3533, 32817}, {3545, 7811}, {3552, 21843}, {3618, 7856}, {3619, 7944}, {3620, 5107}, {3628, 3933}, {3734, 7749}, {3763, 6393}, {3815, 7754}, {3839, 11057}, {3972, 32971}, {4187, 16992}, {4441, 27529}, {5007, 33261}, {5023, 19687}, {5025, 7800}, {5055, 7776}, {5056, 7768}, {5068, 7860}, {5071, 7809}, {5206, 33007}, {5210, 33250}, {5254, 11285}, {5304, 7878}, {5305, 11174}, {5475, 7780}, {5490, 5591}, {5491, 26338}, {5552, 17143}, {5569, 33208}, {6119, 32807}, {6179, 32987}, {6292, 7844}, {6376, 26363}, {6656, 13881}, {6680, 16898}, {6722, 7867}, {6781, 33280}, {7486, 7814}, {7529, 15574}, {7603, 7759}, {7615, 7833}, {7617, 7810}, {7694, 9863}, {7697, 9754}, {7736, 7760}, {7737, 7793}, {7738, 32978}, {7745, 13468}, {7747, 33016}, {7748, 32965}, {7755, 7808}, {7756, 18546}, {7758, 7777}, {7761, 14063}, {7762, 8667}, {7764, 17131}, {7765, 15482}, {7775, 7826}, {7778, 33249}, {7781, 33003}, {7783, 33015}, {7784, 8556}, {7785, 14023}, {7787, 33020}, {7790, 16043}, {7794, 7862}, {7798, 9698}, {7804, 33269}, {7816, 32964}, {7821, 33270}, {7823, 33013}, {7830, 33017}, {7831, 32974}, {7835, 32970}, {7841, 11168}, {7842, 18424}, {7846, 16045}, {7847, 32990}, {7849, 33277}, {7850, 15022}, {7851, 8362}, {7853, 33283}, {7857, 14001}, {7868, 8361}, {7869, 12815}, {7883, 32984}, {7891, 16923}, {7898, 32993}, {7899, 32969}, {7900, 33010}, {7901, 16986}, {7904, 14041}, {7906, 17005}, {7907, 17006}, {7909, 32976}, {7910, 32982}, {7911, 16041}, {7918, 33202}, {7919, 32956}, {7929, 33011}, {7934, 32972}, {7935, 18362}, {7936, 32980}, {7937, 33180}, {7949, 20080}, {8359, 16509}, {8369, 8860}, {8588, 33254}, {8781, 18840}, {9166, 33190}, {10072, 25303}, {10198, 30963}, {10200, 31997}, {11547, 18027}, {14712, 33018}, {15513, 33244}, {16895, 16984}, {16999, 33045}, {17095, 20925}, {18142, 29477}, {20573, 30529}, {22253, 31467}, {22329, 30435}, {25264, 31497}, {31168, 33285}

X(32832) = anticomplement of X(31455)
X(32832) = {X(2),X(3926)}-harmonic conjugate of X(7769)


X(32833) = (name pending)

Barycentrics    3 SA^2 + S2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 4*b^2*c^2 + c^4 : :
Barycentrics    3 cot^2 A + 1 : :
Barycentrics    2 cot^2 A + csc^2 A : :

X(32833) lies on these lines: {2, 39}, {3, 32820}, {4, 7796}, {5, 32821}, {6, 6661}, {20, 7768}, {30, 315}, {32, 33255}, {69, 74}, {115, 7908}, {141, 31859}, {148, 7897}, {183, 549}, {187, 33266}, {193, 3972}, {298, 10654}, {299, 10653}, {304, 17078}, {316, 3543}, {317, 1238}, {325, 381}, {340, 18533}, {345, 17079}, {350, 10072}, {384, 7758}, {385, 33246}, {524, 1003}, {543, 7818}, {574, 14148}, {599, 6393}, {620, 17008}, {626, 11648}, {671, 16041}, {754, 33007}, {1007, 5071}, {1078, 3524}, {1285, 11008}, {1909, 10056}, {1992, 5039}, {2548, 7906}, {2549, 3314}, {2979, 14917}, {3091, 7814}, {3096, 7738}, {3146, 7860}, {3534, 7750}, {3545, 7752}, {3552, 14023}, {3582, 3760}, {3584, 3761}, {3620, 7831}, {3734, 7753}, {3785, 7782}, {3830, 7776}, {3839, 7871}, {3845, 7773}, {3849, 33193}, {4234, 17378}, {5007, 14037}, {5152, 11177}, {5254, 7881}, {5306, 7754}, {5319, 7892}, {5485, 8781}, {5976, 8724}, {6179, 32973}, {6658, 7946}, {7618, 33273}, {7735, 7835}, {7737, 7779}, {7747, 7916}, {7748, 7895}, {7751, 7863}, {7756, 7896}, {7759, 14035}, {7760, 14001}, {7761, 33263}, {7764, 16924}, {7765, 7869}, {7767, 8703}, {7770, 9300}, {7771, 15589}, {7772, 16898}, {7775, 33016}, {7780, 32964}, {7781, 7791}, {7783, 7800}, {7790, 33223}, {7792, 22253}, {7798, 7820}, {7802, 11001}, {7810, 33008}, {7812, 14033}, {7816, 7855}, {7821, 14063}, {7840, 11361}, {7843, 14068}, {7848, 15301}, {7850, 10513}, {7854, 32965}, {7856, 14069}, {7858, 32971}, {7868, 15048}, {7873, 32997}, {7878, 33198}, {7883, 32986}, {7888, 18362}, {7891, 17129}, {7898, 20094}, {7909, 14064}, {7917, 15682}, {7922, 32974}, {7936, 33023}, {8369, 14614}, {8370, 9766}, {8591, 33264}, {8598, 15533}, {9740, 26613}, {9741, 21356}, {9753, 32515}, {9754, 15561}, {9770, 32983}, {9939, 33265}, {11179, 12215}, {11288, 22329}, {14070, 22241}, {14929, 15686}, {14994, 32429}, {15670, 16992}, {18546, 33006}, {18906, 20423}, {20925, 32851}, {20943, 26364}, {26619, 32810}, {26620, 32811}, {31652, 33258}, {32419, 32808}, {32421, 32809}

X(32833) = isotomic conjugate of X(34288)
X(32833) = anticomplement of X(5309)
X(32833) = {X(2),X(3926)}-harmonic conjugate of X(7799)
X(32833) = {X(11128),X(11129)}-harmonic conjugate of X(69)


X(32834) = (name pending)

Barycentrics    2 SA^2 + 3 S2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 10*b^2*c^2 + c^4 : :
Barycentrics    2 csc^2 A + 1 : :

X(32834) lies on these lines: {2, 39}, {3, 32822}, {4, 7767}, {5, 32823}, {20, 183}, {69, 3091}, {85, 28808}, {99, 15717}, {115, 33200}, {140, 32817}, {141, 33180}, {148, 33023}, {193, 7921}, {230, 33181}, {235, 32000}, {279, 20925}, {311, 6527}, {315, 3832}, {325, 5056}, {339, 3547}, {385, 32971}, {1007, 7486}, {1078, 3522}, {1235, 3089}, {1270, 32488}, {1271, 32489}, {1656, 32818}, {1909, 14986}, {1975, 3523}, {2548, 7890}, {2896, 32982}, {3085, 3760}, {3086, 3761}, {3090, 3933}, {3146, 3785}, {3314, 32972}, {3525, 6390}, {3543, 7750}, {3545, 7776}, {3619, 7851}, {3620, 5025}, {3734, 33201}, {3839, 32006}, {3843, 14929}, {3854, 7768}, {4441, 7080}, {5059, 14907}, {5068, 7917}, {5129, 16992}, {5254, 33202}, {5304, 7770}, {5305, 16045}, {5485, 8359}, {6337, 10303}, {6381, 19843}, {7507, 32001}, {7615, 7825}, {7620, 7810}, {7697, 9748}, {7735, 33198}, {7738, 15271}, {7752, 15022}, {7754, 32968}, {7758, 31404}, {7760, 14930}, {7762, 32983}, {7766, 33269}, {7771, 21734}, {7774, 32987}, {7779, 32962}, {7785, 20080}, {7789, 33203}, {7793, 32981}, {7800, 7872}, {7855, 31415}, {7866, 18840}, {7868, 33182}, {7879, 16041}, {7881, 32969}, {7893, 33016}, {7897, 32963}, {7900, 32995}, {7904, 33272}, {7906, 32999}, {7928, 16990}, {7929, 32996}, {7938, 10008}, {7939, 33006}, {7941, 33005}, {7947, 32998}, {8370, 9740}, {9605, 32957}, {11160, 33013}, {11168, 15815}, {13881, 33199}, {14853, 14994}, {15048, 32960}, {16999, 33039}, {17004, 32989}, {17008, 17128}, {17130, 33205}, {20065, 32979}, {31859, 32978}

X(32834) = anticomplement of X(31400)
X(32834) = {X(2),X(3926)}-harmonic conjugate of X(32835)


X(32835) = (name pending)

Barycentrics    2 SA^2 - 3 S2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 - 2*b^2*c^2 + 5*c^4 : :

X(32835) lies on these lines: {2, 39}, {3, 32823}, {5, 32822}, {6, 33203}, {20, 1007}, {69, 10303}, {99, 3832}, {140, 15589}, {193, 7907}, {315, 15717}, {325, 3523}, {439, 7785}, {574, 33025}, {620, 33205}, {631, 7767}, {1078, 10513}, {1656, 32817}, {1975, 5056}, {2548, 33201}, {2996, 32967}, {3053, 9770}, {3090, 6390}, {3091, 6337}, {3146, 7752}, {3522, 7802}, {3524, 7776}, {3525, 3933}, {3593, 15293}, {3595, 15294}, {3618, 33183}, {3620, 7947}, {3785, 7917}, {3815, 33198}, {3854, 32826}, {5013, 33180}, {5024, 32951}, {5059, 7782}, {5068, 15031}, {5304, 32970}, {5305, 32959}, {5319, 31274}, {5395, 33255}, {7618, 7825}, {7736, 33181}, {7738, 33199}, {7750, 15692}, {7754, 32977}, {7762, 33216}, {7766, 33262}, {7774, 32989}, {7777, 32973}, {7778, 33202}, {7779, 33206}, {7783, 32972}, {7788, 15721}, {7804, 31407}, {7814, 21734}, {7867, 31450}, {7872, 33200}, {7881, 32978}, {7891, 32971}, {7897, 33012}, {7906, 33000}, {7912, 33023}, {7921, 16925}, {7925, 32974}, {7928, 32990}, {8369, 18842}, {18845, 32981}, {9605, 33189}, {10304, 32006}, {11185, 15022}, {12040, 33190}, {14069, 31406}, {15048, 32955}, {15815, 22110}, {16045, 31467}, {17005, 32987}, {31859, 32969}

X(32835) = {X(2),X(3926)}-harmonic conjugate of X(32834)


X(32836) = (name pending)

Barycentrics    3 SA^2 + 2 S2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 10*b^2*c^2 + c^4 : :

X(32836) lies on these lines: {2, 39}, {3, 32824}, {4, 7788}, {5, 32825}, {20, 7811}, {30, 69}, {99, 10304}, {148, 33278}, {183, 3524}, {193, 3734}, {298, 5334}, {299, 5335}, {304, 17079}, {312, 17078}, {315, 3543}, {316, 10513}, {325, 3545}, {345, 20925}, {346, 20924}, {376, 1975}, {381, 3933}, {385, 33255}, {439, 7780}, {524, 14033}, {543, 33272}, {549, 6337}, {599, 10008}, {626, 2996}, {631, 32820}, {671, 32458}, {754, 11160}, {1007, 5055}, {1078, 15692}, {1992, 11286}, {2549, 3620}, {2782, 10519}, {2896, 33263}, {3090, 32821}, {3091, 7796}, {3146, 7768}, {3314, 33251}, {3534, 7767}, {3618, 22253}, {3619, 15048}, {3760, 10072}, {3761, 10056}, {3830, 32006}, {3839, 7809}, {3845, 7776}, {5054, 6390}, {5068, 7814}, {5071, 32818}, {5254, 33223}, {5306, 14001}, {5395, 7838}, {5461, 8781}, {5485, 33285}, {6179, 33201}, {6393, 11287}, {6661, 7754}, {7620, 14041}, {7735, 33220}, {7737, 20080}, {7750, 11001}, {7751, 32973}, {7753, 7758}, {7759, 32979}, {7760, 33198}, {7764, 32987}, {7771, 15705}, {7781, 32990}, {7789, 33224}, {7793, 33266}, {7794, 11648}, {7821, 32980}, {7837, 17128}, {7840, 33016}, {7854, 33023}, {7855, 14537}, {7860, 17578}, {7863, 32989}, {7883, 33210}, {7888, 32988}, {7906, 31404}, {7909, 33199}, {7922, 33200}, {7946, 14068}, {8591, 33207}, {8667, 32985}, {8716, 33215}, {9766, 32983}, {9878, 20094}, {9939, 33193}, {11008, 18907}, {11057, 15683}, {11128, 22512}, {11129, 22513}, {11297, 11543}, {11298, 11542}, {13468, 33216}, {13571, 33269}, {14023, 32981}, {14039, 14614}, {14376, 28431}, {14853, 32515}, {15682, 32819}, {16992, 17561}, {17129, 33246}, {19686, 20065}, {22329, 33191}, {23115, 28721}, {31407, 33020}

X(32836) = anticomplement of X(7739)
X(32836) = {X(2),X(3926)}-harmonic conjugate of X(32837)


X(32837) = (name pending)

Barycentrics    3 SA^2 - 2 S2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 + 2*b^2*c^2 + 5*c^4 : :

X(32837) lies on these lines: {2, 39}, {3, 32825}, {5, 32824}, {6, 33224}, {20, 7809}, {69, 549}, {99, 3543}, {183, 15702}, {193, 620}, {315, 10304}, {316, 15683}, {325, 376}, {381, 1007}, {439, 7759}, {524, 10008}, {631, 32821}, {1003, 9770}, {1078, 15708}, {1975, 3545}, {1992, 6393}, {3090, 32820}, {3146, 7814}, {3522, 11057}, {3523, 7796}, {3524, 3785}, {3534, 32006}, {3620, 7908}, {3839, 7752}, {3933, 5054}, {5071, 32817}, {6337, 32816}, {6661, 7736}, {7618, 7818}, {7738, 33219}, {7750, 19708}, {7758, 32989}, {7760, 33203}, {7764, 32973}, {7767, 15693}, {7768, 15717}, {7771, 10513}, {7773, 15682}, {7774, 33246}, {7776, 8703}, {7778, 33223}, {7781, 32972}, {7783, 33251}, {7785, 33187}, {7802, 15697}, {7811, 15692}, {7816, 18845}, {7821, 33023}, {7837, 16925}, {7858, 33201}, {7863, 32971}, {7865, 32990}, {7869, 31450}, {7871, 15705}, {7888, 32974}, {7891, 33255}, {7909, 33202}, {7912, 33278}, {8716, 16041}, {9166, 11148}, {9300, 14001}, {9723, 14070}, {9752, 15561}, {9766, 32985}, {11001, 32823}, {11163, 14039}, {11165, 33184}, {11180, 12215}, {11184, 32983}, {12040, 21356}, {14537, 32981}, {14891, 14929}, {14961, 28431}, {15589, 15721}, {18362, 32988}, {19569, 33244}, {20080, 21843}, {22332, 33221}, {23334, 33193}

X(32837) = {X(2),X(3926)}-harmonic conjugate of X(32836)


X(32838) = (name pending)

Barycentrics    SA^2 + 4 S2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 - 10*b^2*c^2 + 3*c^4 : :

X(32838) lies on these lines: {2, 39}, {3, 32826}, {5, 3785}, {6, 32975}, {32, 5395}, {69, 1656}, {99, 10303}, {115, 32990}, {141, 32969}, {148, 33012}, {183, 3090}, {187, 32979}, {193, 1506}, {230, 32968}, {315, 5056}, {316, 5068}, {325, 5067}, {385, 31404}, {547, 7776}, {574, 2996}, {626, 32988}, {631, 32815}, {1007, 3628}, {1078, 3091}, {1975, 3525}, {2896, 32963}, {3053, 32983}, {3054, 32970}, {3086, 25303}, {3096, 33199}, {3146, 7771}, {3314, 32998}, {3523, 11185}, {3524, 32819}, {3526, 6337}, {3533, 32824}, {3543, 15031}, {3545, 7750}, {3619, 8361}, {3734, 32989}, {3832, 14907}, {3839, 7802}, {3933, 5070}, {5055, 7767}, {5071, 7773}, {5254, 32978}, {7486, 7752}, {7603, 14023}, {7610, 7745}, {7615, 7756}, {7617, 7830}, {7735, 32992}, {7737, 32991}, {7749, 32973}, {7761, 32980}, {7774, 16922}, {7778, 32976}, {7780, 31415}, {7783, 33003}, {7784, 11168}, {7785, 33009}, {7787, 33261}, {7789, 32977}, {7792, 18841}, {7793, 32962}, {7800, 32972}, {7814, 10513}, {7815, 32974}, {7823, 33005}, {7831, 33200}, {7851, 32960}, {7857, 33198}, {7867, 12815}, {7868, 32955}, {7877, 9740}, {7903, 11160}, {7904, 33006}, {7912, 33270}, {7938, 33277}, {8369, 23053}, {8797, 11484}, {10314, 28724}, {10527, 25278}, {12812, 14929}, {13881, 16043}, {14061, 33180}, {14064, 15271}, {14712, 32995}, {15597, 32985}, {15702, 32822}, {16921, 17008}, {16924, 17004}, {16925, 17006}, {16986, 33248}, {16990, 32967}, {16999, 33052}, {17128, 33000}, {18840, 32958}, {20065, 33002}, {21843, 32981}, {32490, 32805}, {32491, 32806}

X(32838) = {X(2),X(3926)}-harmonic conjugate of X(32839)


X(32839) = (name pending)

Barycentrics    SA^2 - 4 S2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 - 6*b^2*c^2 + 5*c^4 : :

X(32839) lies on these lines: {2, 39}, {3, 32827}, {5, 32826}, {6, 32977}, {69, 3526}, {83, 33203}, {99, 5056}, {140, 1007}, {148, 33270}, {183, 3533}, {193, 7749}, {315, 10303}, {316, 15717}, {325, 3525}, {439, 5475}, {549, 32006}, {574, 32972}, {620, 32971}, {625, 33023}, {631, 7750}, {1506, 32973}, {1656, 6337}, {1975, 5067}, {2548, 32989}, {2549, 32988}, {2896, 33188}, {3055, 32968}, {3090, 32815}, {3311, 32805}, {3312, 32806}, {3314, 33003}, {3523, 7752}, {3524, 7773}, {3589, 33222}, {3618, 10008}, {3620, 7888}, {3815, 32970}, {3832, 7782}, {5013, 32969}, {5070, 6390}, {5071, 32819}, {5254, 32976}, {7486, 11185}, {7603, 32979}, {7736, 33233}, {7738, 33249}, {7745, 33216}, {7767, 15694}, {7774, 16923}, {7777, 33000}, {7778, 32978}, {7783, 32998}, {7785, 33206}, {7787, 31407}, {7789, 32975}, {7792, 32959}, {7793, 33204}, {7802, 15692}, {7809, 15721}, {7816, 32991}, {7844, 31450}, {7851, 32958}, {7862, 32974}, {7891, 32999}, {7899, 33202}, {7912, 33012}, {7925, 33001}, {7935, 32990}, {8781, 31274}, {9771, 32985}, {11174, 33189}, {11548, 19583}, {14001, 31489}, {15515, 33272}, {15702, 32823}, {15815, 16041}, {16925, 17005}, {31275, 31457}, {31415, 32981}

X(32839) = {X(2),X(3926)}-harmonic conjugate of X(32838)


X(32840) = (name pending)

Barycentrics    4 SA^2 + S2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 + 10*b^2*c^2 + 3*c^4 : :

X(32840) lies on these lines: {2, 39}, {20, 3933}, {69, 3522}, {193, 33201}, {253, 11413}, {279, 345}, {315, 5059}, {325, 3832}, {346, 348}, {385, 33205}, {728, 738}, {1007, 15022}, {1238, 31304}, {1270, 6459}, {1271, 6460}, {1434, 4869}, {1975, 3146}, {3091, 32818}, {3314, 33025}, {3523, 6390}, {3543, 7776}, {3552, 20080}, {3620, 7783}, {3785, 21734}, {3839, 32823}, {3854, 11185}, {3964, 14118}, {4175, 14826}, {5024, 18840}, {5068, 32821}, {5304, 7789}, {5305, 33183}, {5395, 7774}, {6337, 15589}, {6393, 32965}, {6527, 30698}, {7488, 22241}, {7754, 33181}, {7767, 10304}, {7779, 32981}, {7788, 15683}, {7796, 17578}, {7800, 14148}, {7871, 32827}, {7881, 33180}, {7897, 32982}, {7906, 32971}, {7939, 33272}, {7947, 32972}, {9605, 18841}, {11148, 33190}, {14069, 22253}, {14929, 17538}, {14930, 33198}, {14994, 32522}, {17129, 32989}, {17130, 31404}, {20094, 32458}, {31859, 33202}

X(32840) = {X(2),X(3926)}-harmonic conjugate of X(32841)


X(32841) = (name pending)

Barycentrics    4 SA^2 - S2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 + 6*b^2*c^2 + 5*c^4 : :

X(32841) lies on these lines: {2, 39}, {3, 10513}, {20, 6390}, {69, 15717}, {99, 5059}, {193, 7891}, {279, 32851}, {325, 3146}, {346, 17095}, {439, 7779}, {1007, 5068}, {1151, 1270}, {1271, 33365}, {1975, 3832}, {3091, 32817}, {3522, 6337}, {3523, 3933}, {3543, 32823}, {3839, 32822}, {3854, 7752}, {3964, 22467}, {6393, 20080}, {7618, 7896}, {7754, 33203}, {7767, 15692}, {7774, 33201}, {7783, 33025}, {7796, 21734}, {7814, 32826}, {7881, 33202}, {7897, 33023}, {7906, 32973}, {7947, 32974}, {11148, 11318}, {14001, 14930}, {14035, 18845}, {14482, 33185}, {14929, 21735}, {15048, 33182}, {15683, 32006}, {17578, 32816}, {22253, 33189}, {31859, 33180}

X(32841) = {X(2),X(3926)}-harmonic conjugate of X(32840)

leftri

Centers of degree 3 with coefficients in {-1,0,1}: X(32842)-X(32866

rightri

Centers X(32842)-X(32866) were contributed by Peter Moses, June 21, 2019:

Each center in this section has barycentrics of the form p(a,b,c) : : , where p(a,b,c) is a polynomial homogeneous of degree 3 in a,b,c, with coefficents in the set {-1, 0 , 1}. For more of these, see also X(32771)-X(32784), X(32911)-X(32950), and X(33064)-X(33175).


X(32842) = X(1)X(2)∩X(38)X(2895)

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

X(32842) lies on these lines: {1, 2}, {38, 2895}, {69, 4392}, {100, 5078}, {149, 740}, {345, 17127}, {536, 5057}, {584, 5839}, {594, 17726}, {726, 17484}, {1155, 28538}, {3210, 6327}, {3218, 5847}, {3315, 4966}, {3416, 4850}, {3891, 4417}, {3896, 4514}, {3966, 28606}, {3994, 30578}, {3999, 17374}, {4000, 25959}, {4266, 5282}, {4388, 17147}, {4440, 17491}, {4442, 17160}, {4645, 17495}, {4886, 4981}, {4956, 17133}, {4971, 10707}, {5009, 16704}, {5739, 7226}, {9335, 18141}, {9782, 24176}, {17061, 30831}, {17126, 17740}, {17140, 17778}, {17155, 17483}, {17299, 17721}, {17766, 20095}, {19785, 25958}, {20290, 26840}, {24165, 26842}, {24349, 31034}, {26098, 28605}, {30579, 31301}

X(32842) =


X(32843) = X(1)X(26580)∩X(2)X(2308)

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

X(32843) lies on these lines: {1, 26580}, {2, 2308}, {6, 25760}, {9, 29643}, {11, 524}, {31, 4417}, {36, 540}, {42, 4388}, {43, 6327}, {63, 29849}, {69, 30942}, {75, 24725}, {81, 3846}, {100, 752}, {124, 2323}, {149, 519}, {171, 5741}, {193, 11269}, {238, 3936}, {239, 3120}, {244, 320}, {726, 17484}, {740, 5057}, {748, 18134}, {750, 5233}, {899, 4645}, {908, 5847}, {940, 25960}, {1125, 26064}, {1150, 17717}, {1155, 28570}, {1193, 1330}, {1203, 3454}, {1386, 29834}, {1647, 27912}, {1654, 30970}, {1699, 17156}, {1743, 29857}, {1757, 3006}, {1914, 10026}, {2238, 30969}, {2887, 29850}, {2895, 3741}, {3187, 3944}, {3218, 17770}, {3219, 29671}, {3240, 4660}, {3305, 29854}, {3550, 20064}, {3632, 21283}, {3666, 4683}, {3681, 4865}, {3685, 4062}, {3687, 4418}, {3689, 28566}, {3720, 17778}, {3771, 17127}, {3775, 31143}, {3792, 3909}, {3821, 17012}, {3935, 17766}, {3971, 26792}, {4001, 24239}, {4003, 17345}, {4138, 26723}, {4362, 31053}, {4383, 25957}, {4416, 29639}, {4425, 17011}, {4429, 31134}, {4430, 29844}, {4434, 28498}, {4439, 4756}, {4442, 4716}, {4519, 17372}, {4643, 17723}, {4655, 4850}, {4679, 4851}, {4703, 28606}, {4886, 21020}, {4892, 4974}, {5208, 20961}, {5211, 17449}, {5739, 26098}, {5905, 17155}, {6542, 17777}, {6679, 30831}, {7290, 29638}, {9345, 17378}, {12047, 27368}, {14555, 26037}, {14997, 25959}, {15485, 29830}, {15523, 27064}, {16469, 29855}, {16475, 29636}, {16825, 31019}, {17017, 27184}, {17020, 24169}, {17123, 18139}, {17125, 17234}, {17184, 29821}, {17272, 29826}, {17297, 25531}, {17300, 30950}, {17374, 24709}, {17375, 26069}, {17483, 24165}, {17491, 17495}, {17740, 24695}, {19856, 27081}, {19998, 21282}, {20095, 28562}, {24988, 31151}, {25453, 25958}, {25527, 29852}, {27065, 29653}, {27131, 29649}, {27644, 30984}, {28650, 29829}, {29637, 31017}

X(32843) =


X(32844) = X(1)X(3454)∩X(2)X(4434)

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

X(32844) lies on these lines: {1, 3454}, {2, 4434}, {6, 4144}, {8, 21805}, {10, 5315}, {11, 5846}, {31, 3705}, {38, 256}, {42, 4514}, {43, 5014}, {55, 29849}, {79, 596}, {80, 519}, {81, 29655}, {100, 17766}, {149, 740}, {238, 3006}, {239, 4766}, {244, 4645}, {319, 31136}, {320, 17449}, {333, 29690}, {354, 17376}, {386, 4894}, {497, 3930}, {524, 9318}, {537, 17484}, {595, 30171}, {612, 25960}, {614, 17282}, {661, 3907}, {726, 5057}, {742, 24712}, {748, 17338}, {752, 3218}, {758, 16110}, {978, 5300}, {982, 6327}, {984, 29832}, {995, 4680}, {1001, 29643}, {1150, 29676}, {1155, 28566}, {1193, 5015}, {1201, 7270}, {1279, 29632}, {1386, 29631}, {1572, 4165}, {1621, 29671}, {1836, 17155}, {2238, 3966}, {2298, 4071}, {2887, 7191}, {2901, 4857}, {2975, 30366}, {3112, 7018}, {3214, 5100}, {3416, 17721}, {3616, 16498}, {3662, 31134}, {3703, 17340}, {3706, 20693}, {3720, 17317}, {3744, 29846}, {3745, 29845}, {3769, 29662}, {3836, 7292}, {3846, 3920}, {3871, 17748}, {3873, 29844}, {3883, 29639}, {3891, 3944}, {3914, 24212}, {3935, 17765}, {3938, 4417}, {3961, 5741}, {3994, 17777}, {4026, 17726}, {4085, 17012}, {4153, 5299}, {4358, 24709}, {4361, 31140}, {4362, 11680}, {4392, 4655}, {4423, 29854}, {4438, 17127}, {4450, 17596}, {4649, 29835}, {4650, 20064}, {4660, 4850}, {4703, 7226}, {4972, 29821}, {5272, 25961}, {5284, 29653}, {5847, 26015}, {6679, 29872}, {7290, 29857}, {8050, 29824}, {10453, 17373}, {15523, 17285}, {17017, 17380}, {17024, 25958}, {17138, 24478}, {17145, 20042}, {17154, 17491}, {17156, 24392}, {17184, 17598}, {17300, 17450}, {17323, 17599}, {17495, 21282}, {17717, 26227}, {17719, 20045}, {18139, 29820}, {19786, 29819}, {20292, 24165}, {20889, 30660}, {24349, 24725}, {24390, 27368}, {24542, 29862}, {25496, 29667}, {29638, 30811}, {29656, 30831}, {29675, 30834}

X(32844) =


X(32845) = X(1)X(16393)∩X(2)X(17593)

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

X(32845) lies on these lines: {1, 16393}, {2, 17593}, {11, 28530}, {31, 3210}, {44, 4706}, {55, 17155}, {75, 4414}, {81, 4970}, {88, 4871}, {100, 726}, {149, 17764}, {171, 17147}, {190, 899}, {192, 750}, {238, 4427}, {239, 896}, {244, 3685}, {320, 4062}, {321, 17596}, {345, 25957}, {519, 3245}, {524, 14459}, {536, 1155}, {537, 3935}, {596, 3746}, {712, 5091}, {740, 3218}, {748, 17490}, {846, 4359}, {908, 28526}, {1054, 4358}, {1086, 3712}, {1125, 24200}, {1266, 3011}, {1580, 5161}, {1621, 24165}, {1738, 3977}, {1768, 29016}, {1836, 29849}, {2177, 24349}, {2225, 24578}, {2239, 17759}, {2549, 4165}, {2796, 5057}, {2901, 3336}, {2975, 8720}, {3006, 24715}, {3035, 28556}, {3187, 4650}, {3550, 3891}, {3666, 4418}, {3687, 4683}, {3689, 28582}, {3750, 17140}, {3782, 29846}, {3797, 24602}, {3911, 28557}, {3916, 27368}, {3923, 4850}, {3928, 17156}, {3980, 28606}, {3994, 5205}, {3995, 17122}, {3999, 4702}, {4009, 9458}, {4023, 17334}, {4038, 27804}, {4365, 14829}, {4366, 31348}, {4387, 30957}, {4413, 17262}, {4432, 7292}, {4434, 28516}, {4480, 5212}, {4552, 9364}, {4659, 29828}, {4672, 17012}, {4693, 18201}, {4697, 17011}, {4716, 16704}, {4781, 20045}, {4831, 4969}, {4854, 29845}, {4892, 27757}, {5121, 24709}, {5259, 24176}, {5262, 24850}, {5524, 24821}, {5695, 17595}, {5880, 29643}, {6154, 9053}, {6174, 28297}, {6745, 17132}, {7283, 24443}, {9350, 27538}, {9352, 29649}, {17125, 24620}, {17301, 29636}, {17484, 17767}, {17591, 24552}, {17601, 26227}, {17740, 24248}, {17765, 20095}, {17776, 25961}, {19998, 30579}, {20292, 29671}, {26015, 28580}


X(32846) = X(1)X(141)∩X(2)X(3791)

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

X(32846) lies on these lines: {1, 141}, {2, 3791}, {6, 29674}, {8, 4699}, {10, 86}, {37, 24697}, {42, 30965}, {69, 984}, {81, 15523}, {100, 4062}, {171, 306}, {190, 6541}, {192, 4655}, {238, 3912}, {239, 3836}, {291, 30941}, {320, 726}, {333, 29653}, {334, 30940}, {335, 740}, {345, 4650}, {346, 24695}, {516, 4693}, {518, 3792}, {519, 1738}, {524, 1757}, {594, 24342}, {732, 3864}, {752, 3685}, {756, 2895}, {894, 3773}, {1001, 17311}, {1046, 3695}, {1089, 3770}, {1100, 3844}, {1125, 17307}, {1150, 29643}, {1211, 1961}, {1215, 17778}, {1255, 6536}, {1279, 28538}, {1386, 17231}, {1449, 1698}, {1503, 18788}, {1654, 3842}, {1963, 20653}, {1999, 2887}, {2901, 24851}, {3008, 31252}, {3097, 24691}, {3187, 25957}, {3243, 3632}, {3564, 6211}, {3619, 25539}, {3661, 20132}, {3679, 17392}, {3687, 17122}, {3696, 17372}, {3763, 29646}, {3769, 3771}, {3775, 16830}, {3790, 17364}, {3821, 4360}, {3823, 4725}, {3826, 17362}, {3883, 16484}, {3923, 17233}, {3936, 17719}, {3943, 17768}, {3966, 26102}, {3969, 4418}, {3979, 4030}, {3993, 17315}, {3994, 17484}, {3995, 4683}, {4078, 4416}, {4307, 29616}, {4349, 29594}, {4362, 18134}, {4365, 20292}, {4417, 29649}, {4429, 17377}, {4432, 28498}, {4439, 17771}, {4440, 28516}, {4478, 4733}, {4518, 7779}, {4660, 17386}, {4671, 24725}, {4672, 17280}, {4676, 17240}, {4702, 28566}, {4722, 20086}, {4727, 28484}, {4865, 10453}, {4883, 4914}, {4938, 21805}, {5263, 17295}, {5278, 29854}, {5695, 17309}, {5849, 16560}, {5852, 24821}, {5880, 17299}, {6788, 20006}, {7146, 12588}, {7238, 28472}, {7262, 17776}, {8050, 29824}, {10026, 20531}, {12587, 18161}, {14829, 29671}, {16468, 17279}, {16475, 17284}, {16477, 17353}, {16823, 17312}, {16825, 17234}, {17000, 17363}, {17063, 18141}, {17239, 19856}, {17266, 31289}, {17285, 24295}, {17314, 24248}, {17375, 24349}, {17592, 26034}, {17721, 31137}, {17722, 30942}, {17723, 29827}, {17751, 25284}, {19596, 20872}, {19943, 23816}, {20016, 25351}, {20055, 24693}, {20080, 27549}, {20499, 21043}, {24563, 26594}, {24692, 28522}, {25010, 26639}, {25471, 25665}, {26098, 34255}, {29658, 30811}, {29683, 30831}

X(32846) = anticomplement of X(4974)


X(32847) = X(1)X(2)∩X(36)X(4447)

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

X(32847) lies on these lines: {1, 2}, {36, 4447}, {44, 28538}, {75, 24693}, {80, 4876}, {171, 3703}, {190, 752}, {192, 4660}, {238, 3932}, {304, 4737}, {312, 4865}, {320, 537}, {344, 15485}, {345, 3550}, {355, 29331}, {514, 4088}, {515, 18788}, {517, 20715}, {518, 3792}, {527, 24821}, {528, 3943}, {536, 24699}, {678, 4933}, {726, 4440}, {730, 3864}, {740, 2643}, {742, 984}, {1016, 1110}, {1086, 28503}, {1145, 19557}, {1334, 17744}, {1478, 9902}, {1757, 3717}, {1909, 1930}, {1959, 5176}, {2295, 5280}, {3208, 3496}, {3583, 20556}, {3685, 6541}, {3695, 5255}, {3750, 4030}, {3751, 4901}, {3769, 4438}, {3773, 5263}, {3780, 5299}, {3790, 3923}, {3836, 17769}, {3883, 4078}, {3891, 25957}, {3971, 4388}, {3974, 26098}, {3975, 3992}, {3994, 5057}, {3995, 28599}, {4085, 4360}, {4256, 24614}, {4358, 24709}, {4385, 17789}, {4407, 17271}, {4424, 12783}, {4432, 17264}, {4473, 4759}, {4517, 5692}, {4675, 31178}, {4723, 25298}, {4732, 5564}, {4738, 14210}, {4937, 30578}, {4966, 9053}, {4969, 16786}, {5011, 5525}, {5252, 7146}, {5839, 16779}, {6381, 20345}, {8616, 17776}, {12782, 24464}, {16484, 17243}, {16496, 17296}, {16503, 17362}, {17233, 20179}, {17297, 24841}, {17717, 30824}, {17719, 30823}, {17722, 30818}, {17725, 30811}, {19786, 28595}, {24325, 27487}

X(32847) =


X(32848) = X(2)X(3773)∩X(8)X(2177)

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

X(32848) lies on these lines: {2, 3773}, {8, 2177}, {11, 3943}, {31, 345}, {38, 306}, {42, 3703}, {75, 29643}, {149, 4693}, {192, 25760}, {244, 3912}, {312, 29849}, {321, 25385}, {344, 17125}, {518, 4062}, {519, 3722}, {524, 4141}, {536, 3120}, {594, 30970}, {726, 3936}, {740, 3006}, {748, 17776}, {750, 17740}, {752, 4427}, {756, 3687}, {896, 3977}, {899, 3932}, {902, 3712}, {908, 3994}, {1109, 3262}, {1193, 3695}, {1211, 3989}, {1738, 21026}, {2321, 29639}, {2340, 2968}, {2886, 4365}, {2887, 17147}, {2901, 30171}, {3178, 4968}, {3187, 4438}, {3210, 25957}, {3416, 4414}, {3666, 3844}, {3701, 17748}, {3704, 10459}, {3706, 29690}, {3717, 21805}, {3729, 24725}, {3741, 3969}, {3752, 29687}, {3771, 3891}, {3797, 4766}, {3823, 4706}, {3836, 17495}, {3846, 3995}, {3875, 29857}, {3896, 29673}, {3946, 30768}, {3952, 4439}, {3971, 5741}, {4003, 17231}, {4037, 24071}, {4085, 31079}, {4358, 6541}, {4359, 29653}, {4360, 29631}, {4442, 21241}, {4527, 21242}, {4671, 17717}, {4850, 29674}, {4860, 17311}, {4892, 28516}, {4966, 17449}, {4970, 4972}, {4981, 21085}, {5256, 26061}, {6535, 29688}, {6679, 17150}, {9345, 17316}, {11269, 17314}, {16704, 17772}, {17061, 29865}, {17132, 31177}, {17155, 18134}, {17233, 30942}, {17243, 30950}, {17281, 17723}, {17286, 29826}, {17490, 25961}, {17491, 17767}, {17592, 29667}, {17599, 24943}, {17605, 22034}, {17719, 27757}, {17724, 28503}, {17759, 30969}, {17764, 21282}, {17769, 20045}, {18139, 24165}, {19785, 31237}, {19804, 29854}, {20182, 29647}, {24248, 31134}, {29682, 31993}

X(32848) =


X(32849) = X(2)X(37)∩X(8)X(3746)

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

X(32849) lies on these lines: {2, 37}, {8, 3746}, {21, 3695}, {23, 100}, {63, 17296}, {81, 17390}, {89, 29583}, {110, 17977}, {144, 6350}, {149, 3006}, {190, 3936}, {306, 2895}, {323, 1332}, {333, 3969}, {390, 31091}, {594, 5235}, {726, 29632}, {759, 16086}, {846, 15523}, {908, 2325}, {968, 29667}, {1016, 1252}, {1150, 17233}, {1255, 6703}, {1500, 25060}, {1621, 3703}, {1757, 4062}, {2475, 7283}, {2901, 24883}, {3120, 29862}, {3159, 25645}, {3161, 31018}, {3218, 3912}, {3584, 4125}, {3617, 13736}, {3618, 17013}, {3687, 27065}, {3704, 5260}, {3717, 3935}, {3729, 31019}, {3790, 26227}, {3834, 20092}, {3914, 29873}, {3923, 29643}, {3971, 29846}, {3980, 29854}, {3993, 29631}, {3994, 17719}, {4011, 29849}, {4035, 17781}, {4078, 5297}, {4080, 4582}, {4141, 17449}, {4387, 11680}, {4391, 17494}, {4414, 29674}, {4415, 30831}, {4417, 26792}, {4418, 29653}, {4427, 4645}, {4488, 5905}, {4641, 20086}, {4933, 21805}, {4970, 29850}, {5273, 5361}, {5294, 17011}, {5300, 20066}, {5372, 34255}, {5718, 17340}, {6057, 6690}, {6541, 17763}, {6646, 31017}, {7270, 15680}, {13136, 14919}, {14996, 16785}, {14997, 26685}, {17012, 17353}, {17155, 29642}, {17165, 29839}, {17244, 26627}, {17261, 26580}, {17262, 30811}, {17267, 17595}, {17268, 24627}, {17314, 24597}, {17319, 29833}, {17332, 31143}, {17350, 31034}, {17373, 31303}, {17483, 18134}, {17591, 29677}, {17592, 26061}, {17594, 29679}, {17596, 29687}, {18139, 26842}, {18141, 23958}, {20073, 30991}, {20533, 31093}, {21026, 24715}, {22024, 25689}, {24165, 29851}, {24210, 29872}, {24248, 25959}, {24349, 29830}, {24616, 29616}, {26793, 27523}, {27131, 30568}

X(32849) = isotomic conjugate of X(21907)


X(32850) = X(7)X(8)∩X(10)X(82)

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

X(32850) lies on these lines: {1, 3836}, {2, 1279}, {4, 341}, {7, 8}, {10, 82}, {11, 5205}, {19, 3692}, {40, 1760}, {42, 30969}, {43, 4865}, {44, 391}, {55, 25494}, {100, 3006}, {144, 10005}, {145, 3834}, {149, 4358}, {171, 29673}, {190, 516}, {200, 4417}, {210, 4388}, {239, 5846}, {240, 24028}, {306, 3996}, {312, 3434}, {333, 25006}, {344, 390}, {345, 17784}, {346, 5819}, {350, 13576}, {355, 15310}, {497, 18743}, {513, 4397}, {517, 16086}, {519, 1738}, {527, 4899}, {528, 3685}, {673, 3912}, {726, 24715}, {740, 2643}, {752, 1757}, {765, 1861}, {908, 3699}, {962, 1265}, {984, 4660}, {1001, 17263}, {1018, 20605}, {1086, 9053}, {1088, 8817}, {1125, 31252}, {1220, 28026}, {1222, 10106}, {1376, 3705}, {1478, 4737}, {1698, 4894}, {1836, 30615}, {1890, 3710}, {1914, 20483}, {1997, 5274}, {2177, 29643}, {2239, 31330}, {2475, 3770}, {2809, 20924}, {2886, 7081}, {2887, 3961}, {2899, 5225}, {3161, 30332}, {3219, 4450}, {3242, 3662}, {3243, 17298}, {3246, 9780}, {3257, 13532}, {3263, 4872}, {3436, 11677}, {3509, 4119}, {3550, 4438}, {3583, 3992}, {3616, 17370}, {3618, 4344}, {3621, 17373}, {3622, 31243}, {3626, 17770}, {3661, 20172}, {3681, 6327}, {3684, 4071}, {3712, 6154}, {3722, 21026}, {3729, 4901}, {3750, 29653}, {3752, 29840}, {3753, 30892}, {3755, 4360}, {3757, 3925}, {3758, 4307}, {3790, 5695}, {3797, 6653}, {3826, 16823}, {3827, 17789}, {3869, 20713}, {3870, 18134}, {3886, 17233}, {3888, 8679}, {3891, 19796}, {3920, 4972}, {3935, 3936}, {3938, 25957}, {3952, 5057}, {3957, 18139}, {3975, 20556}, {4008, 10573}, {4009, 17777}, {4026, 16830}, {4389, 7174}, {4416, 24393}, {4439, 17764}, {4440, 28582}, {4445, 20181}, {4641, 20101}, {4642, 17446}, {4651, 4886}, {4668, 17771}, {4673, 5082}, {4678, 20072}, {4682, 29837}, {4693, 6541}, {4723, 5080}, {4753, 28498}, {4847, 14829}, {4850, 29832}, {4862, 4929}, {4863, 10453}, {4876, 20593}, {5086, 17787}, {5178, 17751}, {5211, 16610}, {5218, 30741}, {5223, 17347}, {5423, 9812}, {5698, 17336}, {5750, 16786}, {6063, 18043}, {6542, 28581}, {7290, 17352}, {7292, 24988}, {7354, 9369}, {8236, 29627}, {8715, 30172}, {9021, 20432}, {9055, 24699}, {9347, 29829}, {9580, 30568}, {9710, 16824}, {10039, 28980}, {12587, 21280}, {12701, 19582}, {17063, 29844}, {17122, 29655}, {17165, 20292}, {17276, 31302}, {17307, 19868}, {17469, 29850}, {17555, 23050}, {17598, 24169}, {17715, 29642}, {17716, 25453}, {17719, 21241}, {17740, 31091}, {17767, 24821}, {17776, 20075}, {17788, 21867}, {18037, 20718}, {19785, 20020}, {19808, 29667}, {20056, 21949}, {20058, 31029}, {20156, 29576}, {20539, 20947}, {24231, 24841}, {24392, 30567}, {24552, 29679}, {24703, 27538}, {24987, 25903}, {26629, 30763}, {29848, 31237}, {31138, 31145}

X(32850) = isotomic conjugate of anticomplement of X(39048)


X(32851) = X(2)X(37)∩X(3)X(7270)

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

X(32851) lies on these lines: {2, 37}, {3, 7270}, {5, 7283}, {7, 30828}, {8, 2320}, {9, 4070}, {10, 4256}, {11, 3685}, {31, 29849}, {35, 5015}, {38, 29846}, {43, 4438}, {44, 26070}, {55, 3705}, {57, 3719}, {63, 4417}, {69, 5744}, {85, 3926}, {95, 306}, {99, 24630}, {100, 3006}, {140, 3695}, {141, 24627}, {171, 29671}, {190, 908}, {219, 28920}, {239, 26629}, {244, 29632}, {261, 284}, {304, 7763}, {319, 1150}, {320, 2245}, {322, 6350}, {325, 4872}, {341, 5552}, {348, 21605}, {354, 29839}, {498, 4385}, {643, 1936}, {650, 3975}, {726, 17719}, {750, 29643}, {846, 3846}, {894, 5718}, {940, 17391}, {942, 25650}, {982, 3771}, {1016, 1429}, {1040, 4123}, {1043, 6734}, {1054, 3836}, {1155, 4645}, {1211, 17252}, {1220, 5530}, {1264, 28935}, {1265, 27383}, {1266, 25529}, {1279, 5211}, {1330, 3916}, {1376, 29641}, {1465, 17789}, {1760, 24611}, {1818, 23691}, {1962, 29845}, {1999, 17388}, {2318, 27391}, {2325, 4582}, {2348, 5273}, {2550, 30741}, {2796, 27759}, {2887, 17596}, {2968, 7360}, {3035, 3932}, {3161, 5328}, {3219, 5741}, {3262, 20920}, {3306, 3692}, {3550, 4865}, {3582, 4975}, {3584, 4692}, {3662, 17595}, {3670, 25645}, {3699, 3717}, {3701, 27529}, {3703, 5432}, {3704, 4999}, {3710, 27385}, {3718, 28793}, {3729, 5219}, {3744, 29840}, {3750, 29655}, {3757, 6690}, {3759, 24597}, {3821, 17593}, {3823, 26073}, {3834, 30577}, {3886, 5231}, {3891, 29665}, {3923, 17717}, {3996, 4847}, {4007, 4119}, {4030, 4995}, {4066, 20104}, {4085, 29861}, {4153, 24047}, {4189, 5016}, {4357, 30832}, {4361, 31187}, {4376, 31120}, {4388, 4640}, {4414, 24723}, {4427, 5057}, {4429, 29857}, {4440, 30823}, {4513, 17244}, {4526, 28831}, {4585, 22128}, {4660, 17601}, {4673, 10527}, {4680, 5010}, {4781, 21282}, {4972, 29872}, {5081, 17515}, {5087, 17777}, {5088, 6390}, {5100, 8715}, {5121, 25531}, {5153, 17012}, {5241, 17260}, {5247, 17748}, {5263, 29639}, {5316, 25101}, {5326, 6057}, {5435, 18141}, {5440, 16086}, {5791, 9534}, {5955, 19853}, {6675, 16817}, {6679, 29821}, {7292, 24542}, {7321, 30834}, {7664, 24582}, {7799, 17078}, {9335, 29870}, {9360, 26048}, {9369, 12607}, {9371, 27542}, {11064, 23983}, {16586, 17923}, {16824, 24953}, {17063, 29642}, {17075, 17080}, {17122, 29653}, {17124, 29854}, {17184, 30831}, {17255, 27184}, {17258, 26580}, {17261, 30867}, {17333, 27739}, {17336, 31018}, {17487, 27751}, {17591, 26128}, {17592, 29635}, {17598, 29656}, {17599, 29634}, {17600, 29645}, {17715, 29844}, {17718, 24349}, {17774, 24392}, {17785, 24177}, {18139, 27003}, {18235, 21321}, {18359, 20887}, {18668, 20956}, {19582, 25681}, {20182, 29841}, {21241, 24715}, {21361, 29529}, {24325, 29640}, {24552, 29680}, {25440, 30172}, {25728, 31142}, {26582, 30763}, {26770, 27068}, {27509, 28807}, {29596, 31268}, {30567, 31231}, {30568, 30827}, {31020, 31093}

X(32851) = isotomic conjugate of X(2006)
X(32851) = complement of X(37759)


X(32852) = X(2)X(3791)∩X(2)X(15523)

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

X(32852) lies on these lines: {2, 3791}, {6, 15523}, {8, 2650}, {10, 19684}, {31, 306}, {38, 69}, {42, 3416}, {55, 4062}, {141, 17017}, {192, 4683}, {193, 4722}, {239, 25957}, {319, 31330}, {320, 17155}, {321, 24725}, {322, 17871}, {329, 3994}, {333, 29643}, {345, 896}, {354, 17374}, {519, 3891}, {524, 3703}, {599, 17599}, {614, 17296}, {740, 6327}, {748, 3912}, {750, 3687}, {756, 5739}, {984, 2895}, {1100, 29647}, {1150, 29671}, {1211, 5311}, {1215, 31034}, {1386, 24943}, {1836, 4365}, {1999, 25760}, {2177, 4028}, {2887, 3187}, {3011, 4035}, {3630, 4884}, {3632, 12559}, {3706, 17372}, {3720, 3966}, {3744, 28538}, {3759, 29850}, {3763, 29684}, {3769, 29846}, {3773, 26223}, {3844, 29663}, {3896, 4660}, {3923, 3969}, {3925, 17362}, {3936, 4362}, {3938, 5846}, {3989, 4643}, {3995, 4703}, {4383, 29687}, {4387, 17309}, {4388, 6542}, {4417, 17763}, {4423, 17311}, {4438, 16704}, {4649, 29667}, {4655, 17147}, {4854, 17388}, {4865, 17135}, {4886, 26037}, {5264, 21081}, {5278, 29653}, {5300, 23682}, {5711, 20653}, {5737, 29682}, {5741, 29649}, {5839, 21026}, {5849, 26934}, {6536, 16777}, {7081, 31120}, {10327, 21805}, {10371, 10459}, {10453, 17373}, {14829, 29849}, {16825, 18139}, {16998, 17363}, {17150, 26128}, {17231, 29677}, {17277, 29854}, {17723, 31241}, {20011, 28599}, {20064, 28498}, {20655, 21076}, {29658, 30831}, {29847, 30832}


X(32853) = X(1)X(333)∩X(2)X(3775)

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

X(32853) lies on these lines: {1, 333}, {2, 3775}, {6, 3741}, {8, 171}, {10, 940}, {31, 16704}, {38, 3187}, {42, 1150}, {43, 2274}, {44, 4011}, {48, 3684}, {55, 519}, {63, 740}, {69, 2887}, {72, 17733}, {75, 8033}, {81, 31330}, {141, 25453}, {145, 3750}, {193, 21242}, {200, 4434}, {210, 29649}, {238, 10453}, {239, 982}, {306, 4438}, {312, 1757}, {320, 17889}, {354, 16825}, {385, 3705}, {394, 26013}, {518, 4362}, {524, 2886}, {614, 4974}, {748, 19742}, {750, 4651}, {752, 3434}, {984, 1999}, {1100, 29644}, {1125, 19732}, {1211, 29635}, {1215, 3751}, {1376, 4685}, {1386, 29652}, {1621, 4921}, {1654, 29837}, {1707, 3886}, {1737, 28920}, {1746, 10439}, {1836, 17770}, {2177, 20011}, {2308, 24552}, {2895, 25760}, {3178, 5791}, {3210, 4716}, {3240, 5372}, {3416, 29673}, {3550, 3632}, {3681, 17763}, {3685, 7262}, {3686, 5275}, {3696, 3980}, {3706, 3923}, {3720, 5278}, {3742, 17348}, {3759, 29821}, {3769, 3961}, {3840, 4383}, {3842, 5287}, {3846, 5739}, {3868, 27368}, {3879, 16992}, {3896, 4414}, {3914, 4001}, {3936, 24892}, {3966, 29655}, {3971, 5220}, {4028, 5745}, {4085, 26034}, {4361, 24165}, {4386, 17362}, {4393, 17600}, {4416, 4703}, {4423, 19723}, {4425, 4643}, {4640, 28581}, {4658, 19858}, {4710, 19807}, {4722, 26223}, {4734, 17593}, {4847, 4865}, {4851, 29653}, {4863, 17766}, {4883, 24331}, {4891, 15254}, {4892, 17064}, {4966, 29642}, {4981, 5311}, {5247, 10449}, {5256, 6682}, {5271, 24325}, {5361, 17018}, {5741, 29662}, {5786, 12545}, {5905, 17771}, {6327, 31303}, {6679, 24597}, {7075, 21384}, {7751, 20544}, {8666, 16678}, {10436, 27798}, {10980, 16833}, {12513, 23361}, {13478, 29311}, {16994, 17391}, {17026, 30982}, {17123, 17349}, {17147, 17162}, {17149, 30940}, {17259, 25501}, {17277, 26102}, {17299, 17735}, {17360, 29861}, {17490, 18201}, {17767, 20078}, {18169, 29767}, {18792, 29766}, {19684, 30970}, {20064, 21283}, {20142, 31028}, {20290, 31134}, {20340, 21001}, {21805, 30801}, {24003, 30567}, {24996, 26625}, {29865, 31229}, {31017, 31237}

X(32853) =


X(32854) = X(1)X(2)∩X(31)X(3703)

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

X(32854) lies on these lines: {1, 2}, {31, 3703}, {37, 4914}, {38, 3416}, {321, 4865}, {345, 902}, {536, 4799}, {726, 6327}, {740, 4137}, {748, 3932}, {756, 3966}, {1386, 26061}, {1953, 3930}, {2177, 4030}, {2280, 17362}, {2887, 3891}, {2901, 4894}, {3058, 3943}, {3434, 4365}, {3695, 3915}, {3773, 24552}, {3782, 28503}, {3994, 24703}, {4641, 28538}, {4645, 17155}, {4660, 17147}, {17061, 31237}, {17275, 21840}, {17723, 31264}, {17725, 30831}, {20064, 28512}, {20068, 20290}, {20942, 24709}, {21026, 24789}, {21217, 32453}, {21747, 26065}, {21805, 30615}

X(32854) =


X(32855) = X(1)X(3704)∩X(2)X(3773)

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

X(32855) lies on these lines: {1, 3704}, {2, 3773}, {8, 19278}, {43, 3703}, {75, 29671}, {141, 17591}, {171, 17740}, {192, 3846}, {238, 345}, {239, 4438}, {306, 982}, {321, 17717}, {497, 4693}, {519, 3769}, {536, 3944}, {726, 4417}, {740, 3705}, {846, 3966}, {978, 3695}, {984, 3687}, {1125, 19827}, {1266, 4138}, {2321, 24239}, {2887, 3210}, {3158, 3612}, {3416, 17596}, {3550, 5846}, {3661, 6682}, {3706, 29676}, {3712, 8616}, {3741, 3795}, {3752, 29674}, {3816, 3943}, {3836, 17490}, {3838, 4686}, {3840, 17233}, {3873, 4062}, {3891, 17725}, {3912, 17063}, {3932, 16569}, {3936, 17155}, {3969, 30942}, {3971, 5233}, {3977, 7262}, {3994, 27131}, {3995, 25960}, {4035, 24231}, {4085, 4734}, {4359, 29643}, {4360, 29635}, {4365, 11680}, {4385, 17748}, {4439, 27538}, {4650, 5847}, {4689, 4914}, {4850, 15523}, {5087, 22034}, {5524, 30615}, {6536, 28606}, {6541, 18743}, {11814, 20942}, {16477, 26065}, {17012, 26061}, {17064, 17151}, {17123, 17776}, {17147, 25760}, {17243, 25502}, {17289, 29650}, {17296, 18193}, {17495, 25957}, {17593, 26034}, {17759, 30953}, {18134, 24165}, {19804, 29653}, {19808, 29644}, {21020, 29664}, {23955, 28634}, {24589, 29854}, {24789, 29862}, {29657, 31993}

X(32855) =


X(32856) = X(1)X(535)∩X(2)X(18201)

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

X(32856) lies on these lines: {1, 535}, {2, 18201}, {7, 750}, {8, 31134}, {10, 31161}, {11, 17449}, {31, 5905}, {38, 226}, {42, 3782}, {171, 17483}, {190, 29632}, {238, 17484}, {244, 908}, {320, 17763}, {329, 748}, {335, 4766}, {516, 3722}, {518, 3120}, {519, 4442}, {527, 896}, {536, 4062}, {537, 3006}, {545, 3712}, {612, 4654}, {614, 28609}, {726, 3936}, {752, 17491}, {756, 5249}, {851, 21320}, {899, 1086}, {902, 17724}, {982, 31053}, {984, 31019}, {1109, 20360}, {1215, 17184}, {1647, 3999}, {1738, 21805}, {1836, 3938}, {2177, 24248}, {2239, 20347}, {2292, 13407}, {2308, 17061}, {2635, 12831}, {2650, 13161}, {2887, 17165}, {3218, 17719}, {3487, 10448}, {3649, 10459}, {3662, 31083}, {3681, 17889}, {3683, 29689}, {3717, 21026}, {3720, 4415}, {3757, 4683}, {3758, 29636}, {3773, 31017}, {3775, 31025}, {3834, 4009}, {3836, 3952}, {3838, 29690}, {3846, 17140}, {3868, 21935}, {3873, 3944}, {3912, 3994}, {3935, 24715}, {3961, 20292}, {3967, 29687}, {3971, 18139}, {3989, 17056}, {4023, 7263}, {4080, 29824}, {4358, 21093}, {4392, 17717}, {4407, 31030}, {4414, 17276}, {4417, 17155}, {4427, 17767}, {4439, 31029}, {4650, 29665}, {4655, 26227}, {4672, 26230}, {4676, 29638}, {4694, 11813}, {4831, 28333}, {4871, 30566}, {4880, 17734}, {4887, 6745}, {4933, 17132}, {4980, 21085}, {5205, 31129}, {5255, 14450}, {5542, 17450}, {5741, 24165}, {6763, 24160}, {6788, 31160}, {7262, 29681}, {8620, 16592}, {10129, 29676}, {11809, 12081}, {14459, 17160}, {16704, 17771}, {17063, 27131}, {17122, 26842}, {17123, 26792}, {17125, 31018}, {17126, 17725}, {17274, 29828}, {17365, 17602}, {17605, 21342}, {17765, 21282}, {17794, 30969}, {18193, 30852}, {18210, 21326}, {20593, 20974}, {21077, 24443}, {21325, 21807}, {24325, 26580}, {24349, 25760}, {24821, 29862}, {25527, 26061}, {25557, 30950}, {25961, 27538}, {26128, 26223}, {26132, 31237}, {26738, 29657}

X(32856) =


X(32857) = X(1)X(7)∩X(4)X(3551)

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

X(32857) lies on these lines: {1, 7}, {4, 3551}, {8, 4821}, {10, 6646}, {11, 18201}, {36, 1284}, {38, 20292}, {42, 17483}, {43, 5905}, {46, 1423}, {57, 3944}, {63, 17889}, {75, 4655}, {79, 256}, {144, 7613}, {149, 17449}, {171, 3782}, {190, 3836}, {191, 28287}, {226, 17596}, {238, 1086}, {239, 6650}, {244, 5057}, {320, 740}, {329, 16569}, {498, 26125}, {511, 4014}, {517, 1463}, {518, 24715}, {524, 4716}, {527, 1738}, {545, 3932}, {553, 24210}, {596, 17153}, {726, 4440}, {752, 903}, {846, 5249}, {894, 3821}, {899, 17484}, {908, 1054}, {942, 24851}, {982, 1836}, {984, 5880}, {986, 5725}, {1046, 23537}, {1111, 1733}, {1125, 9791}, {1149, 5180}, {1155, 17719}, {1193, 14450}, {1266, 5847}, {1279, 28534}, {1400, 3336}, {1447, 5988}, {1469, 5903}, {1478, 22650}, {1698, 4480}, {1699, 18193}, {1707, 23681}, {1737, 17950}, {1745, 10052}, {1756, 20367}, {1861, 24411}, {2108, 20335}, {2796, 3685}, {3120, 3218}, {3245, 24222}, {3474, 3550}, {3583, 3667}, {3662, 3923}, {3679, 4899}, {3696, 17345}, {3717, 24821}, {3720, 26842}, {3729, 29674}, {3739, 24697}, {3741, 26840}, {3772, 4650}, {3775, 17273}, {3783, 20347}, {3791, 19796}, {3792, 20718}, {3823, 4912}, {3826, 17334}, {3842, 17258}, {3912, 28526}, {3916, 24161}, {3928, 17064}, {3943, 28556}, {3976, 12699}, {3977, 29862}, {3980, 27184}, {3993, 17300}, {4000, 16468}, {4003, 17722}, {4038, 4854}, {4357, 19856}, {4359, 4683}, {4388, 24165}, {4414, 29640}, {4415, 17122}, {4418, 17184}, {4422, 31252}, {4427, 29632}, {4432, 28546}, {4527, 17295}, {4644, 28650}, {4649, 17365}, {4654, 17594}, {4660, 24349}, {4672, 16706}, {4684, 28580}, {4693, 4966}, {4697, 19786}, {4703, 19804}, {4850, 24725}, {4860, 24217}, {4871, 17777}, {4970, 17778}, {4974, 28558}, {5205, 21093}, {5695, 7232}, {5698, 15485}, {5718, 17593}, {5762, 9441}, {5832, 24341}, {6327, 17155}, {6542, 28522}, {7262, 24789}, {7321, 24325}, {9364, 24465}, {9776, 25502}, {9902, 21281}, {11415, 21214}, {12047, 30097}, {14206, 17888}, {14956, 18173}, {15310, 20358}, {15488, 17114}, {16477, 17366}, {16484, 25557}, {17063, 24703}, {17139, 18792}, {17154, 21282}, {17160, 17772}, {17291, 24295}, {17297, 28542}, {17304, 29646}, {17374, 28484}, {17491, 17495}, {17591, 26098}, {17595, 17717}, {17601, 17718}, {17765, 24841}, {18208, 29057}, {19987, 19996}, {20593, 24484}, {20861, 24289}, {21616, 30037}, {23958, 29662}, {24169, 27064}, {24627, 25385}, {24837, 29229}, {27191, 31289}

X(32857) =


X(32858) = X(1)X(2)∩X(9)X(2895)

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

X(32858) lies on these lines: {1, 2}, {9, 2895}, {63, 17296}, {69, 3219}, {72, 26911}, {75, 3969}, {81, 4851}, {141, 28606}, {192, 17184}, {226, 4671}, {304, 8024}, {312, 1230}, {314, 17173}, {318, 445}, {319, 5278}, {321, 17233}, {329, 914}, {333, 17295}, {344, 5739}, {345, 3218}, {346, 5905}, {740, 25957}, {908, 4035}, {940, 17311}, {956, 16439}, {1211, 17243}, {1621, 3416}, {1943, 28776}, {2276, 30965}, {2321, 5249}, {2325, 17781}, {3151, 20533}, {3210, 17232}, {3578, 17360}, {3662, 17147}, {3666, 17231}, {3681, 3932}, {3685, 6327}, {3693, 18607}, {3695, 3868}, {3703, 3873}, {3717, 4661}, {3729, 17483}, {3763, 20182}, {3782, 3943}, {3790, 17165}, {3826, 4046}, {3838, 4519}, {3879, 5294}, {3896, 4429}, {3914, 25959}, {3966, 5284}, {3995, 17242}, {4071, 30985}, {4104, 9330}, {4197, 5295}, {4358, 4417}, {4359, 17234}, {4361, 26724}, {4365, 17889}, {4383, 17267}, {4387, 5057}, {4430, 4684}, {4445, 19732}, {4641, 17374}, {4648, 19822}, {4649, 26061}, {4654, 4873}, {4886, 17263}, {5047, 5814}, {5260, 10371}, {5333, 17303}, {5372, 5745}, {5687, 16438}, {5695, 20292}, {5741, 18743}, {5847, 17127}, {8025, 17391}, {13567, 26669}, {17229, 31993}, {17241, 19804}, {17268, 27064}, {17280, 17778}, {17289, 19684}, {17293, 19701}, {17298, 26842}, {17299, 20483}, {17314, 19785}, {17315, 19786}, {17317, 19808}, {17363, 19742}, {17368, 19717}, {17720, 30831}, {17740, 18141}, {17786, 28654}, {17791, 20919}, {18359, 20928}, {19806, 29984}, {19810, 29981}, {20078, 21296}, {20336, 27127}, {20942, 30566}, {21071, 31060}, {22038, 24061}, {24210, 25958}, {25091, 26540}, {26792, 30568}, {27129, 31045}, {31035, 31037}

X(32858) =


X(32859) = X(1)X(540)∩X(2)X(44)

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

X(32859) lies on these lines: {1, 540}, {2, 44}, {6, 17184}, {7, 4359}, {8, 4018}, {9, 18139}, {31, 17770}, {42, 4655}, {57, 5741}, {63, 3936}, {69, 321}, {75, 2895}, {81, 17202}, {141, 26223}, {144, 17776}, {193, 19785}, {226, 1150}, {238, 29853}, {306, 527}, {312, 17361}, {319, 28605}, {329, 4358}, {333, 31019}, {345, 20078}, {346, 20214}, {518, 5014}, {524, 3187}, {536, 20017}, {752, 3938}, {758, 20896}, {896, 3771}, {940, 26580}, {1211, 17365}, {1255, 17391}, {1330, 3868}, {1757, 25957}, {1836, 17135}, {2277, 18601}, {2308, 26128}, {2887, 17771}, {3175, 17374}, {3218, 4417}, {3219, 17347}, {3305, 17298}, {3416, 17165}, {3578, 4654}, {3666, 17345}, {3681, 4645}, {3683, 29830}, {3686, 3982}, {3703, 5852}, {3720, 4703}, {3729, 3969}, {3741, 24725}, {3744, 20064}, {3751, 4972}, {3765, 17137}, {3772, 16704}, {3870, 4450}, {3873, 4388}, {3891, 5847}, {3896, 24248}, {3909, 26893}, {3912, 17781}, {3966, 17140}, {3977, 4035}, {3995, 4851}, {4044, 4056}, {4061, 30424}, {4101, 4292}, {4346, 20043}, {4357, 19684}, {4371, 19826}, {4383, 7232}, {4389, 17011}, {4416, 5249}, {4430, 4514}, {4442, 17156}, {4650, 29846}, {4651, 5880}, {4657, 19717}, {4672, 24943}, {4685, 24692}, {4722, 25453}, {4725, 20046}, {4850, 26840}, {4863, 21282}, {4886, 7321}, {4892, 24892}, {5057, 10453}, {5233, 27003}, {5256, 17274}, {5300, 5904}, {5333, 17248}, {5743, 26627}, {5745, 30834}, {5839, 19789}, {6515, 17862}, {6646, 17778}, {7179, 26243}, {7222, 19825}, {7262, 29632}, {9965, 17740}, {10371, 17164}, {10381, 23154}, {11433, 20905}, {11679, 31164}, {13567, 26651}, {14555, 24589}, {14829, 31053}, {16477, 29852}, {17018, 24723}, {17019, 17378}, {17023, 19738}, {17147, 17276}, {17173, 29767}, {17174, 29766}, {17206, 27187}, {17234, 27065}, {17253, 19701}, {17255, 20182}, {17277, 27186}, {17288, 27064}, {17325, 19722}, {17344, 31993}, {17349, 26724}, {18141, 31018}, {18743, 26792}, {19742, 24789}, {19804, 26842}, {19851, 26729}, {20080, 30699}, {20942, 30578}, {21281, 25298}, {24514, 30965}, {24597, 26132}, {24703, 29824}, {26932, 28950}, {26942, 28968}, {27558, 28646}, {27659, 29984}, {28388, 30052}, {29673, 31134}, {30566, 30567}

X(32859) =


X(32860) = X(1)X(3896)∩X(2)X(740)

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

X(32860) lies on these lines: {1, 3896}, {2, 740}, {3, 27368}, {6, 4418}, {8, 38}, {10, 4970}, {31, 239}, {37, 26037}, {39, 22184}, {42, 75}, {43, 321}, {51, 6007}, {55, 4361}, {57, 17156}, {81, 3980}, {100, 4362}, {141, 4046}, {165, 29016}, {171, 3187}, {192, 756}, {200, 17151}, {210, 536}, {244, 10453}, {306, 1738}, {312, 899}, {333, 4414}, {354, 28581}, {386, 4647}, {404, 17733}, {518, 17155}, {519, 3873}, {524, 11246}, {537, 4661}, {612, 3875}, {614, 3886}, {726, 3681}, {730, 29617}, {748, 3685}, {750, 1999}, {846, 5278}, {869, 17143}, {968, 4384}, {976, 19805}, {978, 3702}, {982, 17135}, {984, 4651}, {1043, 3924}, {1051, 19738}, {1150, 17596}, {1201, 4673}, {1215, 3240}, {1278, 21805}, {1376, 17763}, {1403, 7235}, {1574, 21827}, {1575, 21345}, {1621, 16825}, {1698, 2901}, {1943, 9316}, {2177, 3757}, {2225, 21387}, {2292, 9534}, {2308, 3759}, {2321, 26242}, {2345, 21840}, {2476, 17748}, {2650, 20018}, {2886, 29849}, {2895, 4655}, {3009, 17144}, {3120, 4417}, {3175, 3740}, {3178, 4197}, {3190, 18690}, {3214, 4385}, {3216, 25591}, {3474, 5839}, {3663, 4061}, {3666, 3696}, {3679, 4981}, {3683, 17348}, {3687, 3914}, {3701, 6048}, {3706, 3752}, {3715, 17262}, {3720, 19804}, {3726, 17299}, {3741, 4709}, {3745, 4852}, {3765, 4489}, {3772, 29846}, {3773, 29679}, {3791, 17126}, {3821, 21085}, {3826, 29854}, {3891, 3961}, {3912, 25961}, {3925, 29643}, {3931, 31339}, {3936, 17889}, {3938, 3996}, {3944, 4442}, {3969, 29674}, {3971, 28522}, {3994, 27538}, {4009, 22034}, {4023, 4415}, {4028, 5249}, {4038, 26627}, {4062, 18134}, {4065, 27785}, {4085, 29667}, {4220, 24257}, {4307, 20043}, {4358, 16569}, {4360, 5311}, {4372, 17798}, {4383, 5695}, {4395, 29638}, {4427, 7262}, {4429, 15523}, {4443, 20966}, {4457, 7226}, {4512, 16833}, {4650, 16704}, {4683, 5739}, {4686, 4849}, {4693, 17123}, {4699, 21806}, {4714, 30116}, {4726, 21870}, {4740, 31161}, {4819, 7263}, {4854, 5743}, {4886, 24723}, {4974, 17127}, {5205, 9350}, {5224, 8013}, {5263, 17017}, {5271, 17594}, {5320, 24264}, {5429, 16393}, {5880, 14459}, {6327, 24715}, {9778, 28850}, {9902, 25298}, {10440, 29347}, {10448, 16824}, {10449, 24443}, {16062, 20653}, {16610, 30957}, {16706, 24943}, {17012, 25496}, {17018, 24325}, {17027, 24629}, {17061, 29848}, {17063, 29824}, {17140, 20011}, {17150, 17716}, {17165, 19998}, {17233, 29687}, {17278, 29851}, {17289, 29663}, {17314, 26040}, {17366, 29852}, {17459, 21868}, {17751, 24440}, {17781, 28526}, {18398, 24176}, {19684, 24342}, {19808, 29647}, {20012, 24349}, {20923, 28247}, {21027, 29682}, {21242, 29680}, {24210, 25378}, {24552, 29821}, {24589, 26102}, {24789, 29632}, {26724, 29642}, {26752, 27285}

X(32860) =


X(32861) = X(1)X(1211)∩X(2)X(3791)

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

X(32861) lies on these lines: {1, 1211}, {2, 3791}, {8, 1215}, {10, 4886}, {38, 2895}, {43, 3416}, {69, 982}, {141, 29821}, {171, 3687}, {192, 4703}, {238, 306}, {239, 2887}, {319, 3741}, {320, 24165}, {333, 29671}, {345, 7262}, {355, 546}, {385, 3705}, {519, 4514}, {595, 21081}, {740, 4388}, {984, 5739}, {1150, 29849}, {1621, 4062}, {1757, 3703}, {1961, 5743}, {1999, 3846}, {2886, 5949}, {3187, 25760}, {3210, 4655}, {3661, 25496}, {3679, 5725}, {3742, 17374}, {3750, 3883}, {3759, 25453}, {3773, 27064}, {3879, 4038}, {3896, 14459}, {3912, 17123}, {3914, 4716}, {3961, 5846}, {3994, 26792}, {3996, 17766}, {4011, 17233}, {4357, 17600}, {4360, 4425}, {4361, 17889}, {4362, 4417}, {4365, 5057}, {4383, 29674}, {4650, 17740}, {4683, 17147}, {4851, 26102}, {4966, 29820}, {4969, 29861}, {4970, 24723}, {5224, 29644}, {5233, 29649}, {5235, 29682}, {5263, 21085}, {5272, 17296}, {5278, 29643}, {5294, 16477}, {5737, 29657}, {5741, 17763}, {5752, 5904}, {6327, 24715}, {7186, 9025}, {8167, 17311}, {10453, 17793}, {11679, 17717}, {16825, 18134}, {17150, 31037}, {17277, 29653}, {17299, 24703}, {17317, 25501}, {17495, 20290}, {17778, 24325}, {18805, 27490}, {19998, 28599}, {20101, 28498}, {24477, 24685}, {24697, 28606}, {24725, 28605}, {29645, 30832}

X(32861) =


X(32862) = X(1)X(26061)∩X(2)X(1390)

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

X(32862) lies on these lines: {1, 26061}, {2, 1390}, {8, 405}, {10, 4970}, {22, 100}, {37, 29667}, {38, 29674}, {141, 7226}, {149, 4387}, {190, 6327}, {192, 4972}, {306, 3681}, {312, 3006}, {321, 3790}, {329, 4756}, {344, 5284}, {346, 3434}, {497, 31091}, {726, 25957}, {908, 4082}, {968, 3679}, {982, 29687}, {984, 15523}, {1089, 2476}, {1215, 29643}, {1962, 29659}, {2321, 25006}, {2886, 4671}, {2887, 4439}, {2895, 5220}, {2979, 4553}, {3219, 3416}, {3610, 27396}, {3617, 3704}, {3661, 4981}, {3666, 29679}, {3685, 5014}, {3701, 11681}, {3705, 4358}, {3710, 3869}, {3729, 20292}, {3772, 29873}, {3773, 31330}, {3782, 25959}, {3836, 17155}, {3870, 4901}, {3873, 3912}, {3925, 28605}, {3935, 30615}, {3944, 3994}, {3952, 4417}, {3966, 27065}, {3967, 31053}, {3971, 25760}, {3995, 31079}, {4009, 27131}, {4115, 24056}, {4125, 7951}, {4135, 21241}, {4193, 30171}, {4392, 4884}, {4415, 25958}, {4429, 17147}, {4430, 4966}, {4438, 17763}, {4514, 17264}, {4680, 11114}, {4767, 5423}, {4903, 30566}, {4914, 15254}, {5300, 7283}, {5687, 20831}, {5739, 27549}, {5741, 27538}, {5743, 9330}, {5846, 17127}, {6541, 29673}, {7191, 17279}, {14594, 28774}, {16439, 34255}, {16684, 17135}, {17140, 17234}, {17165, 18134}, {17243, 29814}, {17267, 17597}, {17280, 24552}, {17347, 20290}, {17357, 29666}, {17490, 24988}, {17550, 30149}, {17598, 29677}, {17600, 29663}, {17720, 29872}, {17724, 29866}, {17725, 29865}, {17889, 21026}, {18018, 20336}, {18139, 24349}, {20486, 31060}, {24165, 25961}, {24325, 29854}, {29657, 31264}, {29680, 30818}

X(32862) =


X(32863) = X(1)X(6)∩X(7)X(6358)

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

X(32863) lies on these lines: {2, 6}, {7, 6358}, {8, 2891}, {63, 17296}, {75, 26842}, {76, 1029}, {144, 26871}, {145, 4201}, {149, 6327}, {239, 24790}, {306, 3218}, {312, 17361}, {319, 4359}, {320, 321}, {329, 30578}, {346, 20078}, {488, 21567}, {593, 5337}, {980, 7854}, {1255, 4364}, {1330, 5046}, {1621, 4966}, {1757, 29687}, {1999, 10452}, {2003, 28780}, {2308, 29637}, {2475, 10449}, {2896, 6542}, {2897, 7560}, {2979, 10477}, {3175, 17345}, {3187, 3662}, {3210, 17373}, {3219, 3912}, {3336, 21081}, {3416, 3873}, {3564, 19649}, {3621, 11851}, {3666, 17374}, {3687, 27003}, {3706, 20292}, {3751, 29679}, {3785, 21508}, {3834, 26724}, {3879, 17011}, {3883, 29817}, {3926, 21537}, {3933, 21495}, {3957, 4684}, {3969, 17295}, {3995, 6646}, {4023, 9342}, {4035, 27757}, {4062, 17596}, {4357, 17019}, {4358, 26792}, {4388, 20290}, {4416, 27065}, {4641, 17231}, {4645, 17135}, {4661, 10327}, {4671, 5905}, {4717, 11552}, {4720, 11112}, {4851, 28606}, {4886, 24589}, {4980, 7321}, {5271, 17298}, {5273, 24616}, {5287, 17272}, {5847, 7191}, {5852, 6057}, {6846, 11487}, {6926, 11411}, {7767, 21511}, {9776, 32099}, {9965, 29616}, {10479, 26131}, {11269, 25958}, {11319, 20077}, {11679, 31019}, {11898, 16434}, {16468, 29677}, {16475, 29666}, {17018, 26034}, {17074, 26942}, {17145, 28599}, {17152, 29588}, {17360, 19804}, {17364, 26223}, {17376, 31993}, {17740, 23958}, {17751, 20060}, {18136, 30939}, {18144, 21287}, {18151, 21739}, {20055, 21281}, {20236, 30690}, {21255, 26723}, {21802, 29569}, {25417, 26626}, {27131, 30567}, {28650, 29663}

X(32863) =


X(32864) = X(1)X(4981)∩X(2)X(3775)

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

X(32864) lies on these lines: {1, 4981}, {2, 3775}, {6, 4042}, {8, 31}, {9, 17156}, {10, 81}, {38, 239}, {42, 333}, {43, 1150}, {44, 3706}, {69, 25957}, {72, 27368}, {100, 4685}, {141, 29850}, {171, 4651}, {190, 4365}, {210, 17763}, {238, 17135}, {319, 15523}, {321, 1757}, {354, 17348}, {519, 1621}, {524, 3925}, {740, 3219}, {748, 10453}, {756, 1999}, {846, 3896}, {873, 17731}, {894, 4722}, {899, 14829}, {902, 3996}, {940, 26037}, {984, 3187}, {1001, 19723}, {1206, 3780}, {1211, 29631}, {1215, 4753}, {1468, 9534}, {1738, 4001}, {1746, 29311}, {1914, 3703}, {2177, 20012}, {2205, 5291}, {2280, 5839}, {2308, 5263}, {2650, 16824}, {2651, 5086}, {2887, 2895}, {3175, 15481}, {3240, 5361}, {3293, 18169}, {3578, 4972}, {3632, 8616}, {3661, 26061}, {3681, 4362}, {3683, 28581}, {3686, 5276}, {3696, 4418}, {3720, 17277}, {3750, 20011}, {3751, 5271}, {3759, 17017}, {3791, 3920}, {3842, 17019}, {3873, 16825}, {3876, 17733}, {3914, 4416}, {3989, 4360}, {3995, 17162}, {4135, 4756}, {4361, 17155}, {4383, 30942}, {4387, 16885}, {4400, 20486}, {4417, 24892}, {4658, 16828}, {4663, 31993}, {4697, 4732}, {4716, 17147}, {4851, 29854}, {4854, 17332}, {4966, 29851}, {4974, 7191}, {5224, 29647}, {5233, 29662}, {5739, 25760}, {5743, 29845}, {5847, 25006}, {6536, 17256}, {6682, 17012}, {7081, 21805}, {8013, 19808}, {10448, 20018}, {11269, 14555}, {14552, 26034}, {16468, 24552}, {16833, 24596}, {16998, 17363}, {17123, 29824}, {17124, 26038}, {17187, 29767}, {17352, 29677}, {17483, 17771}, {17770, 20292}, {18192, 31855}, {19684, 28650}, {19734, 31339}, {20142, 31027}, {25783, 25842}, {29863, 30832}

X(32864) =


X(32865) = X(1)X(3925)∩X(2)X(2177)

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

X(32865) lies on these lines: {1, 3925}, {2, 2177}, {5, 6048}, {8, 2887}, {9, 21956}, {10, 312}, {11, 16569}, {43, 2886}, {63, 24715}, {75, 29673}, {100, 24892}, {120, 5272}, {149, 748}, {171, 2550}, {200, 17064}, {209, 5903}, {210, 3944}, {238, 3434}, {239, 4865}, {333, 4660}, {497, 17123}, {516, 7262}, {518, 17889}, {519, 18134}, {528, 8616}, {740, 29641}, {899, 11680}, {978, 24390}, {982, 1738}, {984, 3914}, {1211, 3679}, {1714, 5255}, {1757, 1836}, {1834, 9710}, {2476, 3214}, {2895, 31134}, {2999, 17722}, {3058, 15485}, {3120, 3681}, {3314, 17117}, {3617, 21935}, {3661, 28595}, {3706, 29674}, {3722, 29681}, {3741, 4429}, {3752, 29676}, {3755, 17592}, {3771, 3996}, {3772, 3961}, {3811, 24161}, {3813, 21214}, {3826, 26102}, {3836, 10453}, {3838, 4849}, {3880, 25137}, {3896, 29643}, {3924, 5178}, {4000, 17598}, {4361, 20541}, {4383, 31140}, {4384, 26590}, {4417, 4685}, {4421, 31187}, {4479, 5224}, {4514, 16825}, {4651, 25760}, {4677, 24222}, {4693, 17776}, {4850, 29690}, {4972, 31330}, {5121, 24386}, {5263, 25453}, {5300, 27368}, {5529, 5886}, {5745, 17601}, {5853, 17715}, {6734, 24440}, {7951, 31855}, {8715, 24880}, {10916, 24174}, {11269, 17122}, {16496, 23681}, {16592, 24528}, {16593, 31200}, {16706, 29652}, {17026, 26582}, {17063, 26015}, {17135, 25957}, {17163, 31079}, {17278, 29820}, {17749, 24387}, {18201, 24477}, {19742, 21282}, {19804, 29655}, {21020, 29667}, {21027, 29685}, {21805, 31053}, {24175, 24216}, {24552, 29850}, {24988, 30957}, {25961, 29824}, {29659, 31993}

X(32865) =


X(32866) = X(1)X(2)∩X(75)X(4865)

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

X(32866) lies on these lines: {1, 2}, {75, 4865}, {141, 17598}, {149, 4365}, {171, 5846}, {238, 3703}, {256, 24454}, {319, 17457}, {345, 8616}, {726, 4388}, {740, 4514}, {846, 3883}, {982, 3416}, {984, 3966}, {2174, 3684}, {3058, 4693}, {3210, 4660}, {3550, 17740}, {3666, 4914}, {3790, 4011}, {3846, 17769}, {3891, 25760}, {3932, 17123}, {3996, 17765}, {4026, 17600}, {4135, 17777}, {4361, 20541}, {4415, 28503}, {4645, 24165}, {4906, 17231}, {6327, 17155}, {15485, 17776}, {16706, 28595}, {17154, 20290}, {17495, 28599}, {17591, 26034}, {17781, 24821}, {20101, 28512}, {21026, 26724}

X(32866) =

leftri

Points h SB SC + k S^2 on the line X(2)X(39): X(32867)-X(32898)

rightri

Centers X(32867)-X(32898) were contributed by Clark Kimberling, June 20, 2019.

The appearance of h k n in the following table means that h SB SC + k S^2 = X(n)

0 1 2
1 0 4
1 1 5
1 -1 3
1 2 3090
1 -2 631
2 -1 3091
2 -1 20
1 3 1656
1 -3 140
3 1 381
3 -1 30
2 3 5056
2 -3 3523
2 -3 3523
3 2 3545
3 -2 376
1 4 5067
1 -4 3525
1 5 3628
1 -5 3526
2 5 7486
2 -5 10303
3 5 5055
3 -5 549
4 5 15022
4 -5 15717
5 1 546
5 -1 382
5 2 3855
5 -2 3529
5 3 3851
5 -3 550
5 4 3544
5 -4 3528
1 6 32867
1 -6 3533
5 6 32868
5 -6 10299
6 5 32869
6 -5 10304
1 7 5070
1 -1 632
2 7 32870
2 -7 32871
3 7 547
3 -7 5054
4 7 32872
4 -7 32873
5 7 5079
5 -7 3530
6 7 32874
6 -7 15692
7 1 3843
7 -1 3627
7 2 32875
7 -2 32876
7 3 3850
7 -3 1657
7 4 32877
7 -4 17538
7 5 5072
7 -5 548
7 6 32878
7 -6 21735
8 1 32879
8 -1 17578
8 3 3854
8 -3 5059
8 5 32880
8 -5 32881
8 7 32882
8 -7 21734
1 8 32883
1 -8 32884
3 8 32885
3 -8 15702
5 8 32886
5 -8 32887
7 8 32888
7 -8 32889
11 6 32890
11 -6 32891
9 8 32892
9 -8 19708
6 11 32893
6 -11 15708
8 9 32894
8 -9 32895
9 2 32896
9 -2 15682
2 9 32897
2 -9 32898

X(32867) = (name pending)

Barycentrics    SA^2 + 6 S^2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 - 14*b^2*c^2 + 5*c^4 : :

X(32867) lies on these lines: {2, 39}, {20, 15031}, {69, 3628}, {140, 32815}, {141, 32976}, {148, 33188}, {183, 5067}, {187, 32991}, {230, 32975}, {315, 7486}, {316, 15022}, {631, 32819}, {632, 6337}, {1007, 5070}, {1078, 5056}, {1656, 7767}, {1975, 3533}, {2896, 33270}, {3053, 15597}, {3054, 14001}, {3090, 3785}, {3091, 7802}, {3523, 32826}, {3525, 32822}, {3620, 7862}, {3763, 10008}, {3832, 7771}, {5055, 32006}, {5068, 14907}, {5071, 7750}, {7615, 15515}, {7737, 18845}, {7749, 32971}, {7766, 31407}, {7776, 15699}, {7793, 33009}, {7800, 32988}, {7815, 32972}, {7868, 32958}, {7872, 32990}, {7917, 15589}, {7921, 16922}, {7928, 32961}, {8860, 18842}, {10303, 11185}, {13881, 32978}, {14061, 33202}, {15271, 32969}, {16924, 17006}, {17004, 32999}, {21843, 32979}, {23055, 30435}

X(32867) =


X(32868) = (name pending)

Barycentrics    5 SA^2 + 6 S^2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 22*b^2*c^2 + c^4 : :

X(32868) lies on these lines: {2, 39}, {69, 546}, {183, 3528}, {382, 7767}, {550, 32815}, {1975, 10299}, {3091, 7917}, {3529, 3785}, {3851, 32816}, {3855, 7773}, {3933, 5079}, {6337, 14869}, {7802, 15589}, {7855, 32991}, {7871, 15022}, {14269, 32006}, {15031, 32827}, {15598, 33226}, {15720, 32824}, {17131, 32971}

X(32868) =


X(32869) = (name pending)

Barycentrics    6 SA^2 + 5 S^2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 22*b^2*c^2 + c^4 : :

X(32869) lies on these lines: {2, 39}, {69, 3543}, {183, 15692}, {312, 17079}, {346, 20925}, {376, 15589}, {549, 32817}, {599, 33210}, {1003, 9740}, {1078, 15705}, {1232, 6527}, {1975, 10304}, {3534, 32822}, {3545, 3933}, {3620, 7924}, {3832, 7809}, {3839, 7788}, {5055, 32818}, {5059, 11057}, {5066, 32823}, {5068, 7796}, {5304, 6661}, {5485, 33184}, {6337, 15708}, {6390, 15702}, {7486, 32821}, {7620, 7818}, {7751, 33201}, {7767, 11001}, {7768, 17578}, {7794, 33200}, {7811, 15683}, {7837, 32971}, {7865, 33025}, {10303, 32820}, {10513, 11185}, {11160, 11361}, {14929, 15684}, {15022, 32825}, {15640, 32819}, {15717, 32824}, {17129, 33255}

X(32869) =


X(32870) = (name pending)

Barycentrics    2 SA^2 + 7 S^2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 - 18*b^2*c^2 + 5*c^4 : :

X(32870) lies on these lines: {2, 39}, {69, 7486}, {183, 5056}, {193, 32999}, {315, 15022}, {547, 32823}, {632, 32817}, {1078, 3832}, {2996, 33001}, {3090, 7776}, {3091, 7750}, {3620, 32967}, {3785, 5068}, {5054, 32822}, {5059, 7771}, {5070, 32818}, {5071, 7767}, {5304, 32992}, {7749, 33205}, {7793, 18845}, {7805, 31407}, {7815, 33025}, {7838, 31404}, {7935, 33200}, {11185, 15717}, {13881, 33202}, {15271, 33180}, {15692, 32819}, {16990, 32988}, {17004, 32971}, {17006, 32989}, {17008, 32987}, {21734, 32826}

X(32870) =


X(32871) = (name pending)

Barycentrics    2 SA^2 - 7 S^2 : :
Barycentrics    9*a^4 - 18*a^2*b^2 + 9*b^4 - 18*a^2*c^2 - 10*b^2*c^2 + 9*c^4 : :

X(32871) lies on these

X(32871) = lines: {2, 39}, {99, 15022}, {193, 16923}, {547, 32822}, {632, 32818}, {1007, 10303}, {1506, 33201}, {3523, 32006}, {3526, 15589}, {3620, 33003}, {3815, 33203}, {5024, 32958}, {5054, 32823}, {5070, 32817}, {5304, 32977}, {5395, 16925}, {6337, 7486}, {7750, 15708}, {7752, 15717}, {7767, 15709}, {7773, 15692}, {7776, 15702}, {7802, 15705}, {7857, 14930}, {7862, 33200}, {17005, 32973}, {18841, 32954}, {21734, 32827}, {31404, 33205}, {31406, 32959}, {31467, 33189}, {31489, 33198}


X(32872) = (name pending)

Barycentrics    4 SA^2 + 7 S^2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 - 22*b^2*c^2 + 3*c^4 : :

X(32872) lies on these lines: {2, 39}, {5, 10513}, {69, 5068}, {183, 3146}, {315, 3854}, {385, 5395}, {3260, 30698}, {3785, 17578}, {3832, 15589}, {3839, 7767}, {3933, 7486}, {4441, 27525}, {5059, 11185}, {5305, 18841}, {7620, 7830}, {7745, 9740}, {14930, 32968}, {15692, 32822}, {16990, 33200}, {17008, 33201}, {17128, 33205}, {17129, 32987}, {17131, 31404}, {18840, 33182}, {20080, 32962}, {21605, 28808}, {21734, 32815}

X(32872) =


X(32873) = (name pending)

Barycentrics    4 SA^2 - 7 S^2 : :
Barycentrics    11*a^4 - 22*a^2*b^2 + 11*b^4 - 22*a^2*c^2 - 6*b^2*c^2 + 11*c^4 : :

X(32873) lies on these lines: {2, 39}, {99, 3854}, {1007, 3522}, {3523, 7776}, {5059, 7752}, {5068, 6337}, {6390, 7486}, {7750, 15717}, {7767, 15721}, {7777, 33205}, {7925, 33025}, {10303, 10513}, {14930, 33203}, {15692, 32823}, {21734, 32816}, {31406, 33183}

X(32873) =


X(32874) = (name pending)

Barycentrics    6 SA^2 + 7 S^2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 26*b^2*c^2 + c^4 : :

X(32874) lies on these lines: {2, 39}, {30, 15589}, {69, 3839}, {99, 15705}, {183, 10304}, {547, 32818}, {1975, 15692}, {2996, 7924}, {3091, 7788}, {3146, 7811}, {3620, 33251}, {3785, 15683}, {3933, 5071}, {5054, 32817}, {5306, 33198}, {5485, 11287}, {6337, 15721}, {6390, 15709}, {7750, 15640}, {7767, 15682}, {7796, 15022}, {7809, 10513}, {8703, 32822}, {9740, 14033}, {11057, 32826}, {11160, 33016}, {11648, 33025}, {17078, 28808}, {17130, 33201}, {19709, 32823}

X(32874) =


X(32875) = (name pending)

Barycentrics    7 SA^2 + 2 S^2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 + 18*b^2*c^2 + 5*c^4 : :

X(32875) lies on these lines: {2, 39}, {69, 548}, {1657, 3933}, {3627, 7776}, {3785, 21735}, {3843, 32816}, {3850, 32825}, {6337, 15712}, {7750, 17538}, {7767, 14093}, {7796, 32826}, {14148, 32990}, {15684, 32006}

X(32875) =


X(32876) = (name pending)

Barycentrics    7 SA^2 - 2 S^2 : :
Barycentrics    9*a^4 - 18*a^2*b^2 + 9*b^4 - 18*a^2*c^2 + 10*b^2*c^2 + 9*c^4 : :

X(32876) lies on these lines: {2, 39}, {69, 15712}, {548, 6337}, {1007, 5072}, {1657, 6390}, {3627, 32816}, {3630, 10008}, {3843, 32815}, {3850, 32824}, {5395, 7764}, {7767, 15706}, {7776, 15686}, {14148, 32972}, {17538, 32818}, {21735, 32821}

X(32876) =


X(32877) = (name pending)

Barycentrics    7 SA^2 + 4 S^2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 + 22*b^2*c^2 + 3*c^4 : :

X(32877) lies on these lines: {2, 39}, {69, 1657}, {548, 3785}, {1007, 12812}, {1975, 17538}, {3627, 32006}, {3843, 3933}, {5395, 7758}, {7767, 15689}, {7776, 14893}, {21735, 32824}

X(32877) =


X(32878) = (name pending)

Barycentrics    7 SA^2 + 6 S^2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 26*b^2*c^2 + c^4 : :

X(32878) lies on these lines: {2, 39}, {69, 3627}, {1657, 7767}, {1975, 21735}, {3620, 7872}, {3785, 17538}, {3850, 32816}, {3933, 5072}, {6337, 12108}, {7620, 7939}, {7776, 23046}, {7890, 32971}, {7917, 32827}, {15712, 32824}

X(32878) =


X(32879) = (name pending)

Barycentrics    7*a^4 - 14*a^2*b^2 + 7*b^4 - 14*a^2*c^2 + 18*b^2*c^2 + 7*c^4 : :

X(32879) lies on these lines: {2, 39}, {69, 21734}, {1975, 17578}, {3146, 7776}, {3522, 3933}, {3832, 32818}, {3854, 32821}, {5059, 32820}, {6390, 15717}, {7750, 10513}, {22253, 33183}


X(32880) = (name pending)

Barycentrics    8 SA^2 + 5 S^2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 + 26*b^2*c^2 + 3*c^4 : :

X(32880) lies on these lines: {2, 39}, {69, 5059}, {346, 21605}, {3832, 3933}, {5395, 17128}, {10513, 17578}, {15022, 32818}, {15589, 21734}, {15683, 32822}, {15717, 32817}, {17129, 33205} -

X(32880) =


X(32881) = (name pending)

Barycentrics    8 SA^2 - 5 S^2 : :
Barycentrics    13*a^4 - 26*a^2*b^2 + 13*b^4 - 26*a^2*c^2 + 6*b^2*c^2 + 13*c^4 : :

X(32881) lies on these lines: {2, 39}, {1007, 3854}, {3522, 7776}, {3832, 6390}, {5059, 6337}, {7750, 21734}, {15022, 32817}, {15683, 32823}, {15717, 32818}

X(32881) =


X(32882) = (name pending)

Barycentrics    8 SA^2 + 7 S^2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 30*b^2*c^2 + c^4 : :

X(32882) lies on these lines: {2, 39}, {69, 17578}, {1975, 21734}, {3832, 7776}, {3933, 5068}, {4452, 4696}, {4461, 26563}, {5059, 7750}, {7620, 7896}, {7767, 15683}, {17129, 33201}

X(32882) =


X(32883) = (name pending)

Barycentrics    SA^2 + 8 S^2 : :
Barycentrics    7*a^4 - 14*a^2*b^2 + 7*b^4 - 14*a^2*c^2 - 18*b^2*c^2 + 7*c^4 : :

X(32883) lies on these lines: {2, 39}, {69, 5070}, {547, 32006}, {631, 32826}, {1078, 7486}, {1656, 3785}, {3054, 32968}, {3090, 7750}, {3525, 32815}, {3628, 7776}, {5067, 32816}, {5068, 7771}, {7749, 32987}, {7767, 15703}, {7815, 32988}, {7935, 32972}, {10304, 15031}, {14907, 15022}, {15271, 32976}, {15702, 32819}, {17004, 31404}, {17006, 32999}, {21843, 32991}

X(32883) =


X(32884) = (name pending)

Barycentrics    SA^2 - 8 S^2 : :
Barycentrics    9*a^4 - 18*a^2*b^2 + 9*b^4 - 18*a^2*c^2 - 14*b^2*c^2 + 9*c^4 : :

X(32884) lies on these lines: {2, 39}, {140, 32006}, {439, 7603}, {631, 32827}, {632, 1007}, {1506, 5395}, {3055, 32970}, {3090, 32826}, {3525, 32816}, {3526, 3785}, {5067, 32815}, {5070, 6337}, {7750, 15709}, {7773, 15702}, {7776, 10124}, {7782, 15022}, {7802, 15708}, {11614, 20080}, {15491, 33222}, {18841, 32959}, {31404, 33000}, {31489, 32977}

X(32884) =


X(32885) = (name pending)

Barycentrics    3 SA^2 + 8 S^2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 - 22*b^2*c^2 + 5*c^4 : :

X(32885) lies on these lines: {2, 39}, {69, 5055}, {99, 15708}, {183, 3545}, {376, 32826}, {381, 3785}, {1007, 15699}, {1078, 3543}, {1975, 15702}, {3090, 7788}, {3091, 7811}, {3524, 32815}, {3525, 32824}, {3933, 15703}, {5066, 32006}, {5067, 32825}, {5071, 32816}, {5306, 32968}, {6337, 15694}, {7603, 20080}, {7610, 14033}, {7615, 33272}, {7620, 33008}, {7753, 32987}, {7767, 19709}, {7768, 15022}, {7776, 10109}, {7780, 32991}, {7800, 18362}, {7809, 15589}, {7837, 31404}, {8556, 16041}, {8860, 33191}, {10008, 33240}, {10304, 11185}, {11168, 32986}, {11286, 23055}, {11287, 16509}, {11648, 32990}, {13468, 32983}, {13881, 33223}, {14537, 18845}, {14892, 14929}, {17004, 33255}, {18842, 22329}, {19708, 32819}

X(32885) =


X(32886) = (name pending)

Barycentrics    5 SA^2 + 8 S^2 : :
Barycentrics    3*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 - 26*b^2*c^2 + 3*c^4 : :

X(32886) lies on these lines: {2, 39}, {69, 3851}, {183, 3529}, {382, 3785}, {546, 14929}, {3528, 32815}, {3854, 7850}, {3855, 32827}, {7620, 7904}, {7767, 14269}, {7776, 11737}, {10008, 33241}, {15598, 33238}, {15715, 32822}, {17131, 32987}

X(32886) =


X(32887) = (name pending)

Barycentrics    5 SA^2 - 8 S^2 : :
Barycentrics    13*a^4 - 26*a^2*b^2 + 13*b^4 - 26*a^2*c^2 - 6*b^2*c^2 + 13*c^4 : :

X(32887) lies on these lines: {2, 39}, {550, 1007}, {3528, 32816}, {3529, 32827}, {3530, 7776}, {3785, 15720}, {3851, 6337}, {3855, 32826}, {7750, 10299}, {7838, 32989}, {7917, 15708}, {15715, 32823}

X(32887) =


X(32888) = (name pending)

Barycentrics    7 SA^2 + 8 S^2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 30*b^2*c^2 + c^4 : :

X(32888) lies on these lines: {2, 39}, {69, 3843}, {183, 21735}, {1657, 3785}, {3850, 7776}, {7750, 32826}, {7767, 15684}, {14893, 32006}, {17538, 32815}

X(32888) =


X(32889) = (name pending)

Barycentrics    7 SA^2 - 8 S^2 : :
Barycentrics    15*a^4 - 30*a^2*b^2 + 15*b^4 - 30*a^2*c^2 - 2*b^2*c^2 + 15*c^4 : :

X(32889) lies on these lines: {2, 39}, {548, 32006}, {1007, 3627}, {3843, 6337}, {7776, 14891}, {17538, 32816}

X(32889) =


X(32890) = (name pending)

Barycentrics    11 SA^2 + 6 S^2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 + 34*b^2*c^2 + 5*c^4 : :

X(32890) lies on these lines: {2, 39}, {69, 15704}, {3858, 32816}, {5073, 32815}, {7759, 18845}, {7767, 15696}

X(32890) =


X(32891) = (name pending)

Barycentrics    11 SA^2 - 6 S^2 : :
Barycentrics    17*a^4 - 34*a^2*b^2 + 17*b^4 - 34*a^2*c^2 + 10*b^2*c^2 + 17*c^4 : :

X(32891) lies on these lines: {2, 39}, {3858, 32815}, {5073, 32816}

X(32891) =


X(32892) = (name pending)

Barycentrics    9 SA^2 + 8 S^2 : :
Barycentrics    a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 34*b^2*c^2 + c^4 : :

X(32892) lies on these lines: {2, 39}, {69, 3830}, {183, 15698}, {1975, 19708}, {3524, 32824}, {3534, 3785}, {3620, 11648}, {3860, 7776}, {3933, 19709}, {5071, 32825}, {6337, 15701}, {7767, 15685}, {7788, 32827}, {11001, 32815}, {12101, 32006}, {13665, 32811}, {13785, 32810}, {14537, 20080}, {15589, 15697}, {15682, 32826}, {15702, 32820}, {23249, 32809}, {23259, 32808}

X(32892) =


X(32893) = (name pending)

Barycentrics    6 SA^2 + 11 S^2 : :
Barycentrics    5*a^4 - 10*a^2*b^2 + 5*b^4 - 10*a^2*c^2 - 34*b^2*c^2 + 5*c^4 : :

X(32893) lies on these

X(32893) = lines: {2, 39}, {183, 3543}, {381, 14929}, {1975, 15708}, {5068, 7809}, {7837, 32987}, {7865, 33200}, {9740, 32983}, {11057, 17578}, {11160, 33005}, {11185, 15683}, {12100, 32822}, {15694, 32817}, {15697, 32819}, {15699, 32818}, {18845, 20065}


X(32894) = (name pending)

Barycentrics    8 SA^2 + 9 S^2 : :
Barycentrics    (a^2 - b^2 - 6*b*c - c^2)*(a^2 - b^2 + 6*b*c - c^2) : :

X(32894) lies on these lines: {2, 39}, {183, 21734}, {2996, 7928}, {3146, 7767}, {3522, 32822}, {3854, 7773}, {3933, 15022}, {5059, 15589}, {5068, 32823}

X(32894) =


X(32895) = (name pending)

Barycentrics    8 SA^2 - 9 S^2 : :
Barycentrics    17*a^4 - 34*a^2*b^2 + 17*b^4 - 34*a^2*c^2 - 2*b^2*c^2 + 17*c^4 : :

X(32895) lies on these lines: {2, 39}, {1007, 17578}, {3522, 32823}, {3854, 32819}, {5059, 7773}, {5068, 32822}, {6390, 15022}, {7776, 15705}, {7921, 33205}

X(32895) =


X(32896) = (name pending)

Barycentrics    9 SA^2 + 2 S^2 : :
Barycentrics    7*a^4 - 14*a^2*b^2 + 7*b^4 - 14*a^2*c^2 + 22*b^2*c^2 + 7*c^4 : :

X(32896) lies on these lines: {2, 39}, {30, 32824}, {69, 8703}, {99, 15697}, {376, 32820}, {381, 32825}, {1975, 15682}, {3534, 3933}, {3543, 7796}, {3545, 32821}, {3620, 14148}, {3785, 19708}, {3830, 32815}, {3845, 32816}, {6337, 12100}, {6390, 15693}, {7788, 11001}, {7809, 32826}, {9541, 32808}, {10008, 22165}, {10513, 11057}

X(32896) =


X(32897) = (name pending)

Barycentrics    2 SA^2 + 9 S^2 : :
Barycentrics    7*a^4 - 14*a^2*b^2 + 7*b^4 - 14*a^2*c^2 - 22*b^2*c^2 + 7*c^4 : :

X(32897) lies on these lines: {2, 39}, {140, 32822}, {183, 7486}, {193, 16922}, {1078, 5068}, {1285, 18843}, {1656, 15589}, {3054, 33203}, {3090, 7767}, {3146, 15031}, {3523, 32819}, {3620, 32998}, {3785, 15022}, {3832, 7802}, {3854, 14907}, {5056, 7773}, {5304, 32975}, {7620, 15515}, {7749, 33201}, {7771, 17578}, {7815, 33200}, {7921, 32999}, {7928, 32972}, {15271, 33199}, {17004, 32987}, {17006, 32973}

X(32897) =


X(32898) = (name pending)

Barycentrics    2 SA^2 - 9 S^2 : :
Barycentrics    11*a^4 - 22*a^2*b^2 + 11*b^4 - 22*a^2*c^2 - 14*b^2*c^2 + 11*c^4 : :

X(32898) lies on these lines: {2, 39}, {140, 32823}, {1506, 33205}, {1656, 32822}, {3523, 7773}, {3525, 7767}, {3533, 15589}, {3854, 7782}, {5056, 32819}, {7750, 15721}, {7776, 15709}, {7802, 15717}, {7862, 33025}, {7921, 33000}, {15022, 15031}, {15708, 32006}, {17005, 32989}, {31467, 32959}, {31489, 33181}

X(32898) =


X(32899) = ISOGONAL CONJUGATE OF X(9897)

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

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29100.

X(32899) lies on these lines: {484,4511}, {2323,19297}

X(32899) = isogonal conjugate of X(9897)
X(32899) = barycentric quotient X(6)/X(9897)
X(32899) = trilinear quotient X(1)/X(9897)

X(32900) = X(1)X(381)∩X(3)X(3633)

Barycentrics    -8 a^4+7 a^3 b+6 a^2 b^2-7 a b^3+2 b^4+7 a^3 c-14 a^2 b c+7 a b^2 c+6 a^2 c^2+7 a b c^2-4 b^2 c^2-7 a c^3+2 c^4 : :
X(32900) = 7*X[1]-3*X[381], 3*X[3]+X[3633], 7*X[8]-15*X[631], 7*X[10]-9*X[11539], 3*X[140]-2*X[4691], X[145]+X[3579], 3*X[355]-7*X[3622], 3*X[549]-X[3625], 7*X[944]+X[3146], X[1071]+X[10284], 5*X[1482]-X[9589], X[1657]+3*X[11224], 5*X[1698]-9*X[10246], 7*X[3241]+X[11001], 9*X[3524]-X[20053], 17*X[3544]-21*X[5886], 5*X[3617]-9*X[3653], 7*X[3632]-27*X[15707], 2*X[3636]-X[18357], 7*X[3654]-11*X[15715], 3*X[3656]-7*X[20057], 5*X[4668]-9*X[5054], 9*X[5657]-X[20054], X[5881]-3*X[11230], 3*X[5885]-2*X[10107], 2*X[6684]-3*X[31662], 3*X[10247]-X[22793], 3*X[11231]-X[12645], 7*X[12702]-15*X[15695], 9*X[17502]+X[20014]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29100.

X(32900) lies on these lines: {1,381}, {3,3633}, {8,631}, {10,11539}, {30,3635}, {79,11011}, {140,4691}, {145,3579}, {355,3622}, {515,3853}, {517,550}, {519,12100}, {549,3625}, {572,4727}, {944,3146}, {950,12735}, {952,1125}, {971,26200}, {1071,10284}, {1317,2771}, {1482,9589}, {1657,11224}, {1698,10246}, {2099,31776}, {2646,7972}, {3241,11001}, {3524,20053}, {3544,5886}, {3617,3653}, {3632,15707}, {3636,18357}, {3654,15715}, {3656,20057}, {3746,12773}, {3847,10942}, {3880,13145}, {4301,28168}, {4668,5054}, {5657,20054}, {5844,31663}, {5881,11230}, {5885,10107}, {5901,28236}, {6684,31662}, {10106,16137}, {10247,22793}, {10950,25405}, {11231,12645}, {12702,15695}, {13464,28224}, {17502,20014}, {22791,28208}, {22935,24927}

X(32900) = midpoint of X(i) and X(j) for these lines: {i,j}: {145,3579}, {944,10222}, {1071,10284}, {1483,5882}, {11278,18481}
X(32900) = reflection of X(i) in X(j) for these lines: {i,j}: {9955,1}, {9956,15178}, {13369,26089}, {15178,13607}, {18357,3636}
X(32900) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {1,18526,18480}, {145,3655,3579}, {944,3623,12699 {3241,18481,11278}, {3623,12699,10222}


X(32901) = X(8593)X(15533)∩X(9208)X(11643)

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

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29100.

X(32901) lies on these lines: {8593,15533}, {9208,11643}


X(32902) = (name pending)

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

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29100.

X(32902) lies on this line: {1511,5562}


X(32903) = MIDPOINT OF X(20) AND X(10282)

Barycentrics    8 a^10-15 a^8 b^2-a^6 b^4+13 a^4 b^6-3 a^2 b^8-2 b^10-15 a^8 c^2+28 a^6 b^2 c^2-13 a^4 b^4 c^2-6 a^2 b^6 c^2+6 b^8 c^2-a^6 c^4-13 a^4 b^2 c^4+18 a^2 b^4 c^4-4 b^6 c^4+13 a^4 c^6-6 a^2 b^2 c^6-4 b^4 c^6-3 a^2 c^8+6 b^2 c^8-2 c^10 : :
X(32903) = 3*X[3]-X[18383], X[20]+X[10282], X[64]-9*X[15689], 9*X[376]-X[14216], 3*X[548]-X[6696], X[1657]+3*X[11202], X[2883]+3*X[15686], X[3357]-5*X[15696], 5*X[3522]-X[18381], 7*X[3523]-3*X[18376], 7*X[3528]-3*X[23329], 9*X[3534]-X[5925], X[3627]-3*X[10182], X[6225]+15*X[17538], 3*X[8703]-X[20299], 3*X[11204]-X[14864], 3*X[15681]+5*X[17821]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29100.

X(32903) lies on these lines: {3,18383}, {20,10282}, {64,15689}, {376,14216}, {389,10295}, {548,6696}, {550,1216}, {1657,11202}, 2071,23358}, {2777,12103}, {2883,15686}, {3357,15696}, {3522,18381}, {3523,18376}, {3528,23329}, {3534,5925}, {3627,10182}, {6225,17538}, {8703,20299}, {10628,15644}, {11204,14864}, {13367,13619}, {13754,15332}, {13851,17506}, {15681,17821}

X(32903) = midpoint of X(i) and X(j) for these lines: {i,j}: {20,10282}, {14864,17845}
X(32903) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {11204,17845,14864}


X(32904) = MIDPOINT OF X(20414) AND X(30484)

Barycentrics    2 a^16-10 a^14 b^2+25 a^12 b^4-44 a^10 b^6+55 a^8 b^8-42 a^6 b^10+15 a^4 b^12-b^16-10 a^14 c^2+38 a^12 b^2 c^2-58 a^10 b^4 c^2+27 a^8 b^6 c^2+35 a^6 b^8 c^2-47 a^4 b^10 c^2+13 a^2 b^12 c^2+2 b^14 c^2+25 a^12 c^4-58 a^10 b^2 c^4+34 a^8 b^4 c^4+7 a^6 b^6 c^4+23 a^4 b^8 c^4-39 a^2 b^10 c^4+8 b^12 c^4-44 a^10 c^6+27 a^8 b^2 c^6+7 a^6 b^4 c^6+18 a^4 b^6 c^6+26 a^2 b^8 c^6-34 b^10 c^6+55 a^8 c^8+35 a^6 b^2 c^8+23 a^4 b^4 c^8+26 a^2 b^6 c^8+50 b^8 c^8-42 a^6 c^10-47 a^4 b^2 c^10-39 a^2 b^4 c^10-34 b^6 c^10+15 a^4 c^12+13 a^2 b^2 c^12+8 b^4 c^12+2 b^2 c^14-c^16 : :
X(32904) = 3*X[5066]-X[32536], 7*X[14869]+X[15619], X[27868]+X[32551]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29100.

X(32904) lies on these lines: {5,6150}, {140,13470}, {252,3574}, {539,13856}, {3850,10275}, {5066,32536}, {10289,32423}, {14869,15619}, {27868,32551}

X(32904) = midpoint of X(i) and X(j) for these lines: {i,j}: {20414,30484}, {27868,32551}
X(32904) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {5,30484,20414}


X(32905) = MIDPOINT OF X(145) AND X(6796)

Barycentrics    4*a^7-8*(b+c)*a^6-(3*b^2-22*b*c+3*c^2)*a^5+(b+c)*(15*b^2-31*b*c+15*c^2)*a^4-(6*b^2+25*b*c+6*c^2)*(b-c)^2*a^3-(b^2-c^2)*(b-c)*(6*b^2-17*b*c+6*c^2)*a^2+(b^2-c^2)^2*(5*b^2-9*b*c+5*c^2)*a-(b^2-c^2)^3*(b-c) : :
X(32905) = X(5450)-3*X(7967), X(6705)-3*X(13607)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29101.

X(32905) lies on these lines: {1, 6830}, {145, 6796}, {515, 1483}, {952, 24387}, {1071, 1317}, {3244, 24474}, {3746, 5450}, {3825, 19907}, {6705, 13607}, {7972, 21740}, {7982, 11015}, {10572, 25485}, {12608, 21630}

X(32905) = midpoint of X(145) and X(6796)
X(32905) = reflection of X(24387) in X(26087)


X(32906) = ISOGONAL CONJUGATE OF X(22998)

Barycentrics    (SB+SC)*((9*SB-4*SW)*S^2+sqrt(3)*(3*SB-SW)*(SC+SA)*S+3*SA*SC*SW)*((-4*SW+9*SC)*S^2+sqrt(3)*(3*SC-SW)*(SA+SB)*S+3*SA*SB*SW) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29101.

X(32906) lies on these lines: {187, 6105}, {623, 11133}, {10677, 32301}

X(32906) = isogonal conjugate of X(22998)


X(32907) = REFLECTION OF X(2) IN X(20415)

Barycentrics    -2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*sqrt(3)*S+5*a^6-8*(b^2+c^2)*a^4+2*(2*b^4-3*b^2*c^2+2*c^4)*a^2-(b^4-c^4)*(b^2-c^2) : :
Barycentrics    3*SB*SC*SW+(9*SA-8*SW)*S^2-2*sqrt(3)*S*(S^2+3*SB*SC) : :
X(32907) = 3*X(13)-X(381), 4*X(13)-X(22796), 4*X(381)-3*X(22796), 2*X(547)-3*X(5459), 2*X(549)-3*X(6771), 3*X(616)-7*X(15702), 3*X(618)-4*X(10124), X(3543)+3*X(6770), X(3543)-3*X(25154), 5*X(5071)-3*X(5617), 3*X(5463)-5*X(15694), 3*X(5473)-5*X(14093), 3*X(5478)-2*X(14893), 3*X(9166)-X(22507), 2*X(11737)-3*X(20252), 3*X(13103)+X(15681), 7*X(15700)-9*X(21156), 7*X(15703)-9*X(22489)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29101.

X(32907) lies on these lines: {2, 20415}, {6, 13}, {30, 16001}, {182, 22492}, {376, 9735}, {530, 549}, {543, 25559}, {547, 5459}, {575, 31694}, {616, 15702}, {618, 10124}, {3543, 6770}, {5071, 5617}, {5463, 15694}, {5473, 14093}, {5478, 14893}, {6036, 9762}, {9166, 22507}, {11302, 12155}, {11737, 20252}, {12243, 22509}, {13103, 15681}, {15700, 21156}, {15703, 22489}, {19924, 20425}

X(32907) = midpoint of X(i) and X(j) for these lines: {i,j}: {6770, 25154}, {6778, 11632}, {12243, 22509}
X(32907) = reflection of X(2) in X(20415)


X(32908) = ISOGONAL CONJUGATE OF X(22997)

Barycentrics    (SB+SC)*((9*SB-4*SW)*S^2-sqrt(3)*(3*SB-SW)*(SC+SA)*S+3*SA*SC*SW)*((-4*SW+9*SC)*S^2-sqrt(3)*(3*SC-SW)*(SA+SB)*S+3*SA*SB*SW) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29101.

X(32908) lies on these lines: {187, 6104}, {624, 11132}, {10678, 32302}

X(32908) = isogonal conjugate of X(22997)


X(32909) = REFLECTION OF X(2) IN X(20416)

Barycentrics    2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*sqrt(3)*S+5*a^6-8*(b^2+c^2)*a^4+2*(2*b^4-3*b^2*c^2+2*c^4)*a^2-(b^4-c^4)*(b^2-c^2) : :
Barycentrics    3*SB*SC*SW+(9*SA-8*SW)*S^2+2*sqrt(3)*S*(S^2+3*SB*SC) : :
X(32909) = 3*X(14)-X(381), 4*X(14)-X(22797), 4*X(381)-3*X(22797), 2*X(547)-3*X(5460), 2*X(549)-3*X(6774), 3*X(617)-7*X(15702), 3*X(619)-4*X(10124), X(3543)+3*X(6773), X(3543)-3*X(25164), 5*X(5071)-3*X(5613), 3*X(5464)-5*X(15694), 3*X(5474)-5*X(14093), 3*X(5479)-2*X(14893), 3*X(9166)-X(22509), 2*X(11737)-3*X(20253), 3*X(13102)+X(15681), 7*X(15700)-9*X(21157), 7*X(15703)-9*X(22490)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29101.

X(32909) lies on these lines: {2, 20416}, {6, 13}, {30, 16002}, {182, 22491}, {376, 9736}, {531, 549}, {543, 25560}, {547, 5460}, {575, 31693}, {617, 15702}, {619, 10124}, {3543, 6773}, {5071, 5613}, {5464, 15694}, {5474, 14093}, {5479, 14893}, {6036, 9760}, {9166, 22509}, {11301, 12154}, {11737, 20253}, {12243, 22507}, {13102, 15681}, {15700, 21157}, {15703, 22490}, {19924, 20426}

X(32909) = midpoint of X(i) and X(j) for these lines: {i,j}: {6773, 25164}, {6777, 11632}, {12243, 22507}
X(32909) = reflection of X(2) in X(20416)


X(32910) = X(80)X(5450)∩X(2800)X(12688)

Barycentrics    4*a^10-11*(b+c)*a^9+(b^2+42*b*c+c^2)*a^8+6*(b+c)*(4*b^2-11*b*c+4*c^2)*a^7-(24*b^4+24*c^4+(29*b^2-114*b*c+29*c^2)*b*c)*a^6-(b+c)*(6*b^4+6*c^4-(95*b^2-177*b*c+95*c^2)*b*c)*a^5+(26*b^4+26*c^4-(10*b^2+99*b*c+10*c^2)*b*c)*(b-c)^2*a^4-(b^2-c^2)*(b-c)*(16*b^4+16*c^4+(24*b^2-83*b*c+24*c^2)*b*c)*a^3-(4*b^4+4*c^4-(43*b^2-79*b*c+43*c^2)*b*c)*(b^2-c^2)^2*a^2+(b^2-c^2)^3*(b-c)*(9*b^2-19*b*c+9*c^2)*a-3*(b^2-c^2)^4*(b-c)^2 : :
X(32910) = 3*X(80)-X(5450), X(11500)+3*X(12747)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29101.

X(32910) lies on these lines: {80, 5450}, {2800, 12688}, {11500, 12747}

leftri

Centers of degree 3 with coefficients in {-1,0,1}: X(32911)-X(32950)

rightri

Centers X(32911)-X(32950) were contributed by Peter Moses, June 21, 2019:

Each center in this section has barycentrics of the form p(a,b,c) : : , where p(a,b,c) is a polynomial homogeneous of degree 3 in a,b,c, with coefficents in the set {-1, 0 , 1}. For more of these, see also X(32771)-X(32784), X(32842)-X(32866), and X(33064)-X(33175). .


X(32911) = X(1)X(748)∩X(2)X(6)

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

X(32911) lies on these lines: {1, 748}, {2, 6}, {3, 16948}, {5, 24883}, {8, 13740}, {9, 5256}, {10, 1203}, {21, 386}, {23, 5347}, {31, 43}, {32, 21495}, {37, 17011}, {38, 1757}, {39, 1931}, {41, 27659}, {42, 238}, {44, 3219}, {45, 17013}, {51, 4224}, {55, 3240}, {56, 27639}, {57, 88}, {58, 404}, {63, 1743}, {72, 5262}, {75, 26223}, {78, 1453}, {83, 213}, {92, 1783}, {101, 24625}, {105, 29363}, {110, 6043}, {145, 1191}, {155, 6944}, {162, 4219}, {171, 899}, {182, 4220}, {190, 17147}, {200, 16469}, {210, 1386}, {218, 329}, {219, 18228}, {220, 17014}, {222, 5435}, {223, 1445}, {226, 26723}, {244, 4722}, {306, 16470}, {312, 3187}, {346, 20043}, {354, 4663}, {371, 16440}, {372, 16441}, {387, 2478}, {390, 7074}, {392, 17015}, {405, 19767}, {411, 580}, {469, 1172}, {498, 16472}, {499, 16473}, {511, 19649}, {518, 7191}, {519, 5315}, {551, 16474}, {572, 21363}, {579, 1817}, {581, 6986}, {582, 3651}, {583, 24530}, {593, 662}, {595, 3293}, {612, 16475}, {614, 3315}, {644, 16834}, {668, 18064}, {673, 8049}, {698, 19700}, {750, 9342}, {757, 1171}, {799, 7304}, {869, 16476}, {894, 4359}, {896, 17596}, {938, 7078}, {948, 1170}, {956, 19243}, {960, 17016}, {964, 9534}, {976, 16478}, {978, 1468}, {980, 7772}, {984, 17017}, {986, 11684}, {993, 5313}, {999, 19241}, {1001, 17018}, {1006, 5396}, {1026, 16479}, {1040, 10394}, {1043, 11319}, {1046, 24443}, {1086, 17483}, {1100, 17019}, {1151, 21567}, {1181, 6848}, {1193, 2975}, {1197, 20669}, {1199, 6949}, {1206, 23660}, {1210, 3562}, {1215, 4974}, {1222, 20041}, {1279, 3957}, {1330, 4202}, {1332, 18743}, {1351, 16434}, {1376, 17126}, {1384, 16431}, {1429, 28387}, {1444, 5069}, {1449, 5287}, {1580, 17795}, {1616, 3623}, {1691, 5371}, {1708, 17080}, {1714, 2476}, {1738, 20292}, {1746, 2051}, {1778, 4261}, {1790, 5053}, {1834, 5046}, {1864, 3100}, {1914, 21904}, {1977, 21792}, {1980, 25142}, {1999, 2300}, {2003, 3911}, {2176, 4393}, {2177, 8616}, {2194, 5012}, {2221, 17740}, {2257, 26669}, {2260, 26747}, {2264, 3101}, {2271, 16367}, {2298, 17368}, {2299, 7466}, {2323, 3452}, {2347, 28274}, {2664, 20985}, {2887, 29850}, {2911, 31018}, {3006, 16791}, {3008, 5249}, {3052, 30653}, {3053, 21537}, {3060, 4259}, {3063, 4776}, {3083, 18991}, {3084, 18992}, {3090, 5707}, {3091, 5706}, {3121, 30646}, {3175, 4852}, {3193, 4193}, {3194, 5125}, {3210, 17350}, {3214, 5255}, {3217, 28395}, {3218, 3752}, {3230, 29584}, {3241, 16483}, {3242, 4661}, {3246, 3748}, {3286, 4210}, {3299, 5393}, {3301, 5405}, {3304, 28370}, {3306, 23511}, {3311, 16432}, {3312, 16433}, {3416, 29679}, {3592, 21568}, {3594, 21565}, {3600, 9370}, {3617, 5710}, {3662, 32859}, {3663, 17781}, {3684, 21764}, {3685, 3896}, {3687, 5294}, {3703, 32842}, {3720, 4649}, {3740, 3745}, {3741, 32864}, {3744, 3935}, {3758, 19804}, {3765, 17033}, {3772, 31053}, {3780, 6542}, {3782, 17366}, {3791, 17763}, {3821, 4683}, {3846, 29631}, {3870, 7290}, {3912, 5299}, {3914, 5057}, {3923, 32860}, {3948, 17034}, {3952, 17150}, {3961, 17469}, {3966, 29667}, {3969, 17280}, {3972, 16046}, {3982, 17067}, {3989, 17600}, {3995, 4360}, {3996, 19998}, {4000, 5905}, {4038, 30950}, {4164, 14404}, {4184, 5132}, {4188, 4252}, {4189, 4255}, {4223, 5943}, {4228, 5640}, {4253, 11349}, {4256, 17549}, {4257, 13587}, {4265, 15246}, {4281, 27660}, {4283, 20966}, {4284, 16574}, {4346, 20214}, {4361, 28605}, {4365, 4716}, {4366, 7109}, {4388, 4972}, {4402, 19819}, {4414, 7262}, {4415, 26792}, {4418, 4672}, {4420, 5266}, {4423, 29814}, {4429, 6327}, {4430, 17597}, {4438, 29849}, {4557, 16687}, {4651, 5263}, {4653, 16858}, {4656, 5526}, {4658, 17534}, {4703, 32776}, {4763, 21758}, {4860, 9335}, {4886, 17289}, {4980, 17117}, {5007, 5337}, {5013, 21508}, {5021, 11329}, {5024, 16436}, {5050, 19544}, {5096, 6636}, {5120, 11350}, {5135, 7465}, {5156, 13588}, {5192, 10449}, {5220, 7226}, {5230, 11681}, {5248, 5312}, {5268, 9347}, {5280, 17023}, {5330, 15955}, {5375, 27942}, {5398, 6905}, {5429, 5529}, {5711, 9780}, {5713, 6991}, {5721, 6840}, {5723, 6354}, {5749, 19822}, {5800, 6997}, {6180, 21454}, {6199, 21561}, {6221, 21560}, {6347, 13883}, {6348, 13936}, {6350, 22119}, {6395, 21558}, {6398, 21559}, {6417, 21548}, {6418, 21547}, {6419, 21492}, {6420, 21553}, {6427, 21549}, {6428, 21546}, {6431, 21569}, {6432, 21564}, {6449, 21574}, {6450, 21573}, {6500, 21550}, {6501, 21545}, {6679, 29846}, {6834, 7592}, {6847, 10982}, {6900, 13408}, {6953, 11441}, {6959, 12161}, {6964, 17814}, {6989, 15805}, {7291, 14557}, {7411, 13329}, {7609, 11203}, {7804, 24271}, {8540, 20359}, {8728, 26131}, {9345, 25502}, {9535, 19645}, {9605, 11343}, {10129, 17064}, {11432, 21484}, {11485, 21475}, {11486, 21476}, {12834, 18165}, {13728, 26064}, {14298, 16757}, {14853, 26118}, {15523, 32861}, {15655, 21497}, {16050, 27109}, {16369, 21820}, {16451, 19762}, {16452, 19763}, {16493, 17780}, {16502, 17316}, {16572, 24635}, {16585, 25065}, {16604, 27646}, {16610, 16671}, {16666, 17021}, {16667, 17022}, {16685, 31035}, {16706, 17184}, {16752, 17682}, {16781, 29585}, {16784, 29574}, {16790, 29832}, {16825, 32771}, {16826, 20963}, {16865, 19765}, {16971, 29580}, {17111, 21293}, {17120, 24589}, {17125, 26102}, {17206, 27162}, {17233, 20017}, {17278, 27186}, {17279, 32858}, {17348, 31993}, {17365, 26842}, {17367, 27184}, {17474, 28371}, {17499, 20913}, {17527, 22136}, {17531, 17749}, {17697, 20018}, {17717, 24892}, {17718, 29681}, {17720, 27131}, {17722, 29690}, {17723, 29664}, {17733, 25591}, {17750, 29576}, {17752, 25298}, {17770, 24169}, {17776, 26685}, {17788, 20896}, {17889, 24725}, {18152, 30940}, {18206, 18601}, {19786, 26580}, {19788, 20921}, {20072, 26840}, {20349, 24366}, {20808, 28813}, {21085, 24295}, {21222, 23141}, {21309, 21539}, {21477, 30435}, {21830, 23533}, {22122, 26942}, {22131, 26872}, {22383, 31209}, {23122, 26871}, {23148, 28833}, {23681, 31164}, {24542, 29839}, {24593, 27002}, {24789, 31019}, {25453, 25760}, {25496, 31330}, {25524, 27625}, {25525, 26738}, {25568, 26228}, {25960, 29635}, {26061, 32778}, {26128, 29852}, {26791, 30566}, {27130, 30855}, {29654, 32775}, {29662, 31272}, {29663, 32784}, {29673, 32844}, {29674, 32852}, {29687, 32846}, {29851, 31289}, {30942, 32853}

X(32911) = isotomic conjugate of polar conjugate of X(4222)
X(32911) = trilinear pole of line X(4057)X(4063)
X(32911) = crossdifference of every pair of points on line X(512)X(4895)
X(32911) = antipode of X(81) in conic {{X(13),X(14),X(15),X(16),X(81)}}
X(32911) = ABC-to-excentral barycentric image of X(6057)


X(32912) = X(1)X(2308)∩X(2)X(1757)

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

X(32912) lies on these lines: {1, 2308}, {2, 1757}, {6, 38}, {8, 1046}, {9, 3720}, {10, 4001}, {31, 518}, {42, 63}, {43, 3218}, {44, 354}, {46, 3214}, {55, 896}, {57, 899}, {58, 976}, {69, 15523}, {72, 1468}, {75, 32864}, {81, 984}, {100, 4650}, {141, 26061}, {171, 3681}, {209, 8679}, {210, 750}, {218, 22164}, {226, 24892}, {238, 3873}, {239, 17155}, {244, 4383}, {320, 25957}, {321, 32853}, {329, 11269}, {333, 32771}, {345, 4062}, {386, 6763}, {524, 3703}, {527, 3914}, {537, 3791}, {540, 4680}, {611, 11031}, {612, 5223}, {614, 1743}, {726, 3187}, {752, 5014}, {756, 940}, {758, 4137}, {846, 17018}, {869, 17187}, {894, 31330}, {902, 1707}, {908, 29662}, {958, 2650}, {968, 3929}, {1051, 17013}, {1054, 23958}, {1150, 1215}, {1155, 4849}, {1253, 10391}, {1254, 9370}, {1376, 21805}, {1458, 1708}, {1471, 17625}, {1621, 7262}, {1724, 3874}, {1754, 2801}, {1935, 4332}, {1961, 14996}, {2160, 7241}, {2177, 4640}, {2242, 21839}, {2292, 3927}, {2340, 20588}, {2886, 24725}, {2887, 17771}, {2895, 32778}, {3052, 3722}, {3120, 5905}, {3240, 17596}, {3242, 17469}, {3305, 30950}, {3333, 28352}, {3337, 17749}, {3338, 27627}, {3434, 24695}, {3475, 29689}, {3550, 3935}, {3555, 3915}, {3618, 29684}, {3629, 4884}, {3662, 29850}, {3666, 4663}, {3677, 16670}, {3705, 32843}, {3706, 17351}, {3724, 20760}, {3729, 4365}, {3740, 17124}, {3741, 26223}, {3742, 17125}, {3758, 32772}, {3772, 32856}, {3779, 26892}, {3782, 5852}, {3792, 23155}, {3868, 3924}, {3894, 30117}, {3917, 20683}, {3923, 17135}, {3925, 17365}, {3936, 4438}, {3944, 17484}, {3952, 29649}, {3957, 8616}, {3961, 4661}, {3973, 10582}, {3977, 4028}, {3980, 4651}, {4011, 29824}, {4030, 4831}, {4042, 4363}, {4336, 24430}, {4357, 29647}, {4362, 16704}, {4388, 20072}, {4392, 29821}, {4423, 16885}, {4425, 29829}, {4427, 20011}, {4649, 28606}, {4655, 4972}, {4672, 24552}, {4683, 17347}, {4715, 31134}, {4854, 17334}, {4871, 26688}, {4878, 22053}, {4883, 15254}, {5278, 24325}, {5294, 24943}, {5712, 29682}, {5745, 29678}, {5847, 32854}, {6327, 17770}, {6536, 17257}, {6646, 32776}, {7174, 29816}, {7191, 16468}, {7290, 29818}, {8013, 19822}, {8620, 23543}, {9310, 21874}, {9345, 15481}, {9355, 9812}, {9440, 11020}, {9441, 11220}, {10453, 17350}, {10822, 23154}, {10900, 28253}, {15485, 29817}, {16475, 29819}, {16477, 17598}, {16496, 21747}, {16569, 27003}, {16669, 21342}, {16825, 17140}, {16973, 21764}, {17011, 28650}, {17012, 17591}, {17064, 31164}, {17150, 20068}, {17184, 25453}, {17300, 29854}, {17353, 29677}, {17364, 29641}, {17483, 17889}, {17766, 20064}, {17778, 29643}, {17781, 24210}, {19717, 29644}, {20078, 24248}, {20290, 31079}, {20292, 32865}, {21352, 21384}, {21375, 29311}, {22199, 30647}, {24231, 26723}, {24551, 26699}, {25527, 29867}, {25958, 29861}, {26098, 29690}, {26102, 27065}, {26580, 29635}, {27064, 30942}, {27184, 29631}, {29671, 31034}, {29674, 32863}, {32780, 32782}, {32846, 32862}

X(32912) = anticomplement of X(33064)
X(32912) = {X(42),X(63)}-harmonic conjugate of X(4414)


X(32913) = X(1)X(21)∩X(2)X(1757)

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

X(32913) lies on these lines: {1, 21}, {2, 1757}, {6, 982}, {7, 17889}, {8, 3980}, {9, 24512}, {35, 22060}, {36, 228}, {37, 4038}, {42, 3099}, {43, 57}, {44, 3742}, {55, 3979}, {56, 20760}, {69, 32778}, {75, 8033}, {89, 4661}, {141, 32780}, {150, 7224}, {171, 518}, {209, 3792}, {210, 17122}, {222, 5018}, {238, 354}, {239, 24165}, {244, 4722}, {284, 22099}, {320, 2887}, {333, 24325}, {497, 24695}, {499, 27287}, {524, 32861}, {527, 24210}, {553, 1738}, {580, 12005}, {614, 16468}, {674, 7186}, {726, 1999}, {750, 3681}, {752, 4514}, {875, 18197}, {893, 22199}, {894, 3741}, {899, 27003}, {902, 3957}, {940, 984}, {942, 5247}, {969, 17038}, {978, 3338}, {999, 22149}, {1001, 7262}, {1015, 30646}, {1051, 5256}, {1100, 17600}, {1150, 32771}, {1203, 3953}, {1215, 14829}, {1281, 29840}, {1376, 5524}, {1386, 17598}, {1449, 5332}, {1572, 16557}, {1698, 25961}, {1699, 9355}, {1721, 30304}, {1724, 18398}, {1743, 5272}, {2260, 20785}, {2308, 7191}, {2663, 16574}, {2886, 17365}, {2943, 11531}, {2944, 10476}, {2999, 18193}, {3052, 17715}, {3120, 17483}, {3187, 17155}, {3216, 3337}, {3219, 3720}, {3240, 23958}, {3242, 17716}, {3243, 3749}, {3293, 3336}, {3305, 25502}, {3306, 16569}, {3333, 21214}, {3475, 29675}, {3496, 20963}, {3550, 3870}, {3555, 5255}, {3662, 25453}, {3666, 4649}, {3677, 16475}, {3683, 4883}, {3703, 32846}, {3705, 7779}, {3722, 9340}, {3735, 9346}, {3750, 4640}, {3752, 4663}, {3758, 25496}, {3775, 19808}, {3779, 3784}, {3819, 20683}, {3821, 26840}, {3840, 27064}, {3846, 17771}, {3896, 32845}, {3914, 32857}, {3923, 10453}, {3928, 17594}, {3938, 4430}, {3944, 5905}, {3976, 16466}, {3989, 17019}, {3999, 16477}, {4011, 17350}, {4063, 8027}, {4084, 15955}, {4090, 5205}, {4253, 5364}, {4256, 4973}, {4359, 32864}, {4362, 24349}, {4383, 4860}, {4388, 17770}, {4392, 17017}, {4414, 17018}, {4415, 5852}, {4418, 17135}, {4424, 4880}, {4425, 6646}, {4438, 18134}, {4644, 24333}, {4645, 29673}, {4654, 17064}, {4655, 32773}, {4666, 15485}, {4694, 5315}, {4697, 5263}, {4703, 17347}, {4710, 19811}, {5221, 24440}, {5223, 5268}, {5269, 16496}, {5284, 17450}, {5293, 5904}, {5294, 29637}, {5311, 7226}, {5329, 22769}, {5573, 16670}, {5588, 8945}, {5589, 8941}, {5708, 24174}, {5712, 29657}, {5745, 29640}, {5847, 32866}, {5880, 32865}, {6147, 24161}, {6679, 29860}, {6685, 24627}, {6686, 27002}, {6758, 13174}, {7277, 17722}, {7304, 18827}, {7672, 9316}, {8167, 16885}, {9263, 30661}, {9335, 14997}, {9440, 11018}, {9441, 10167}, {9965, 24248}, {10025, 11019}, {10436, 30966}, {10439, 21375}, {11246, 24715}, {11680, 24725}, {11814, 26791}, {13476, 18165}, {15523, 32863}, {16684, 18174}, {16704, 17140}, {17027, 17738}, {17150, 17154}, {17165, 17763}, {17184, 29631}, {17260, 25501}, {17300, 29653}, {17379, 29644}, {17766, 20101}, {17778, 29671}, {17795, 20456}, {17874, 20879}, {18203, 18207}, {20086, 32842}, {20284, 23543}, {20988, 24436}, {21077, 30007}, {21369, 24727}, {21747, 29818}, {22086, 30704}, {24217, 24703}, {24342, 31330}, {24892, 31019}, {25527, 29856}, {25760, 32859}, {26034, 29659}, {26037, 26627}, {26128, 29859}, {26223, 30942}, {26580, 29845}, {27065, 30950}, {27184, 29635}, {29662, 31053}, {29829, 32776}, {29849, 31034}

X(32913) = {X(1),X(63)}-harmonic conjugate of X(846)


X(32914) = X(1)X(2)∩X(6)X(32771)

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

X(32914) lies on these lines: {1, 2}, {6, 32771}, {31, 75}, {38, 333}, {55, 4361}, {58, 30599}, {63, 17155}, {81, 3791}, {92, 14024}, {171, 4359}, {199, 8301}, {210, 17348}, {226, 32843}, {238, 321}, {244, 14829}, {274, 20985}, {310, 1965}, {312, 748}, {518, 32864}, {536, 3683}, {595, 4647}, {596, 6763}, {726, 3219}, {740, 1621}, {750, 3769}, {752, 20292}, {756, 17277}, {846, 17147}, {894, 2308}, {902, 17117}, {964, 16478}, {968, 3875}, {982, 1150}, {984, 3891}, {1043, 16065}, {1191, 19737}, {1211, 17061}, {1215, 4974}, {1279, 3706}, {1376, 16687}, {1386, 31993}, {1458, 1943}, {1582, 2206}, {1757, 17165}, {1851, 1890}, {1918, 20174}, {1962, 4360}, {2299, 20883}, {2352, 24435}, {2886, 32844}, {2901, 5259}, {3052, 17119}, {3120, 4388}, {3175, 15254}, {3210, 4414}, {3218, 24165}, {3242, 4042}, {3336, 24176}, {3416, 24789}, {3475, 5839}, {3509, 16547}, {3685, 4365}, {3690, 14839}, {3696, 3744}, {3722, 3996}, {3725, 17445}, {3739, 3745}, {3747, 17143}, {3748, 28581}, {3750, 3896}, {3772, 3966}, {3782, 4683}, {3836, 26724}, {3873, 32853}, {3883, 3914}, {3923, 17127}, {3925, 5846}, {3936, 32861}, {3969, 24542}, {3971, 27065}, {3980, 17126}, {4000, 26034}, {4001, 24231}, {4011, 4671}, {4046, 4399}, {4310, 14552}, {4358, 17123}, {4372, 21010}, {4392, 5361}, {4422, 6057}, {4450, 24715}, {4512, 17151}, {4640, 32845}, {4968, 5247}, {5014, 32865}, {5220, 19723}, {5249, 5847}, {5263, 17469}, {5264, 28612}, {5282, 17157}, {5540, 16555}, {5737, 17599}, {5741, 17719}, {5743, 17602}, {6327, 17889}, {6535, 17280}, {6679, 32779}, {7263, 11246}, {7411, 28850}, {9022, 16792}, {15253, 26942}, {15931, 29016}, {16468, 26223}, {16704, 17140}, {16706, 32781}, {17116, 21747}, {17122, 24589}, {17125, 18743}, {17142, 17349}, {17278, 25961}, {17483, 17770}, {17495, 17596}, {17720, 25960}, {18134, 32852}, {18139, 32846}, {19785, 32776}, {19789, 24248}, {19796, 24723}, {20966, 24478}, {21093, 26792}, {21327, 30646}, {21680, 25654}, {21726, 25686}, {26128, 32782}, {32774, 32784}

X(32914) = complement of X(33093)
X(32914) = anticomplement of X(29653)


X(32915) = X(1)X(321)∩X(2)X(740)

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

X(32915) lies on these lines: {1, 321}, {2, 740}, {6, 4037}, {8, 756}, {9, 17156}, {10, 27785}, {11, 29849}, {21, 17733}, {31, 1999}, {37, 3706}, {38, 192}, {42, 312}, {43, 3896}, {45, 4042}, {55, 17763}, {57, 32845}, {69, 4683}, {75, 3720}, {76, 18059}, {81, 3923}, {100, 29649}, {141, 4854}, {145, 3994}, {149, 4865}, {171, 4693}, {210, 28581}, {238, 3187}, {239, 748}, {244, 3210}, {304, 21415}, {306, 24210}, {314, 10458}, {345, 11269}, {350, 561}, {354, 536}, {386, 25591}, {405, 27368}, {497, 3930}, {518, 3175}, {519, 3681}, {537, 4430}, {553, 28557}, {612, 3886}, {614, 3263}, {726, 3873}, {730, 17389}, {846, 1150}, {899, 18743}, {902, 3769}, {908, 4028}, {940, 4418}, {968, 11679}, {982, 17147}, {984, 3995}, {995, 4975}, {1215, 4671}, {1278, 17450}, {1468, 7283}, {1621, 4362}, {1699, 29016}, {1738, 25961}, {1740, 20440}, {1836, 4851}, {1959, 20557}, {1978, 20356}, {2099, 7211}, {2177, 7081}, {2225, 7075}, {2292, 10449}, {2308, 4676}, {2476, 3178}, {2886, 29643}, {2887, 32858}, {2895, 4703}, {3058, 5846}, {3120, 18134}, {3159, 5904}, {3190, 24026}, {3219, 32853}, {3241, 31161}, {3244, 4135}, {3644, 17449}, {3666, 30942}, {3687, 25960}, {3696, 26037}, {3703, 3943}, {3705, 32848}, {3730, 4099}, {3741, 3993}, {3742, 28484}, {3743, 10479}, {3744, 4702}, {3750, 26227}, {3752, 30957}, {3772, 29632}, {3773, 29667}, {3782, 4966}, {3791, 4432}, {3797, 17027}, {3840, 4850}, {3846, 25378}, {3907, 4931}, {3912, 3914}, {3917, 6007}, {3925, 17243}, {3936, 3944}, {3950, 4847}, {3952, 20011}, {3966, 17299}, {3969, 32778}, {3989, 4664}, {4009, 4849}, {4046, 5743}, {4062, 4417}, {4078, 25006}, {4085, 29679}, {4193, 17748}, {4359, 26102}, {4360, 17017}, {4361, 4423}, {4388, 6542}, {4414, 14829}, {4425, 32782}, {4427, 4650}, {4429, 29687}, {4438, 32849}, {4442, 17889}, {4514, 32854}, {4649, 26223}, {4651, 31035}, {4655, 32863}, {4673, 10459}, {4679, 14459}, {4687, 22316}, {4697, 14996}, {4706, 16602}, {4716, 17123}, {4718, 21342}, {4722, 17350}, {4972, 29674}, {5014, 32847}, {5224, 6536}, {5263, 5311}, {5283, 21820}, {5284, 16825}, {5295, 6051}, {6327, 32846}, {6535, 29685}, {6541, 29673}, {7262, 16704}, {9812, 28850}, {10439, 29069}, {10582, 17151}, {11246, 28530}, {11680, 29671}, {13244, 13478}, {13746, 17188}, {14210, 21416}, {15523, 17233}, {15569, 31993}, {15571, 16678}, {16552, 24049}, {16706, 29677}, {17011, 25496}, {17061, 29638}, {17063, 17495}, {17144, 21352}, {17145, 20068}, {17162, 19742}, {17187, 24696}, {17242, 29641}, {17279, 29850}, {17280, 26061}, {17289, 29647}, {17310, 31134}, {17318, 17599}, {17380, 29684}, {17490, 30947}, {17591, 31137}, {17602, 29848}, {17715, 20045}, {17720, 29846}, {17778, 24725}, {17871, 20171}, {17874, 20236}, {19582, 20018}, {19649, 24257}, {19786, 24943}, {19791, 30969}, {19804, 30950}, {19874, 31327}, {20012, 21805}, {20017, 32861}, {20363, 21877}, {21096, 25087}, {21242, 29664}, {21806, 31264}, {24165, 28522}, {24217, 32855}, {24325, 28605}, {24551, 26665}, {24589, 25502}, {24620, 26103}, {24703, 32843}, {24789, 29851}, {25783, 25856}, {25785, 25853}, {26034, 34255}, {27636, 29982}, {28361, 30090}, {29631, 32777}, {29635, 32779}, {29637, 32774}, {29662, 32851}, {29829, 32780}


X(32916) = X(1)X(3769)∩X(2)X(31)

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

X(32916) lies on these lines: {1, 3769}, {2, 31}, {3, 10}, {6, 6685}, {8, 19278}, {9, 1755}, {35, 10479}, {37, 29649}, {38, 26227}, {42, 1150}, {43, 333}, {55, 3741}, {57, 24325}, {63, 1215}, {75, 17596}, {100, 31330}, {141, 3771}, {165, 18229}, {183, 4357}, {226, 4655}, {312, 846}, {321, 4414}, {332, 17270}, {345, 3773}, {354, 29651}, {404, 31339}, {405, 3831}, {511, 9564}, {516, 2050}, {518, 29670}, {519, 5774}, {612, 4434}, {740, 11679}, {894, 4650}, {896, 26223}, {899, 5278}, {902, 24552}, {908, 4703}, {966, 2267}, {982, 3757}, {984, 7081}, {1001, 3840}, {1010, 1698}, {1054, 19804}, {1125, 1191}, {1155, 3980}, {1211, 5432}, {1279, 29668}, {1329, 15973}, {1386, 29650}, {1460, 3911}, {1468, 26115}, {1486, 24736}, {1621, 30942}, {1707, 4672}, {1740, 16569}, {1836, 25385}, {1999, 17592}, {2049, 3634}, {2177, 17135}, {2209, 16738}, {2305, 17303}, {2321, 31477}, {2886, 4660}, {2999, 4974}, {3011, 26128}, {3035, 5150}, {3072, 26363}, {3210, 17593}, {3218, 32771}, {3240, 5361}, {3305, 24003}, {3416, 29671}, {3434, 21242}, {3550, 5263}, {3666, 4362}, {3683, 4011}, {3706, 4689}, {3742, 24331}, {3744, 29652}, {3745, 29644}, {3750, 10453}, {3752, 16825}, {3772, 3821}, {3775, 5218}, {3791, 5256}, {3828, 19276}, {3842, 5268}, {3878, 31778}, {3883, 24239}, {3923, 4640}, {3931, 17733}, {3936, 29678}, {3944, 24723}, {3974, 4439}, {4026, 29635}, {4042, 4685}, {4090, 5220}, {4104, 6745}, {4135, 17262}, {4413, 11358}, {4423, 4871}, {4425, 17720}, {4432, 4512}, {4514, 29676}, {4643, 25353}, {4657, 29645}, {4683, 31053}, {4716, 4734}, {4865, 29639}, {4892, 31266}, {4972, 24892}, {5014, 29690}, {5110, 17275}, {5235, 13588}, {5264, 19863}, {5284, 30957}, {5287, 10180}, {5372, 17018}, {5783, 20103}, {5814, 17748}, {6376, 6626}, {7262, 27064}, {8616, 29827}, {8852, 32777}, {9364, 27339}, {9565, 15489}, {10448, 16347}, {11285, 29991}, {16817, 24174}, {16823, 17063}, {16824, 24440}, {16999, 17248}, {17595, 24165}, {17676, 21935}, {17719, 27184}, {17763, 28606}, {18134, 29640}, {18139, 29661}, {19786, 29658}, {21240, 25500}, {21241, 31245}, {21264, 24260}, {24169, 24789}, {24542, 29677}, {25531, 31242}, {26061, 26251}, {26064, 27529}, {28595, 29857}, {28605, 32845}, {29665, 32775}, {29679, 31073}, {29680, 32844}, {29846, 32782}, {29861, 30608}, {29867, 31229}, {32778, 32851}


X(32917) = X(1)X(1150)∩X(2)X(31)

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

X(32917) lies on these lines: {1, 1150}, {2, 31}, {3, 31339}, {8, 2177}, {9, 2225}, {10, 21}, {37, 17763}, {38, 3757}, {42, 333}, {43, 5278}, {51, 9564}, {55, 5737}, {63, 32771}, {75, 4414}, {141, 16792}, {149, 21242}, {165, 19645}, {226, 4683}, {244, 16823}, {261, 7122}, {319, 4062}, {321, 846}, {594, 3712}, {595, 19863}, {756, 7081}, {799, 1909}, {894, 896}, {899, 2309}, {902, 5263}, {958, 28348}, {964, 1698}, {966, 2268}, {968, 11679}, {984, 26227}, {993, 4216}, {1001, 30942}, {1011, 1376}, {1054, 24589}, {1125, 5315}, {1155, 3739}, {1193, 19270}, {1211, 6690}, {1213, 2240}, {1215, 3219}, {1430, 17913}, {1441, 1758}, {1460, 16352}, {1582, 5161}, {1621, 3741}, {1918, 27164}, {1962, 1999}, {2298, 5257}, {2330, 15985}, {2550, 30943}, {3011, 4357}, {3035, 5241}, {3120, 24723}, {3187, 17592}, {3218, 24325}, {3416, 29643}, {3570, 17256}, {3616, 9345}, {3681, 29670}, {3696, 4689}, {3720, 14829}, {3745, 16445}, {3750, 17135}, {3769, 5311}, {3771, 32782}, {3772, 32776}, {3773, 32849}, {3791, 17011}, {3831, 5047}, {3840, 5284}, {3842, 4434}, {3873, 29651}, {3883, 29639}, {3931, 27368}, {3936, 29640}, {3961, 4981}, {3966, 29849}, {3994, 17261}, {4009, 16814}, {4023, 17330}, {4026, 29631}, {4195, 9780}, {4224, 5285}, {4359, 17596}, {4362, 28606}, {4364, 4396}, {4413, 16405}, {4417, 29678}, {4418, 4640}, {4423, 30957}, {4427, 31025}, {4438, 29667}, {4512, 18229}, {4514, 29690}, {4598, 23493}, {4642, 16824}, {4643, 17718}, {4649, 16704}, {4655, 31019}, {4657, 29636}, {4669, 4954}, {4703, 31053}, {4781, 27812}, {4831, 7277}, {4850, 16825}, {4865, 29664}, {4933, 29615}, {4974, 17012}, {5057, 25385}, {5205, 17260}, {5230, 13725}, {5247, 10457}, {5248, 10479}, {5264, 19858}, {5271, 17594}, {5273, 5772}, {5361, 17018}, {5372, 29814}, {5432, 5743}, {5705, 27378}, {5718, 32843}, {6536, 29683}, {6646, 32856}, {6649, 17095}, {6682, 7191}, {7262, 26223}, {7270, 21674}, {7290, 29826}, {8616, 24552}, {9316, 27339}, {9332, 26860}, {9350, 26038}, {9364, 17077}, {9458, 16482}, {10180, 17019}, {10434, 13478}, {13733, 26066}, {14012, 19808}, {14459, 17362}, {15254, 30818}, {15485, 29827}, {16452, 25440}, {16466, 19273}, {16468, 29825}, {16484, 29824}, {16796, 29638}, {16817, 24443}, {16997, 17248}, {17150, 17600}, {17306, 29855}, {17495, 17593}, {17588, 17751}, {17719, 24697}, {17958, 27823}, {18134, 29661}, {18165, 22275}, {19843, 26091}, {21935, 26117}, {24169, 26724}, {24542, 29637}, {24678, 27958}, {24892, 32773}, {26128, 29681}, {27064, 31264}, {28595, 29873}, {29856, 31229}

X(32917) = complement of X(33112)


X(32918) = X(2)X(31)∩X(10)X(36)

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

X(32918) lies on these lines: {2, 31}, {10, 36}, {21, 3831}, {38, 7081}, {42, 14829}, {43, 1150}, {55, 30942}, {57, 29828}, {81, 6685}, {100, 3741}, {141, 2330}, {244, 3757}, {312, 4414}, {321, 17596}, {333, 899}, {474, 31339}, {595, 19864}, {672, 26244}, {756, 5205}, {846, 4358}, {894, 31264}, {896, 27064}, {908, 4683}, {968, 30567}, {982, 26227}, {1001, 30957}, {1054, 4359}, {1155, 4418}, {1203, 20108}, {1211, 3035}, {1215, 3218}, {1376, 4191}, {1621, 3840}, {1698, 16454}, {2177, 10453}, {3240, 5372}, {3416, 29849}, {3550, 24552}, {3634, 14005}, {3666, 17763}, {3740, 9458}, {3750, 29824}, {3769, 17017}, {3791, 17012}, {3873, 29670}, {3891, 17591}, {3917, 9564}, {3920, 4434}, {3980, 9352}, {3996, 31136}, {4026, 29845}, {4038, 29822}, {4201, 21935}, {4362, 4850}, {4396, 25349}, {4413, 5737}, {4429, 24892}, {4438, 29679}, {4640, 30818}, {4650, 26223}, {4655, 31053}, {4657, 29847}, {4660, 11680}, {4695, 16821}, {4703, 27131}, {4865, 29680}, {4871, 5284}, {4974, 17020}, {5014, 29676}, {5204, 5793}, {5235, 9342}, {5247, 26030}, {5263, 31241}, {5269, 29826}, {5278, 16569}, {6690, 29632}, {9347, 29644}, {10180, 17021}, {10448, 19278}, {10479, 16451}, {11679, 32860}, {12514, 25591}, {15485, 31242}, {15523, 32851}, {16823, 27002}, {17140, 18201}, {17147, 17593}, {17155, 17595}, {17184, 17719}, {17234, 29661}, {17277, 22343}, {17283, 29869}, {17598, 20045}, {17720, 32776}, {18134, 29678}, {18139, 29640}, {19684, 29825}, {19786, 29683}, {20292, 25385}, {24003, 27065}, {24239, 32844}, {24325, 27003}, {26128, 29665}, {26251, 32780}, {26840, 32856}, {28595, 29872}, {28606, 29649}, {29658, 32774}, {29662, 32773}, {29690, 32850}

X(32918) = complement of X(33107)


X(32919) = X(1)X(1150)∩X(2)X(3775)

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

X(32919) lies on these lines: {1, 1150}, {2, 3775}, {6, 30942}, {8, 750}, {10, 16474}, {11, 524}, {31, 10453}, {36, 100}, {38, 1999}, {42, 14829}, {57, 17156}, {69, 11269}, {81, 3741}, {86, 30970}, {141, 29631}, {145, 2177}, {149, 752}, {171, 17135}, {238, 16704}, {239, 244}, {320, 3120}, {333, 3720}, {350, 799}, {518, 17763}, {540, 3583}, {740, 3218}, {896, 3685}, {940, 31330}, {942, 27368}, {982, 3187}, {1046, 3702}, {1054, 24593}, {1125, 5235}, {1155, 28581}, {1211, 29845}, {1449, 29826}, {1468, 10449}, {1647, 3570}, {1757, 4358}, {1961, 4981}, {2225, 24727}, {2887, 32863}, {2895, 3846}, {2901, 6763}, {3006, 32846}, {3011, 4684}, {3416, 16797}, {3681, 29649}, {3683, 4891}, {3705, 32852}, {3706, 4418}, {3756, 4969}, {3769, 3938}, {3791, 7191}, {3842, 17021}, {3868, 17733}, {3873, 4362}, {3879, 29639}, {3896, 17596}, {3935, 4434}, {3937, 6007}, {3944, 32859}, {4001, 4683}, {4003, 4852}, {4042, 26037}, {4062, 32851}, {4361, 4860}, {4383, 30957}, {4417, 29662}, {4427, 4693}, {4438, 32858}, {4442, 32857}, {4519, 17351}, {4651, 17122}, {4658, 19863}, {4663, 30818}, {4716, 17162}, {4722, 27064}, {4753, 24003}, {4851, 29643}, {4921, 5284}, {4956, 28558}, {4966, 29632}, {4974, 7292}, {5057, 17770}, {5137, 5846}, {5205, 21805}, {5263, 31136}, {5278, 26102}, {5361, 29814}, {5372, 17018}, {5536, 29016}, {5739, 25960}, {5847, 26015}, {6542, 32848}, {6682, 17011}, {8167, 19723}, {10439, 13478}, {11679, 32771}, {16468, 31137}, {16823, 17450}, {16997, 17363}, {17026, 31005}, {17123, 19742}, {17125, 17349}, {17145, 20045}, {17150, 17598}, {17187, 29766}, {17277, 30950}, {17296, 29857}, {17364, 24725}, {17484, 17771}, {17717, 31034}, {17772, 32842}, {17777, 20072}, {17874, 20882}, {18134, 24892}, {18141, 25961}, {20017, 32855}, {20036, 32577}, {20142, 30967}, {24217, 31303}, {24239, 26243}, {25741, 25804}, {28650, 29827}, {29635, 32782}, {29829, 32784}, {29858, 31229}, {30941, 30969}


X(32920) = X(1)X(312)∩X(2)X(17598)

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

X(32920) lies on these lines: {1, 312}, {2, 17598}, {6, 21101}, {8, 2887}, {10, 24789}, {11, 29844}, {31, 17165}, {37, 29651}, {38, 26227}, {42, 3891}, {43, 30982}, {55, 726}, {56, 8669}, {57, 4434}, {63, 537}, {75, 3961}, {100, 17155}, {145, 26098}, {171, 24349}, {190, 8616}, {192, 3750}, {210, 16825}, {226, 519}, {321, 3938}, {335, 24586}, {354, 29649}, {518, 4362}, {536, 24333}, {596, 25440}, {612, 24325}, {668, 18067}, {740, 3870}, {748, 3952}, {750, 17140}, {752, 5905}, {894, 17716}, {976, 4968}, {982, 7081}, {984, 3757}, {1001, 3971}, {1279, 3967}, {1376, 24165}, {1836, 17766}, {1909, 3905}, {1920, 7033}, {2177, 17147}, {2209, 17142}, {2241, 22036}, {2886, 9053}, {3011, 4438}, {3120, 5014}, {3175, 3748}, {3242, 3741}, {3305, 4096}, {3315, 30957}, {3434, 17765}, {3507, 20917}, {3555, 17733}, {3625, 4138}, {3632, 4892}, {3666, 29670}, {3679, 25527}, {3685, 17715}, {3699, 16569}, {3701, 28082}, {3703, 3771}, {3705, 17719}, {3710, 28027}, {3729, 3749}, {3744, 3923}, {3751, 3791}, {3772, 29673}, {3782, 4030}, {3836, 10327}, {3840, 17597}, {3873, 17763}, {3883, 4703}, {3920, 32771}, {3924, 4696}, {3932, 29642}, {3935, 32860}, {3936, 32854}, {3944, 4514}, {4026, 29669}, {4071, 17299}, {4085, 19785}, {4090, 4383}, {4135, 4387}, {4310, 7172}, {4360, 4479}, {4361, 4685}, {4417, 32866}, {4428, 17262}, {4439, 17776}, {4640, 28582}, {4645, 20056}, {4661, 32864}, {4697, 5269}, {4702, 22034}, {4716, 20012}, {4884, 6690}, {4891, 15570}, {5205, 17063}, {5217, 8720}, {5248, 24068}, {5272, 24003}, {5423, 16020}, {5730, 20498}, {6327, 32856}, {6679, 26228}, {6682, 29828}, {6685, 17599}, {9350, 17780}, {11679, 16496}, {14829, 24841}, {17026, 32029}, {17061, 25453}, {17123, 27538}, {17135, 30953}, {17144, 21590}, {17279, 29672}, {17469, 26223}, {17602, 29635}, {17717, 29840}, {17718, 29671}, {17720, 29655}, {17764, 20075}, {17889, 32850}, {18134, 32847}, {18743, 29820}, {19684, 29816}, {19786, 29659}, {20876, 23853}, {21093, 24703}, {26061, 26230}, {28599, 31134}, {29632, 32862}, {29634, 32780}, {29656, 32777}, {29667, 32775}, {29668, 30818}, {29815, 32772}, {29848, 32779}, {31053, 32844}, {31079, 31237}


X(32921) = X(1)X(75)∩X(2)X(3773)

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

X(32921) lies on these lines: {1, 75}, {2, 3773}, {6, 726}, {8, 3775}, {9, 4974}, {10, 3946}, {31, 4427}, {37, 16825}, {38, 3187}, {42, 3891}, {43, 3699}, {55, 4970}, {63, 3791}, {69, 17772}, {81, 17155}, {145, 4310}, {171, 3210}, {190, 16468}, {192, 238}, {193, 17771}, {239, 984}, {291, 17027}, {306, 19834}, {312, 29821}, {321, 17017}, {344, 31289}, {345, 6679}, {386, 12263}, {517, 24257}, {518, 4523}, {519, 599}, {523, 24286}, {536, 1386}, {537, 3751}, {551, 4133}, {596, 2214}, {664, 4334}, {712, 10800}, {748, 3995}, {750, 17495}, {752, 24248}, {940, 24165}, {982, 1999}, {990, 28850}, {995, 17790}, {1001, 3993}, {1125, 2321}, {1215, 5256}, {1468, 17148}, {1471, 4552}, {1698, 17400}, {1757, 3759}, {1961, 19804}, {2177, 20045}, {2276, 17031}, {2325, 4989}, {2887, 19785}, {3008, 4078}, {3175, 4011}, {3216, 18046}, {3244, 4780}, {3262, 23689}, {3293, 29764}, {3570, 24427}, {3589, 28472}, {3616, 4527}, {3624, 4535}, {3629, 5852}, {3644, 4676}, {3662, 32846}, {3663, 4655}, {3666, 4362}, {3679, 17399}, {3703, 25453}, {3706, 29652}, {3729, 4672}, {3741, 17599}, {3745, 3980}, {3752, 29649}, {3757, 17592}, {3769, 17596}, {3771, 17061}, {3772, 29671}, {3790, 17367}, {3826, 4395}, {3836, 4000}, {3842, 4384}, {3844, 17382}, {3873, 6742}, {3879, 24231}, {3892, 24394}, {3896, 3938}, {3914, 4865}, {3920, 32860}, {3932, 17366}, {3966, 4425}, {3969, 24943}, {3971, 4383}, {3989, 5278}, {4026, 17395}, {4065, 4068}, {4252, 8720}, {4255, 8669}, {4260, 14839}, {4283, 12782}, {4307, 4452}, {4359, 5311}, {4365, 24552}, {4393, 4649}, {4398, 32857}, {4429, 32847}, {4432, 7290}, {4439, 5222}, {4464, 4684}, {4483, 4658}, {4660, 5846}, {4663, 28582}, {4671, 17025}, {4681, 15254}, {4753, 5223}, {4850, 17763}, {4856, 5850}, {4891, 4906}, {4966, 17388}, {4972, 32854}, {5145, 18170}, {5211, 24217}, {5248, 16684}, {5695, 28522}, {6535, 29684}, {6541, 17279}, {6682, 11679}, {7226, 32864}, {7283, 16478}, {10453, 17598}, {12699, 29040}, {12721, 24268}, {14829, 17591}, {15523, 32774}, {15569, 24331}, {16476, 25264}, {16477, 17350}, {16706, 29674}, {16823, 17319}, {16826, 27474}, {16830, 17117}, {17011, 32771}, {17122, 17490}, {17125, 31035}, {17126, 32845}, {17184, 32852}, {17230, 26150}, {17233, 29637}, {17247, 24697}, {17276, 17770}, {17281, 24295}, {17289, 29646}, {17292, 25539}, {17351, 28555}, {17380, 29633}, {17390, 25557}, {17723, 25385}, {17767, 24695}, {17889, 19796}, {19786, 32778}, {20131, 27478}, {20142, 27481}, {20990, 25440}, {24280, 28542}, {24524, 24731}, {24789, 29653}, {24883, 25471}, {25760, 32842}, {26098, 30699}, {26724, 29854}, {27184, 32861}, {27787, 27788}, {28605, 32772}, {29584, 31178}, {29636, 32779}, {29644, 31993}, {29654, 32777}, {29658, 32851}, {29850, 32862}, {31034, 32856}, {32773, 32866}


X(32922) = X(1)X(75)∩X(2)X(1390)

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

X(32922) lies on these lines: {1, 75}, {2, 1390}, {6, 24349}, {8, 141}, {10, 10159}, {11, 5211}, {19, 31903}, {21, 16684}, {29, 20883}, {31, 17155}, {37, 16823}, {38, 333}, {43, 30982}, {44, 28582}, {55, 3210}, {57, 3769}, {58, 82}, {69, 4310}, {81, 17140}, {85, 4327}, {100, 17495}, {145, 2550}, {149, 4442}, {171, 24165}, {190, 238}, {192, 1001}, {239, 335}, {244, 17763}, {291, 17031}, {310, 3112}, {312, 614}, {320, 5847}, {321, 7191}, {341, 1722}, {344, 16020}, {354, 1999}, {385, 8301}, {390, 4452}, {404, 20990}, {497, 30699}, {511, 25048}, {516, 1266}, {519, 1738}, {523, 1325}, {536, 1279}, {537, 1757}, {612, 19804}, {664, 1458}, {752, 903}, {894, 1386}, {899, 3699}, {902, 32845}, {958, 19851}, {982, 4362}, {984, 16825}, {1054, 4434}, {1086, 4645}, {1089, 13741}, {1125, 6541}, {1150, 4392}, {1201, 17787}, {1215, 29821}, {1220, 4968}, {1222, 7194}, {1268, 19856}, {1278, 5695}, {1376, 17490}, {1463, 9025}, {1621, 17147}, {1698, 17370}, {1861, 1897}, {1943, 17625}, {2099, 20037}, {2238, 17794}, {2345, 3616}, {2886, 29840}, {2887, 32866}, {2975, 11683}, {3008, 3717}, {3011, 32851}, {3100, 14942}, {3120, 32844}, {3187, 3873}, {3216, 29447}, {3241, 17392}, {3246, 28555}, {3293, 29756}, {3315, 29824}, {3416, 3662}, {3434, 19789}, {3624, 17371}, {3663, 3883}, {3666, 3757}, {3677, 11679}, {3689, 4706}, {3696, 17117}, {3705, 3772}, {3729, 4676}, {3739, 16830}, {3741, 17598}, {3750, 4970}, {3751, 3759}, {3752, 7081}, {3758, 16475}, {3763, 26150}, {3771, 32855}, {3773, 17285}, {3775, 32025}, {3782, 4388}, {3790, 17279}, {3836, 17769}, {3844, 17291}, {3879, 5542}, {3896, 3957}, {3911, 14594}, {3914, 4514}, {3920, 4359}, {3936, 32842}, {3938, 3996}, {3966, 27184}, {3971, 17123}, {3976, 17733}, {3980, 17716}, {3993, 16484}, {3995, 5284}, {4003, 24627}, {4026, 17302}, {4078, 17263}, {4321, 9312}, {4344, 31995}, {4353, 4357}, {4358, 7292}, {4365, 29818}, {4384, 7174}, {4393, 20132}, {4396, 26273}, {4398, 24248}, {4413, 24620}, {4418, 17469}, {4432, 28516}, {4439, 31289}, {4440, 17768}, {4552, 7677}, {4649, 20179}, {4663, 17121}, {4680, 17678}, {4693, 28522}, {4702, 28484}, {4850, 26227}, {4864, 28581}, {4865, 17889}, {4966, 6542}, {4967, 19868}, {5015, 23537}, {5205, 16610}, {5218, 26245}, {5220, 17349}, {5272, 18743}, {5278, 7226}, {5297, 24589}, {5573, 30567}, {5686, 24599}, {5819, 15590}, {5852, 20072}, {6762, 24529}, {7270, 23536}, {7813, 19942}, {8299, 17759}, {8692, 25269}, {8849, 16693}, {9347, 26627}, {9791, 17246}, {10453, 17597}, {11246, 20101}, {12513, 17480}, {12635, 20036}, {13588, 16687}, {15254, 17261}, {15310, 24813}, {15569, 17319}, {15601, 25728}, {16061, 30168}, {16704, 17154}, {17017, 32771}, {17024, 24552}, {17063, 29649}, {17135, 24643}, {17142, 27644}, {17145, 17162}, {17283, 29674}, {17305, 32784}, {17446, 24437}, {17475, 21788}, {17592, 29651}, {17722, 25385}, {17740, 26228}, {17766, 24715}, {19742, 20068}, {19785, 32773}, {20162, 27480}, {21010, 24621}, {21554, 31395}, {23051, 31359}, {23693, 24847}, {24542, 32849}, {24692, 28512}, {24789, 29641}, {24923, 29559}, {25957, 32854}, {26061, 29852}, {26128, 32778}, {26230, 32779}, {28612, 30145}, {29632, 32848}, {29654, 32780}, {29667, 32774}, {29819, 32772}, {29823, 31025}, {30115, 30892}, {30832, 32775}, {32843, 32856}


X(32923) = X(1)X(321)∩X(2)X(17598)

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

X(32923) lies on these lines: {1, 321}, {2, 17598}, {8, 25957}, {10, 26724}, {31, 24349}, {35, 596}, {38, 3757}, {43, 31005}, {55, 17155}, {75, 3938}, {86, 29816}, {100, 24165}, {171, 17140}, {226, 32844}, {238, 17165}, {244, 7081}, {291, 26237}, {333, 24841}, {354, 17763}, {518, 32864}, {519, 5249}, {536, 3748}, {537, 3219}, {551, 1255}, {726, 1621}, {740, 3957}, {752, 17483}, {756, 16823}, {894, 17469}, {982, 26227}, {1086, 4030}, {1215, 7191}, {1280, 4847}, {1909, 3112}, {2177, 3210}, {3120, 4514}, {3242, 31330}, {3243, 17156}, {3315, 3840}, {3555, 27368}, {3677, 29828}, {3681, 16825}, {3683, 28582}, {3703, 29632}, {3706, 4864}, {3744, 4418}, {3750, 17147}, {3870, 32860}, {3873, 4362}, {3883, 4683}, {3889, 17733}, {3896, 3979}, {3920, 24325}, {3925, 9053}, {3932, 29851}, {3936, 32866}, {3952, 17123}, {3961, 4359}, {3971, 5284}, {3995, 16484}, {4075, 25542}, {4126, 17337}, {4310, 26034}, {4358, 29820}, {4361, 30949}, {4385, 28082}, {4388, 32856}, {4430, 32853}, {4434, 27003}, {4438, 29681}, {4450, 32857}, {4649, 17150}, {4692, 30117}, {4716, 20011}, {4850, 29670}, {4865, 31019}, {4906, 30818}, {5014, 17889}, {5253, 8669}, {5259, 24068}, {5271, 16496}, {5299, 18098}, {5322, 24180}, {9350, 24620}, {9458, 16602}, {10327, 25961}, {11680, 29844}, {14829, 17449}, {17024, 25496}, {17061, 29631}, {17125, 27538}, {17135, 30969}, {17143, 21415}, {17278, 30615}, {17279, 29853}, {17289, 29686}, {17597, 30942}, {17600, 29822}, {17602, 29845}, {17716, 31178}, {17718, 29849}, {17724, 29846}, {17766, 20292}, {18134, 32854}, {18139, 32847}, {19786, 29685}, {19993, 26098}, {24592, 32029}, {24631, 26247}, {26128, 29667}, {26230, 32780}, {27064, 31161}, {28606, 29651}, {29638, 32777}, {29642, 32862}, {29656, 32779}, {29659, 32774}, {29839, 32848}


X(32924) = X(1)X(3896)∩X(2)X(3773)

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

X(32924) lies on these lines: {1, 3896}, {2, 3773}, {6, 17155}, {8, 32781}, {31, 3210}, {38, 239}, {43, 3891}, {75, 17017}, {81, 24165}, {171, 17150}, {192, 748}, {238, 17147}, {244, 1999}, {321, 29821}, {354, 4852}, {519, 24169}, {614, 3263}, {740, 7191}, {750, 17490}, {982, 3187}, {1150, 17591}, {1193, 19810}, {1215, 17012}, {1255, 25501}, {1386, 4418}, {1621, 4970}, {1961, 24589}, {1962, 16823}, {2177, 4734}, {2887, 32842}, {3120, 19796}, {3218, 3791}, {3219, 4974}, {3662, 32852}, {3663, 4683}, {3677, 17156}, {3687, 32775}, {3703, 17366}, {3720, 4360}, {3752, 17763}, {3772, 29849}, {3782, 32843}, {3795, 26238}, {3914, 24212}, {3925, 4395}, {3966, 17301}, {3969, 29637}, {3989, 17277}, {3993, 5284}, {3995, 17123}, {4000, 25957}, {4310, 20043}, {4361, 17599}, {4362, 4850}, {4365, 17160}, {4392, 32853}, {4423, 17318}, {4429, 32854}, {4649, 17140}, {4716, 17135}, {4722, 17121}, {4972, 32866}, {5256, 32771}, {5263, 29819}, {5311, 19804}, {6057, 28472}, {6536, 17320}, {8720, 16948}, {10448, 19851}, {10458, 21352}, {15523, 16706}, {16484, 27804}, {16825, 28606}, {17011, 24325}, {17025, 25496}, {17061, 29846}, {17117, 21020}, {17124, 24620}, {17163, 29823}, {17184, 32861}, {17187, 18170}, {17233, 29677}, {17278, 29854}, {17289, 29684}, {17367, 26061}, {17380, 29647}, {17772, 32863}, {19785, 25760}, {19789, 26098}, {24789, 29643}, {26724, 29653}, {29654, 32779}, {29832, 32865}, {29852, 32777}, {32774, 32778}


X(32925) = X(1)X(3159)∩X(2)X(726)

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

X(32925) lies on these lines: {1, 3159}, {2, 726}, {8, 4365}, {10, 28605}, {11, 4884}, {31, 190}, {37, 17157}, {38, 312}, {42, 192}, {43, 3952}, {51, 14839}, {55, 17262}, {63, 17763}, {75, 756}, {141, 6057}, {194, 3009}, {210, 536}, {226, 29643}, {238, 3891}, {244, 18743}, {321, 984}, {329, 32843}, {341, 4642}, {344, 29851}, {345, 29846}, {354, 28582}, {518, 3175}, {519, 3899}, {522, 3158}, {537, 3873}, {545, 11246}, {596, 3624}, {612, 3729}, {614, 30568}, {649, 16557}, {698, 19586}, {700, 24574}, {714, 1962}, {740, 3681}, {846, 26227}, {869, 25264}, {894, 5311}, {896, 3769}, {899, 3210}, {902, 25269}, {908, 29849}, {976, 7283}, {982, 4358}, {986, 3701}, {1086, 25961}, {1201, 19582}, {1215, 28606}, {1376, 32845}, {1698, 4075}, {1707, 25734}, {1757, 3187}, {1897, 1957}, {1978, 8026}, {2292, 4385}, {2308, 17350}, {2325, 29638}, {2887, 4439}, {2901, 5904}, {3006, 3944}, {3058, 9053}, {3120, 29641}, {3218, 29649}, {3219, 4362}, {3240, 4090}, {3242, 4387}, {3247, 24067}, {3416, 4683}, {3550, 4427}, {3644, 21805}, {3661, 6535}, {3662, 29687}, {3663, 4082}, {3666, 3967}, {3679, 17163}, {3685, 3938}, {3703, 4415}, {3706, 22034}, {3710, 13161}, {3715, 4361}, {3717, 3914}, {3720, 24349}, {3740, 28555}, {3741, 4135}, {3745, 17351}, {3752, 4009}, {3757, 17261}, {3771, 32849}, {3773, 32782}, {3782, 3932}, {3790, 15523}, {3821, 29679}, {3840, 4392}, {3920, 3923}, {3948, 12782}, {3974, 4419}, {3980, 5297}, {3985, 26242}, {3993, 17018}, {4011, 7191}, {4066, 10479}, {4078, 5249}, {4096, 28516}, {4151, 27806}, {4188, 8720}, {4189, 8669}, {4388, 32854}, {4389, 32781}, {4414, 7081}, {4417, 32848}, {4425, 29667}, {4442, 32865}, {4659, 7322}, {4676, 17469}, {4685, 28522}, {4697, 9347}, {4712, 20173}, {4718, 4849}, {4865, 5057}, {4918, 12607}, {4942, 32772}, {5220, 32864}, {5223, 17156}, {5283, 22036}, {5294, 29636}, {5300, 24851}, {5741, 32855}, {5847, 17781}, {6327, 32847}, {6534, 25055}, {6541, 32858}, {7248, 24816}, {8616, 20045}, {9316, 14594}, {10327, 24248}, {10453, 31302}, {16468, 17150}, {16569, 17495}, {16825, 27065}, {17017, 27064}, {17140, 26102}, {17184, 29674}, {17280, 24943}, {17302, 29663}, {17304, 31077}, {17353, 29852}, {17459, 21884}, {17752, 25270}, {17776, 29632}, {17777, 29840}, {18134, 32856}, {19785, 29850}, {19786, 26061}, {20068, 29824}, {20681, 32453}, {20688, 22199}, {20703, 29966}, {20889, 21615}, {21093, 29671}, {24080, 27020}, {24295, 29648}, {24703, 32844}, {25385, 29664}, {26580, 32778}, {26792, 32842}, {27549, 30699}, {28593, 30596}, {29653, 31019}, {32775, 32777}, {32846, 32859}


X(32926) = X(1)X(312)∩X(2)X(1390)

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

X(32926) lies on these lines: {1, 312}, {2, 1390}, {8, 1211}, {10, 19786}, {11, 29840}, {31, 190}, {33, 92}, {37, 3757}, {38, 14829}, {42, 308}, {43, 3699}, {51, 25048}, {55, 192}, {57, 14594}, {58, 24068}, {63, 3769}, {75, 612}, {81, 17165}, {86, 5311}, {100, 17147}, {145, 497}, {171, 726}, {181, 14839}, {194, 21010}, {200, 3875}, {210, 239}, {238, 3971}, {321, 3920}, {333, 984}, {388, 20009}, {518, 1999}, {519, 4514}, {595, 3159}, {614, 18743}, {664, 30545}, {668, 18057}, {740, 3961}, {750, 17155}, {756, 17277}, {869, 7033}, {894, 3745}, {940, 24349}, {968, 4664}, {976, 1043}, {982, 29649}, {998, 1120}, {1010, 30142}, {1150, 7226}, {1191, 19582}, {1376, 3210}, {1386, 3967}, {1621, 3995}, {1738, 19796}, {1757, 3791}, {1961, 24325}, {1978, 18064}, {2223, 25264}, {2550, 30699}, {2887, 32847}, {3052, 17262}, {3158, 24685}, {3175, 3685}, {3187, 3681}, {3242, 10453}, {3304, 17480}, {3416, 27184}, {3434, 20020}, {3475, 17316}, {3666, 7081}, {3672, 7172}, {3677, 30567}, {3683, 17261}, {3701, 5262}, {3705, 17720}, {3715, 17349}, {3717, 19815}, {3729, 5269}, {3750, 3993}, {3752, 5205}, {3771, 17725}, {3772, 29641}, {3773, 32783}, {3782, 4645}, {3790, 29634}, {3811, 4123}, {3816, 5211}, {3840, 17598}, {3846, 17769}, {3873, 24841}, {3879, 4872}, {3883, 4656}, {3896, 3935}, {3914, 32850}, {3923, 17716}, {3944, 4865}, {3952, 17150}, {3994, 17469}, {4030, 4854}, {4082, 17353}, {4096, 4974}, {4104, 4886}, {4203, 16687}, {4310, 18141}, {4358, 7191}, {4359, 5297}, {4383, 27538}, {4384, 7322}, {4388, 4415}, {4389, 26034}, {4413, 17490}, {4429, 10327}, {4434, 17596}, {4438, 29658}, {4439, 6679}, {4440, 11246}, {4517, 17033}, {4671, 24552}, {4680, 17677}, {4685, 4716}, {4696, 17016}, {4849, 4852}, {4864, 4891}, {5222, 5423}, {5266, 7283}, {5268, 19804}, {5272, 30829}, {5284, 31035}, {5289, 20037}, {5741, 32842}, {5904, 18417}, {6057, 17280}, {6541, 29656}, {6542, 26590}, {6685, 17600}, {7174, 11679}, {7270, 13161}, {7290, 30568}, {7413, 31395}, {10026, 17388}, {11680, 29832}, {13588, 20990}, {15523, 32775}, {16060, 30167}, {16061, 30138}, {16830, 31993}, {17027, 32029}, {17034, 20683}, {17122, 24165}, {17158, 28043}, {17160, 32860}, {17283, 29687}, {17285, 24943}, {17305, 32781}, {17592, 29670}, {17682, 30130}, {17719, 29671}, {17724, 29839}, {17768, 20101}, {17776, 26228}, {17778, 20069}, {17785, 29862}, {21936, 24478}, {24217, 29844}, {25760, 32854}, {25961, 27191}, {26061, 29636}, {26128, 29674}, {26227, 28606}, {29645, 32780}, {29679, 32774}, {29816, 32772}, {29846, 32848}, {30832, 32778}


X(32927) = X(1)X(996)∩X(2)X(17598)

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

X(32927) lies on these lines: {1, 996}, {2, 17598}, {8, 21935}, {10, 32775}, {11, 9053}, {31, 983}, {35, 24068}, {38, 7081}, {42, 308}, {43, 3891}, {55, 17262}, {80, 519}, {100, 726}, {149, 17765}, {171, 17165}, {190, 902}, {192, 2177}, {200, 17151}, {210, 17348}, {238, 3952}, {239, 21805}, {244, 5205}, {312, 3938}, {321, 3961}, {335, 24602}, {341, 3924}, {518, 17763}, {522, 13266}, {536, 3689}, {537, 3218}, {561, 7033}, {612, 3263}, {714, 3724}, {740, 1109}, {748, 27538}, {750, 24349}, {752, 17484}, {756, 3757}, {894, 31161}, {899, 3699}, {976, 4385}, {984, 26227}, {1155, 28582}, {1215, 3920}, {1279, 4009}, {1376, 17155}, {1458, 14594}, {1621, 3971}, {1911, 4583}, {2205, 22039}, {2225, 3508}, {2239, 17794}, {2975, 8669}, {3006, 17719}, {3009, 7035}, {3011, 3717}, {3120, 32850}, {3159, 3746}, {3214, 19817}, {3242, 30942}, {3315, 4871}, {3589, 29834}, {3681, 4362}, {3685, 3722}, {3703, 29846}, {3711, 4361}, {3744, 3967}, {3750, 3995}, {3771, 32862}, {3772, 30615}, {3810, 19589}, {3873, 29649}, {3932, 17724}, {3936, 32847}, {3944, 5014}, {3992, 30117}, {3996, 4365}, {4030, 4415}, {4075, 5259}, {4080, 21282}, {4096, 27065}, {4119, 17737}, {4152, 4395}, {4388, 20056}, {4396, 9055}, {4417, 32854}, {4438, 29665}, {4439, 32849}, {4645, 32856}, {4661, 32853}, {4692, 30115}, {4716, 19998}, {4766, 6542}, {4852, 21870}, {4863, 4952}, {4865, 31053}, {4884, 5432}, {4901, 29857}, {4929, 5231}, {4968, 5293}, {5057, 17766}, {5276, 21101}, {5280, 21067}, {5297, 24325}, {5311, 17394}, {5531, 29016}, {5741, 32866}, {5846, 32843}, {6154, 28530}, {7172, 26034}, {7174, 29828}, {7292, 24003}, {9350, 17490}, {9458, 16610}, {10327, 25957}, {16484, 31035}, {16519, 21021}, {17061, 29850}, {17122, 17140}, {17154, 18201}, {17279, 29638}, {17319, 21806}, {17449, 24841}, {17469, 27064}, {17480, 32577}, {17495, 17780}, {17597, 30957}, {17602, 29631}, {17716, 26223}, {17717, 29832}, {17718, 29643}, {17755, 26247}, {17764, 20095}, {17769, 32842}, {18098, 22013}, {20020, 26098}, {20962, 25048}, {25496, 29815}, {26061, 29634}, {26128, 29679}, {26245, 27549}, {26627, 31178}, {28606, 29670}, {29848, 32777}, {30837, 31093}


X(32928) = X(1)X(321)∩X(2)X(3773)

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

X(32928) lies on these lines: {1, 321}, {2, 3773}, {31, 192}, {38, 1999}, {42, 308}, {55, 17318}, {75, 5311}, {81, 726}, {100, 4970}, {145, 4388}, {171, 17147}, {190, 2308}, {210, 4852}, {238, 3995}, {239, 756}, {306, 32775}, {312, 17017}, {333, 3989}, {519, 4425}, {536, 3745}, {612, 3875}, {740, 3920}, {750, 3210}, {940, 17155}, {984, 3187}, {1125, 1224}, {1203, 3159}, {1215, 17011}, {1281, 3722}, {1386, 3175}, {1621, 3993}, {1961, 4359}, {1962, 3757}, {2209, 20170}, {2895, 17772}, {3219, 3791}, {3244, 5057}, {3416, 32776}, {3589, 6057}, {3666, 17763}, {3672, 26034}, {3683, 4681}, {3685, 17469}, {3703, 29631}, {3746, 4065}, {3750, 20045}, {3769, 4414}, {3772, 29643}, {3790, 26061}, {3846, 32842}, {3896, 3961}, {3932, 29850}, {3943, 29834}, {3969, 32783}, {3980, 9347}, {3994, 27064}, {4000, 25961}, {4038, 17140}, {4046, 4971}, {4078, 26723}, {4358, 29821}, {4361, 26037}, {4362, 28606}, {4365, 5263}, {4415, 32843}, {4645, 20069}, {4649, 17165}, {4651, 4716}, {4671, 25496}, {4683, 5847}, {4697, 28516}, {4756, 4991}, {4850, 29649}, {4854, 5846}, {4972, 32847}, {4974, 27065}, {4980, 24342}, {5280, 18098}, {5564, 8013}, {6535, 17289}, {6541, 29654}, {6679, 32849}, {6703, 28472}, {6742, 11599}, {7174, 17156}, {7226, 32853}, {15523, 19786}, {16706, 29687}, {16830, 21020}, {17019, 24325}, {17020, 24003}, {17061, 29632}, {17122, 17495}, {17123, 31035}, {17124, 17490}, {17184, 32846}, {17233, 24943}, {17243, 29851}, {17279, 29852}, {17302, 32781}, {17380, 29663}, {17592, 26227}, {17598, 29824}, {17599, 30942}, {17602, 29846}, {17720, 29849}, {17771, 20086}, {17778, 32856}, {19785, 25957}, {20961, 25048}, {20985, 25264}, {24210, 32844}, {24789, 29854}, {25453, 32862}, {26128, 32858}, {26580, 32861}, {27184, 32852}, {29584, 31161}, {29636, 32777}, {29645, 32779}, {29674, 32774}, {29683, 32851}, {29833, 32780}, {32773, 32854}


X(32929) = X(1)X(596)∩X(2)X(968)

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

X(32929) lies on these lines: {1, 596}, {2, 968}, {3, 3702}, {6, 3896}, {8, 90}, {9, 4651}, {19, 346}, {22, 23381}, {31, 740}, {40, 17751}, {42, 3923}, {55, 321}, {57, 29824}, {63, 3886}, {69, 20291}, {75, 1621}, {78, 25253}, {100, 312}, {145, 4339}, {149, 3705}, {165, 4781}, {171, 4693}, {190, 3681}, {192, 3920}, {200, 3952}, {238, 32860}, {239, 17127}, {306, 516}, {314, 4184}, {345, 3006}, {350, 26229}, {354, 4702}, {497, 17740}, {528, 3703}, {536, 3744}, {561, 874}, {593, 11104}, {612, 3995}, {614, 17495}, {726, 3938}, {748, 4432}, {752, 32852}, {835, 30273}, {846, 31330}, {894, 17018}, {896, 32853}, {899, 4011}, {902, 4362}, {956, 3902}, {964, 3931}, {982, 32845}, {999, 4742}, {1001, 4359}, {1018, 21369}, {1043, 3869}, {1054, 30957}, {1089, 8715}, {1096, 14954}, {1150, 3706}, {1215, 2177}, {1259, 23528}, {1376, 4358}, {1402, 11322}, {1468, 24850}, {1486, 20336}, {1707, 16704}, {1759, 21070}, {1836, 3936}, {1999, 17126}, {2082, 26770}, {2258, 3240}, {2321, 5282}, {2550, 17776}, {2886, 3712}, {2887, 17764}, {2901, 5264}, {2975, 4673}, {3120, 3771}, {3210, 7191}, {3218, 10453}, {3263, 26241}, {3295, 4968}, {3416, 3969}, {3550, 17763}, {3621, 9369}, {3666, 24552}, {3683, 3696}, {3689, 3967}, {3695, 5300}, {3701, 4186}, {3704, 5016}, {3720, 3980}, {3729, 3870}, {3741, 4414}, {3749, 20045}, {3750, 32771}, {3751, 20011}, {3755, 5294}, {3757, 28605}, {3765, 4433}, {3772, 4442}, {3782, 28530}, {3790, 20095}, {3821, 24943}, {3838, 30834}, {3848, 24594}, {3871, 4385}, {3875, 17150}, {3913, 4696}, {3944, 29846}, {3957, 24349}, {3977, 4847}, {3993, 5311}, {4028, 31034}, {4037, 4386}, {4043, 15624}, {4054, 13405}, {4085, 26061}, {4113, 15481}, {4195, 17016}, {4417, 5057}, {4423, 24589}, {4428, 4980}, {4436, 16678}, {4441, 26237}, {4487, 8168}, {4512, 5271}, {4551, 28997}, {4552, 8270}, {4641, 28581}, {4645, 32858}, {4647, 5248}, {4659, 10389}, {4660, 15523}, {4671, 7081}, {4692, 25439}, {4734, 17012}, {4865, 32848}, {4966, 11246}, {4970, 17017}, {4972, 32777}, {5223, 25734}, {5249, 29830}, {5259, 28612}, {5263, 28606}, {5268, 31035}, {5284, 19804}, {5698, 5739}, {5741, 24703}, {5847, 20017}, {5880, 18139}, {5905, 24280}, {6051, 16454}, {6057, 6154}, {6542, 20101}, {7262, 32864}, {7292, 17490}, {8299, 26238}, {9342, 30829}, {9350, 24003}, {9371, 27394}, {9778, 34255}, {11680, 32851}, {16496, 20068}, {16824, 16865}, {17143, 23407}, {17184, 24248}, {17280, 29679}, {17302, 29648}, {17350, 20012}, {17592, 32772}, {17596, 30942}, {17766, 32854}, {17768, 32859}, {17777, 27131}, {17889, 29632}, {18134, 20292}, {19785, 26230}, {20173, 26263}, {20901, 20922}, {21877, 30647}, {23868, 27569}, {24169, 29677}, {24295, 29663}, {24542, 24789}, {24715, 25957}, {24723, 32782}, {25385, 29678}, {25941, 26651}, {26228, 30699}, {27000, 29986}, {29641, 32849}, {29839, 31019}, {32773, 32779}, {32776, 32783}, {32844, 32855}, {32850, 32862}

X(32929) = anticomplement of X(3914)


X(32930) = X(1)X(3159)∩X(2)X(846)

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

X(32930) lies on these lines: {1, 3159}, {2, 846}, {3, 25591}, {6, 4037}, {8, 6535}, {9, 3588}, {10, 3583}, {31, 312}, {37, 32772}, {38, 190}, {42, 3685}, {44, 3706}, {57, 30957}, {63, 30942}, {75, 748}, {81, 4672}, {141, 4683}, {149, 29673}, {171, 4358}, {184, 24265}, {192, 17017}, {226, 29632}, {238, 321}, {239, 4365}, {306, 32843}, {344, 29854}, {345, 29849}, {354, 17351}, {404, 24850}, {497, 16561}, {595, 1089}, {612, 30568}, {614, 3729}, {726, 7191}, {750, 18743}, {756, 5263}, {874, 30666}, {894, 3720}, {896, 14829}, {902, 7081}, {908, 29846}, {984, 24552}, {986, 5192}, {1001, 32771}, {1018, 18101}, {1031, 4388}, {1083, 1316}, {1109, 20919}, {1150, 7262}, {1193, 7283}, {1203, 2901}, {1215, 1621}, {1376, 9458}, {1386, 3175}, {1699, 29857}, {1724, 27368}, {1743, 17156}, {1757, 17135}, {1836, 17279}, {1961, 31035}, {1965, 1978}, {1966, 18152}, {1999, 2308}, {2229, 30646}, {2292, 13740}, {2887, 5057}, {3123, 28269}, {3187, 16468}, {3218, 3840}, {3219, 3741}, {3305, 26037}, {3496, 27040}, {3589, 4854}, {3662, 29677}, {3701, 5255}, {3702, 5247}, {3703, 17340}, {3724, 4203}, {3734, 9317}, {3744, 3967}, {3752, 32845}, {3771, 31053}, {3790, 32854}, {3816, 24709}, {3836, 20292}, {3846, 32779}, {3896, 4693}, {3914, 17353}, {3915, 4385}, {3920, 3971}, {3924, 17697}, {3925, 4422}, {3935, 4090}, {3952, 3961}, {3966, 17281}, {3969, 32861}, {3977, 24239}, {3985, 5276}, {3989, 17261}, {3993, 17011}, {3994, 17469}, {3996, 21805}, {4042, 16885}, {4080, 29860}, {4195, 19582}, {4202, 24851}, {4359, 17123}, {4362, 4671}, {4363, 4423}, {4376, 4713}, {4383, 5695}, {4392, 29668}, {4396, 4797}, {4415, 32775}, {4438, 11680}, {4512, 29828}, {4640, 30818}, {4645, 29687}, {4660, 29679}, {4679, 25960}, {4703, 32782}, {4865, 32862}, {4871, 27003}, {4970, 17012}, {5012, 5150}, {5249, 29851}, {5284, 24325}, {5294, 24210}, {5698, 26034}, {5846, 6057}, {5880, 25961}, {6327, 29674}, {7226, 29652}, {7292, 24165}, {7424, 10176}, {8299, 21319}, {8616, 26227}, {10453, 17350}, {11269, 26065}, {13741, 24443}, {15254, 31993}, {16569, 26688}, {16571, 27636}, {16822, 16920}, {16825, 28605}, {17063, 24395}, {17124, 30829}, {17125, 19804}, {17126, 29649}, {17140, 29820}, {17147, 29821}, {17184, 29637}, {17188, 25078}, {17233, 32852}, {17262, 17599}, {17277, 21020}, {17302, 29684}, {17339, 29641}, {17342, 31134}, {17354, 26061}, {17368, 29647}, {17692, 27954}, {17744, 22026}, {17770, 32863}, {17776, 26098}, {17785, 31280}, {17871, 20927}, {18134, 24725}, {19649, 29057}, {19785, 29852}, {20068, 24821}, {20627, 20643}, {20655, 21094}, {20688, 23533}, {21093, 29656}, {21241, 29873}, {24080, 30141}, {24255, 24294}, {24330, 24358}, {24703, 25760}, {24723, 32781}, {24943, 27184}, {24997, 26699}, {25496, 28606}, {25502, 26627}, {25526, 27784}, {26580, 32783}, {26724, 31289}, {29642, 31019}, {29671, 32849}

X(32930) = complement of X(33102)
X(32930) = anticomplement of X(24169)


X(32931) = X(1)X(996)∩X(2)X(38)

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

X(32931) lies on these lines: {1, 996}, {2, 38}, {6, 17763}, {8, 21805}, {9, 2225}, {10, 908}, {31, 7081}, {37, 4009}, {42, 312}, {43, 321}, {55, 32930}, {63, 32918}, {75, 899}, {81, 29649}, {100, 3923}, {171, 26223}, {190, 4414}, {192, 3994}, {210, 31330}, {226, 25957}, {238, 26227}, {329, 4683}, {341, 10459}, {354, 30957}, {373, 17049}, {386, 1089}, {518, 30818}, {594, 4023}, {612, 32772}, {614, 32923}, {661, 19584}, {726, 4850}, {730, 3809}, {740, 3240}, {748, 3757}, {750, 894}, {870, 5378}, {896, 17350}, {902, 4676}, {964, 5293}, {968, 30568}, {976, 13740}, {978, 4968}, {986, 26030}, {995, 4692}, {1150, 1757}, {1155, 17351}, {1193, 4385}, {1376, 4418}, {1621, 4011}, {1644, 25382}, {1738, 4054}, {1961, 19684}, {1962, 4903}, {2176, 21021}, {2177, 3685}, {2239, 24514}, {2308, 3769}, {2345, 21033}, {2887, 29679}, {2901, 5312}, {2999, 32924}, {3006, 17717}, {3011, 17353}, {3112, 7033}, {3120, 4429}, {3219, 32916}, {3416, 32843}, {3452, 25960}, {3589, 17602}, {3596, 21803}, {3616, 25079}, {3661, 4766}, {3662, 31083}, {3666, 3967}, {3678, 10479}, {3681, 3741}, {3690, 9564}, {3699, 5263}, {3703, 29849}, {3706, 4849}, {3710, 5530}, {3712, 17340}, {3715, 5737}, {3717, 29639}, {3720, 18743}, {3729, 32845}, {3739, 30958}, {3740, 26037}, {3751, 32919}, {3752, 17155}, {3772, 29850}, {3790, 32848}, {3821, 21093}, {3831, 3868}, {3836, 31019}, {3840, 3873}, {3846, 27131}, {3891, 29821}, {3920, 25496}, {3932, 5718}, {3936, 29674}, {3944, 4972}, {3961, 24552}, {3971, 6685}, {3976, 26094}, {3992, 30116}, {3995, 17592}, {4003, 28582}, {4062, 17233}, {4073, 27058}, {4135, 4970}, {4359, 16569}, {4362, 32911}, {4363, 4413}, {4383, 32914}, {4415, 32776}, {4417, 15523}, {4427, 17601}, {4431, 5212}, {4434, 4672}, {4465, 24357}, {4519, 21870}, {4645, 24725}, {4655, 17484}, {4660, 5057}, {4664, 4937}, {4686, 4706}, {4699, 25106}, {4703, 26792}, {4713, 24326}, {4892, 25959}, {4938, 17373}, {4974, 14997}, {5044, 31339}, {5218, 14439}, {5219, 29857}, {5249, 25961}, {5256, 32928}, {5282, 26244}, {5284, 29651}, {5328, 5772}, {5741, 32778}, {5835, 21031}, {6679, 29665}, {6686, 24165}, {6708, 18236}, {6745, 17355}, {7174, 29826}, {7191, 32920}, {9364, 28968}, {10327, 26098}, {11269, 28808}, {11679, 32864}, {11680, 29673}, {12263, 17367}, {13741, 28082}, {14459, 17299}, {14829, 32912}, {16823, 17125}, {17012, 32921}, {17017, 32926}, {17056, 29854}, {17061, 29852}, {17123, 26688}, {17164, 24440}, {17279, 17718}, {17354, 24327}, {17450, 30861}, {17720, 29631}, {17722, 29832}, {17724, 29638}, {17725, 26230}, {18134, 29687}, {19647, 29054}, {19786, 29663}, {19846, 24160}, {20108, 24068}, {20909, 24749}, {21020, 25123}, {21101, 26242}, {21415, 21590}, {21951, 25610}, {24217, 29835}, {24542, 29675}, {25124, 27268}, {25378, 29659}, {25958, 28595}, {26251, 26580}, {27184, 32781}, {29671, 32862}, {29822, 31035}, {29846, 32777}, {29862, 30834}, {30748, 30949}, {30829, 30950}, {31034, 32846}

X(32931) = complement of X(4392)


X(32932) = X(1)X(3210)∩X(2)X(968)

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

X(32932) lies on these lines: {1, 3210}, {2, 968}, {8, 20}, {10, 846}, {21, 16824}, {31, 239}, {35, 4647}, {38, 32845}, {42, 894}, {43, 3923}, {46, 10449}, {55, 75}, {56, 4673}, {57, 3886}, {65, 1043}, {69, 3474}, {81, 3896}, {92, 11406}, {98, 100}, {109, 1943}, {165, 11679}, {171, 740}, {181, 6007}, {190, 210}, {192, 612}, {200, 1721}, {292, 21345}, {306, 4645}, {312, 1376}, {313, 16085}, {314, 1402}, {319, 4046}, {320, 11246}, {329, 24280}, {333, 3696}, {344, 26040}, {345, 2550}, {382, 5827}, {404, 3702}, {516, 3687}, {518, 3996}, {519, 32913}, {528, 4514}, {536, 32926}, {553, 4684}, {614, 17490}, {726, 3961}, {750, 32915}, {752, 32861}, {756, 17261}, {874, 1920}, {893, 21877}, {896, 32864}, {899, 32930}, {902, 17117}, {936, 19582}, {946, 30007}, {993, 16821}, {1001, 19804}, {1010, 3931}, {1054, 3840}, {1155, 3706}, {1211, 24723}, {1219, 12632}, {1220, 4646}, {1222, 3893}, {1260, 28058}, {1330, 1770}, {1447, 4441}, {1575, 30646}, {1621, 4359}, {1722, 17697}, {1757, 4685}, {1824, 4451}, {1836, 4417}, {1909, 4433}, {1958, 2187}, {1961, 3993}, {1962, 16826}, {2177, 17116}, {2223, 17143}, {2308, 17121}, {2319, 14199}, {2321, 3509}, {2651, 7058}, {2886, 32851}, {2887, 24715}, {2975, 22060}, {3052, 4361}, {3120, 29846}, {3158, 4659}, {3187, 17126}, {3198, 11683}, {3218, 17135}, {3219, 4427}, {3240, 26223}, {3256, 6358}, {3305, 26038}, {3434, 3705}, {3452, 17777}, {3501, 5364}, {3550, 4362}, {3573, 26885}, {3579, 5295}, {3661, 26034}, {3666, 5263}, {3683, 17277}, {3699, 3967}, {3703, 32850}, {3704, 7270}, {3712, 3925}, {3715, 17336}, {3722, 32923}, {3741, 17596}, {3742, 4702}, {3744, 32922}, {3745, 4360}, {3747, 16827}, {3750, 24325}, {3751, 20012}, {3771, 17889}, {3783, 24259}, {3790, 10327}, {3791, 4716}, {3821, 32783}, {3846, 17764}, {3870, 24349}, {3871, 4968}, {3875, 5269}, {3920, 17147}, {3935, 17165}, {3936, 20292}, {3938, 17155}, {3957, 17140}, {3977, 25006}, {3995, 5297}, {4011, 16569}, {4026, 19808}, {4028, 17778}, {4030, 6154}, {4061, 4416}, {4085, 32780}, {4090, 5524}, {4365, 17763}, {4383, 4676}, {4384, 4512}, {4385, 5687}, {4387, 4413}, {4414, 31330}, {4415, 28530}, {4429, 32777}, {4432, 17123}, {4438, 32865}, {4450, 29315}, {4461, 7172}, {4649, 4697}, {4650, 32853}, {4660, 32778}, {4689, 31993}, {4693, 17122}, {4714, 5251}, {4734, 5256}, {4737, 22149}, {4781, 17163}, {4829, 17103}, {4849, 17351}, {4850, 24552}, {4865, 32855}, {4972, 32779}, {5057, 5741}, {5233, 24703}, {5247, 24850}, {5248, 16817}, {5249, 29839}, {5259, 28611}, {5272, 24620}, {5284, 24589}, {5285, 17797}, {5311, 17319}, {5437, 30947}, {5537, 20237}, {5552, 27287}, {5698, 14555}, {5847, 20101}, {5880, 18134}, {6063, 9446}, {6653, 30179}, {6682, 17593}, {7018, 19637}, {7085, 32117}, {7182, 14189}, {7191, 17495}, {7360, 17860}, {8053, 20174}, {8193, 19845}, {8580, 30568}, {8616, 16825}, {8844, 17787}, {9534, 12514}, {9881, 29615}, {10434, 10447}, {10578, 31995}, {11115, 17016}, {11512, 26093}, {12609, 25650}, {13174, 21085}, {14195, 18021}, {14923, 31785}, {15931, 20882}, {16602, 25531}, {16830, 28606}, {17019, 27804}, {17061, 19796}, {17119, 21000}, {17144, 21010}, {17260, 26037}, {17266, 25961}, {17268, 29687}, {17291, 24943}, {17292, 32781}, {17469, 32924}, {17591, 29652}, {17601, 32916}, {17716, 32921}, {17762, 17798}, {17766, 32866}, {19785, 29634}, {19789, 26228}, {21020, 32917}, {21218, 25242}, {23556, 26178}, {24169, 29637}, {24248, 27184}, {24541, 30543}, {24542, 26724}, {24586, 27474}, {26227, 28605}, {26627, 29814}, {27000, 29960}, {27003, 29824}, {27186, 29830}

X(32932) = anticomplement of X(24210)


X(32933) = X(2)X(45)∩X(6)X(17147)

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

X(32933) lies on these lines: {2, 45}, {6, 17147}, {7, 17776}, {8, 30}, {9, 4359}, {31, 726}, {38, 3923}, {40, 4696}, {43, 32845}, {46, 3701}, {55, 4427}, {56, 25253}, {57, 4358}, {63, 321}, {69, 3969}, {75, 3219}, {79, 30172}, {81, 192}, {92, 20887}, {100, 11689}, {144, 5739}, {171, 32925}, {222, 4552}, {226, 3977}, {238, 17155}, {239, 11352}, {244, 4011}, {306, 527}, {312, 3218}, {320, 32858}, {329, 4488}, {333, 28605}, {345, 3936}, {346, 9965}, {379, 20432}, {516, 5014}, {518, 32929}, {524, 20017}, {525, 22130}, {536, 3187}, {537, 3938}, {553, 2325}, {740, 32912}, {748, 24165}, {750, 3971}, {752, 32854}, {756, 3980}, {799, 6382}, {846, 32771}, {894, 19684}, {896, 4362}, {902, 32920}, {940, 3995}, {958, 17164}, {966, 19825}, {976, 24850}, {982, 32930}, {984, 4418}, {1001, 17140}, {1155, 3967}, {1211, 17334}, {1214, 28968}, {1215, 4414}, {1230, 2245}, {1255, 4704}, {1257, 7538}, {1265, 4190}, {1266, 26723}, {1376, 3952}, {1465, 28997}, {1621, 24349}, {1757, 32860}, {1770, 5300}, {1817, 30905}, {1836, 3006}, {1975, 25257}, {2308, 32921}, {2321, 4001}, {2796, 29673}, {2887, 17767}, {2895, 17347}, {3052, 20045}, {3120, 4438}, {3161, 9776}, {3210, 17350}, {3242, 20068}, {3305, 24589}, {3306, 30568}, {3434, 24280}, {3474, 10327}, {3550, 32927}, {3663, 5294}, {3666, 17351}, {3670, 5192}, {3685, 3873}, {3687, 4480}, {3703, 6327}, {3705, 5057}, {3710, 4292}, {3730, 20913}, {3744, 28582}, {3751, 3896}, {3758, 17011}, {3765, 25733}, {3771, 32856}, {3772, 31229}, {3791, 28516}, {3821, 26061}, {3868, 7283}, {3914, 28526}, {3929, 4659}, {3932, 11246}, {3961, 24821}, {3975, 19809}, {3994, 29649}, {3996, 4661}, {4042, 17163}, {4054, 5745}, {4361, 19742}, {4365, 32853}, {4383, 17495}, {4387, 29824}, {4393, 32107}, {4417, 17484}, {4421, 4781}, {4461, 14552}, {4640, 26227}, {4645, 32862}, {4650, 17763}, {4651, 5220}, {4655, 15523}, {4664, 17019}, {4671, 14829}, {4672, 17017}, {4676, 7191}, {4683, 32778}, {4697, 5311}, {4756, 27538}, {4850, 27064}, {4854, 29829}, {4884, 29832}, {4968, 12514}, {4971, 20046}, {4972, 24248}, {5205, 9352}, {5233, 26792}, {5253, 19582}, {5263, 7226}, {5264, 24068}, {5695, 17135}, {5737, 31025}, {5846, 20064}, {6645, 25270}, {6646, 32782}, {7004, 27394}, {7262, 32914}, {7321, 27186}, {8025, 16777}, {8369, 30884}, {8616, 32923}, {8680, 20896}, {9335, 25531}, {9369, 14923}, {11346, 30117}, {11681, 30448}, {14206, 20237}, {14213, 20881}, {16086, 17579}, {16393, 30115}, {16468, 32924}, {16610, 26688}, {17118, 19732}, {17119, 19723}, {17126, 32926}, {17127, 32922}, {17142, 20992}, {17154, 17597}, {17184, 17276}, {17220, 30052}, {17233, 32863}, {17234, 26842}, {17256, 19797}, {17257, 19822}, {17258, 19808}, {17280, 26840}, {17336, 19804}, {17377, 20086}, {17483, 18134}, {17755, 24596}, {17770, 32852}, {17778, 31300}, {17811, 25243}, {18136, 29423}, {18201, 30957}, {18743, 27003}, {19717, 20182}, {19785, 26065}, {20236, 20879}, {20292, 29641}, {22010, 24220}, {24593, 30567}, {24597, 30699}, {24723, 29667}, {24725, 29671}, {25091, 26651}, {25735, 30625}, {25957, 32857}, {27184, 32779}, {28610, 34255}, {29670, 31161}, {31053, 32851}, {32776, 32780}, {32843, 32855}, {32913, 32915}

X(32933) = anticomplement of X(3782)


X(32934) = X(1)X(4234)∩X(2)X(17593)

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

X(32934) lies on these lines: {1, 4234}, {2, 17593}, {6, 4970}, {31, 4427}, {37, 3980}, {38, 32929}, {43, 190}, {55, 726}, {56, 8720}, {63, 740}, {75, 846}, {100, 32925}, {165, 4434}, {171, 192}, {226, 28526}, {238, 3210}, {239, 7262}, {306, 4655}, {312, 17596}, {321, 4414}, {345, 2887}, {516, 4865}, {527, 4028}, {528, 4884}, {536, 4362}, {537, 3870}, {614, 4432}, {712, 24264}, {748, 17495}, {750, 3995}, {874, 17149}, {894, 17592}, {896, 3187}, {902, 3891}, {940, 3993}, {968, 24325}, {982, 3685}, {986, 7283}, {1001, 24165}, {1054, 18743}, {1086, 29642}, {1150, 4365}, {1155, 3175}, {1215, 3729}, {1376, 3971}, {1580, 3905}, {1621, 17155}, {1707, 3791}, {1709, 28850}, {1836, 2796}, {1961, 4664}, {1999, 4650}, {2177, 17165}, {2276, 24259}, {2886, 28530}, {3058, 29844}, {3159, 25440}, {3218, 32915}, {3219, 32860}, {3434, 17764}, {3550, 32926}, {3644, 3769}, {3663, 26128}, {3666, 3923}, {3683, 16825}, {3687, 4703}, {3693, 24283}, {3703, 4660}, {3712, 3771}, {3741, 5695}, {3750, 24349}, {3752, 4011}, {3773, 26034}, {3797, 24586}, {3821, 32777}, {3836, 17776}, {3840, 4387}, {3846, 17740}, {3896, 32912}, {3914, 3977}, {3916, 17733}, {3944, 32851}, {4003, 29668}, {4042, 4709}, {4062, 32859}, {4099, 17736}, {4136, 9598}, {4388, 32855}, {4389, 32783}, {4418, 28606}, {4439, 10327}, {4440, 29839}, {4442, 24892}, {4450, 32854}, {4552, 9316}, {4643, 21085}, {4671, 32918}, {4672, 5256}, {4676, 29821}, {4681, 4682}, {4685, 5220}, {4689, 29670}, {4693, 10453}, {4702, 21342}, {4734, 17350}, {4847, 28580}, {4850, 32930}, {4854, 29635}, {4918, 7354}, {5057, 29849}, {5217, 8669}, {5745, 28557}, {5880, 29653}, {5905, 17767}, {6327, 32848}, {6679, 19785}, {6690, 28556}, {7075, 16557}, {7081, 17601}, {8616, 32922}, {8715, 24068}, {10180, 10436}, {10448, 17164}, {13405, 17132}, {13478, 29347}, {17123, 17490}, {17124, 31035}, {17126, 32928}, {17127, 32924}, {17279, 24169}, {17301, 29654}, {17765, 20075}, {17771, 20078}, {18134, 32857}, {20292, 29643}, {20760, 21080}, {21101, 31477}, {22036, 31451}, {23160, 23363}, {24003, 30568}, {24280, 26098}, {24715, 29641}, {24723, 32778}, {25269, 27538}, {25957, 32849}, {28605, 32917}, {32776, 32779}


X(32935) = X(1)X(190)∩X(2)X(18201)

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

X(32935) lies on these lines: {1, 190}, {2, 18201}, {6, 726}, {7, 3836}, {8, 752}, {9, 24325}, {10, 527}, {31, 17165}, {38, 25496}, {44, 16825}, {45, 1125}, {63, 1215}, {69, 3773}, {75, 1757}, {81, 32925}, {141, 5852}, {145, 4693}, {192, 4649}, {193, 17772}, {210, 3980}, {226, 4438}, {238, 17350}, {291, 24514}, {312, 32913}, {320, 29674}, {321, 32853}, {329, 3846}, {354, 4011}, {355, 2792}, {518, 3923}, {519, 5695}, {536, 4663}, {612, 4697}, {740, 3729}, {748, 17140}, {750, 3952}, {874, 24524}, {894, 984}, {896, 26227}, {940, 3971}, {968, 25734}, {982, 27064}, {1009, 21320}, {1046, 4385}, {1278, 4716}, {1376, 4090}, {1386, 28582}, {1698, 17250}, {1743, 4974}, {1756, 29698}, {1836, 29673}, {2177, 4427}, {2308, 3891}, {2345, 3775}, {2887, 5905}, {3006, 24725}, {3187, 4722}, {3219, 32771}, {3240, 32845}, {3247, 5625}, {3306, 24003}, {3338, 25079}, {3416, 17770}, {3664, 4078}, {3679, 28558}, {3681, 4418}, {3683, 29651}, {3739, 15481}, {3755, 28526}, {3757, 7262}, {3782, 25453}, {3790, 17364}, {3811, 24850}, {3821, 17276}, {3842, 10436}, {3844, 17345}, {3873, 32930}, {3874, 24425}, {3875, 28516}, {3932, 17365}, {3967, 29649}, {3989, 19684}, {3993, 17262}, {4026, 17334}, {4085, 17767}, {4096, 5268}, {4135, 4942}, {4141, 31179}, {4252, 8669}, {4253, 12263}, {4255, 8720}, {4360, 28650}, {4362, 4641}, {4383, 24165}, {4389, 29633}, {4415, 29635}, {4422, 25557}, {4429, 32857}, {4436, 8715}, {4439, 4644}, {4535, 17294}, {4557, 22458}, {4640, 29670}, {4645, 31300}, {4650, 7081}, {4659, 4753}, {4660, 17768}, {4671, 32919}, {4683, 29667}, {4703, 17781}, {4743, 28542}, {4780, 28557}, {4851, 6541}, {4852, 28555}, {4860, 4871}, {4892, 29857}, {4966, 17340}, {5255, 24351}, {5294, 26128}, {5850, 17355}, {6646, 32784}, {6679, 26065}, {6789, 23343}, {7226, 32772}, {8818, 20546}, {9345, 31035}, {12782, 17499}, {15254, 24331}, {15523, 32859}, {16468, 32922}, {16823, 31178}, {16834, 28554}, {17122, 27538}, {17126, 32927}, {17127, 32923}, {17155, 32911}, {17184, 26061}, {17236, 26083}, {17244, 27949}, {17333, 24697}, {17353, 24231}, {17354, 29637}, {17483, 25957}, {17484, 25760}, {17491, 31079}, {17720, 21093}, {17754, 17793}, {17764, 24280}, {17777, 24217}, {20078, 26034}, {20132, 27481}, {20154, 27478}, {20158, 27494}, {21342, 29668}, {24703, 29655}, {24723, 29659}, {24982, 26659}, {25960, 26792}, {25961, 26842}, {26232, 31111}, {26267, 30801}, {26685, 31289}, {27184, 32780}, {28472, 32455}, {28605, 32864}, {30746, 31121}, {31034, 32848}


X(32936) = X(2)X(17593)∩X(9)X(32860)

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

X(32936) lies on these lines: {2, 17593}, {9, 32860}, {31, 192}, {35, 3159}, {37, 4418}, {38, 3685}, {42, 190}, {45, 26037}, {55, 17262}, {63, 32915}, {81, 3993}, {100, 3971}, {171, 3995}, {191, 2901}, {238, 17147}, {306, 4683}, {312, 4414}, {321, 846}, {333, 4365}, {344, 25961}, {345, 25760}, {346, 26034}, {536, 3683}, {537, 3957}, {726, 1621}, {740, 3219}, {748, 3210}, {756, 17261}, {894, 1962}, {896, 1999}, {902, 32926}, {968, 3729}, {984, 32929}, {1001, 17155}, {1086, 29851}, {1746, 29347}, {1757, 3896}, {1836, 29643}, {2177, 25269}, {2292, 7283}, {2308, 4360}, {2796, 20292}, {2887, 32849}, {3058, 4884}, {3161, 26047}, {3175, 4640}, {3187, 7262}, {3666, 32930}, {3690, 6007}, {3712, 4415}, {3745, 4681}, {3746, 24068}, {3747, 25264}, {3748, 28582}, {3750, 17165}, {3751, 25734}, {3782, 29632}, {3891, 8616}, {3923, 28606}, {3925, 28530}, {3929, 17156}, {3967, 4689}, {3977, 24210}, {3979, 24821}, {3989, 5263}, {3994, 7081}, {4011, 4850}, {4028, 17781}, {4046, 17332}, {4090, 4756}, {4358, 17596}, {4387, 30942}, {4388, 32848}, {4389, 24943}, {4425, 32779}, {4432, 7191}, {4450, 32847}, {4649, 27804}, {4655, 32858}, {4660, 32862}, {4664, 5311}, {4671, 32916}, {4672, 17011}, {4676, 17017}, {4693, 17135}, {4697, 17019}, {4716, 19742}, {4854, 29631}, {4970, 32911}, {5057, 29671}, {5249, 28526}, {5253, 8720}, {5284, 24165}, {5695, 31330}, {5880, 29854}, {6536, 19808}, {8013, 17256}, {8040, 28653}, {11246, 17243}, {15523, 24723}, {16484, 17140}, {17122, 31035}, {17123, 17495}, {17125, 17490}, {17127, 32921}, {17264, 29687}, {17280, 32781}, {17301, 29852}, {17354, 29663}, {17483, 17767}, {17592, 26223}, {17595, 30957}, {17740, 25960}, {17776, 24248}, {18139, 32857}, {24176, 25542}, {24703, 29849}, {25006, 28580}, {27368, 31445}, {29839, 32856}, {32776, 32777}


X(32937) = X(1)X(979)∩X(2)X(38)

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

X(32937) lies on these lines: {1, 979}, {2, 38}, {4, 8}, {6, 32926}, {7, 3263}, {9, 3757}, {10, 17889}, {31, 983}, {33, 30688}, {42, 192}, {43, 726}, {55, 190}, {57, 5205}, {63, 6194}, {65, 341}, {69, 3974}, {75, 210}, {76, 20683}, {100, 11689}, {144, 7172}, {145, 3994}, {181, 3596}, {184, 4579}, {194, 869}, {200, 1721}, {209, 313}, {213, 22039}, {222, 14594}, {226, 3717}, {238, 32920}, {306, 3790}, {312, 518}, {330, 3009}, {333, 5220}, {344, 3475}, {345, 25568}, {346, 3930}, {354, 4009}, {386, 24068}, {388, 1265}, {497, 17777}, {519, 4135}, {536, 4849}, {561, 3212}, {596, 17749}, {612, 894}, {668, 6382}, {714, 3725}, {740, 20012}, {748, 32923}, {846, 29670}, {883, 23612}, {899, 17155}, {908, 3705}, {938, 2899}, {968, 17261}, {976, 4195}, {1089, 5904}, {1201, 17480}, {1222, 2098}, {1257, 27410}, {1278, 21805}, {1376, 3699}, {1478, 16086}, {1621, 4756}, {1757, 4362}, {1836, 30615}, {1897, 3195}, {1909, 4517}, {1920, 25282}, {1962, 4704}, {1965, 7033}, {1999, 3751}, {2177, 25269}, {2340, 25242}, {2550, 18037}, {2664, 24621}, {2975, 13732}, {3006, 31053}, {3161, 10578}, {3177, 17760}, {3190, 25252}, {3219, 26227}, {3240, 4734}, {3305, 16823}, {3508, 5364}, {3552, 18266}, {3616, 13742}, {3617, 17164}, {3644, 21870}, {3678, 9534}, {3683, 17336}, {3685, 3870}, {3687, 21060}, {3690, 3963}, {3701, 3868}, {3703, 4417}, {3715, 17277}, {3730, 21067}, {3740, 19804}, {3742, 30829}, {3744, 4676}, {3745, 3758}, {3752, 28582}, {3769, 4641}, {3779, 21299}, {3782, 4429}, {3811, 7283}, {3829, 17774}, {3873, 4358}, {3876, 4968}, {3891, 32911}, {3912, 4082}, {3920, 26223}, {3923, 3961}, {3925, 4126}, {3932, 18134}, {3935, 32929}, {3936, 32862}, {3938, 32930}, {3944, 21093}, {3953, 25492}, {3976, 25079}, {3992, 5902}, {3995, 17018}, {3996, 4942}, {4015, 28612}, {4037, 17314}, {4054, 25006}, {4061, 4431}, {4318, 28997}, {4359, 26038}, {4383, 32922}, {4393, 32928}, {4415, 32773}, {4418, 24451}, {4419, 24326}, {4425, 29659}, {4430, 29824}, {4432, 17715}, {4434, 4650}, {4446, 21936}, {4454, 6555}, {4488, 9778}, {4512, 25728}, {4514, 24703}, {4554, 31526}, {4645, 5905}, {4651, 28605}, {4661, 4671}, {4672, 17716}, {4692, 5692}, {4699, 26037}, {4713, 9055}, {4847, 4899}, {4901, 28609}, {5121, 27130}, {5211, 26791}, {5223, 11679}, {5226, 30741}, {5294, 29634}, {5311, 17379}, {6057, 17233}, {6063, 21404}, {6327, 17484}, {6646, 26034}, {6679, 17725}, {7292, 26688}, {7322, 10436}, {7360, 20588}, {8026, 20537}, {8055, 10580}, {14740, 17860}, {14839, 23638}, {16569, 24165}, {17034, 24080}, {17127, 20045}, {17141, 18135}, {17142, 17349}, {17149, 19586}, {17184, 29679}, {17232, 29687}, {17236, 32781}, {17358, 24943}, {17383, 29663}, {17449, 30861}, {17596, 24821}, {17597, 24841}, {17753, 21416}, {17757, 30448}, {17763, 32912}, {17776, 29839}, {17784, 24280}, {18059, 30547}, {18193, 27002}, {19565, 21223}, {19579, 20681}, {20101, 24695}, {20347, 21415}, {20715, 21281}, {20947, 30962}, {20966, 26772}, {21272, 25290}, {21330, 27291}, {21345, 24528}, {21865, 30473}, {22034, 28581}, {24443, 26029}, {24477, 28808}, {24592, 27484}, {25106, 27343}, {25120, 26077}, {25279, 26135}, {25957, 32856}, {25958, 31079}, {26580, 29667}, {29649, 32913}, {29814, 31035}, {32843, 32854}

X(32937) = anticomplement of X(982)
X(32937) = isotomic conjugate of isogonal conjugate of X(34247)


X(32938) = X(1)X(11346)∩X(2)X(18201)

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

X(32938) lies on these lines: {1, 11346}, {2, 18201}, {6, 32925}, {7, 25961}, {9, 32771}, {10, 79}, {31, 983}, {38, 27064}, {42, 190}, {43, 32845}, {44, 32914}, {63, 32918}, {81, 3971}, {100, 4090}, {144, 26034}, {171, 3952}, {210, 4418}, {238, 17165}, {312, 32912}, {319, 6535}, {320, 29687}, {321, 1757}, {329, 25760}, {518, 32930}, {524, 6057}, {537, 7191}, {726, 32911}, {748, 24349}, {750, 27538}, {756, 894}, {874, 25286}, {896, 7081}, {968, 25728}, {984, 26223}, {996, 3899}, {1046, 3701}, {1203, 24068}, {1215, 3219}, {1962, 17261}, {1999, 3994}, {2308, 32926}, {2887, 17484}, {2895, 3773}, {3175, 4663}, {3681, 3923}, {3703, 32843}, {3715, 4363}, {3729, 32860}, {3751, 32915}, {3757, 31161}, {3758, 5311}, {3782, 29850}, {3790, 32852}, {3836, 17483}, {3846, 26792}, {3873, 4011}, {3891, 16468}, {3920, 4672}, {3929, 29828}, {3938, 4676}, {3957, 4432}, {3967, 4641}, {3995, 4649}, {4038, 31035}, {4096, 4697}, {4115, 16785}, {4358, 32913}, {4383, 17155}, {4389, 29663}, {4415, 29631}, {4420, 24850}, {4422, 29851}, {4438, 31053}, {4655, 29679}, {4671, 32853}, {4693, 20011}, {4703, 29667}, {4892, 29873}, {5057, 29673}, {5220, 31330}, {5294, 32775}, {5905, 25957}, {6646, 32781}, {7226, 25496}, {7262, 26227}, {8669, 16948}, {10327, 24695}, {11019, 24709}, {15481, 31993}, {15650, 31339}, {16477, 17150}, {17063, 26688}, {17123, 17140}, {17127, 32920}, {17354, 24943}, {17594, 25734}, {17598, 20068}, {17771, 32863}, {24003, 27003}, {24325, 27065}, {24725, 29641}, {24821, 29821}, {24841, 29818}, {25960, 31018}, {26061, 27184}, {26265, 30800}, {26580, 32780}, {28609, 29857}, {29674, 32859}, {30767, 31121}


X(32939) = X(1)X(4234)∩X(2)X(45)

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

X(32939) lies on these lines: {1, 4234}, {2, 45}, {6, 3210}, {7, 345}, {8, 529}, {9, 19804}, {10, 17678}, {19, 27}, {31, 17155}, {38, 4418}, {42, 32845}, {46, 4385}, {55, 24349}, {57, 312}, {69, 2097}, {76, 19807}, {79, 30171}, {81, 4360}, {85, 3719}, {86, 18601}, {99, 2185}, {100, 17165}, {141, 26840}, {144, 14555}, {171, 726}, {192, 940}, {222, 664}, {226, 32851}, {238, 24165}, {239, 4641}, {244, 32930}, {276, 349}, {291, 24259}, {304, 1434}, {306, 320}, {313, 19811}, {314, 29766}, {319, 4001}, {321, 3218}, {329, 5233}, {344, 9776}, {346, 18141}, {354, 3685}, {484, 4692}, {497, 24280}, {514, 2985}, {516, 4514}, {518, 3996}, {527, 3687}, {536, 1999}, {537, 3961}, {553, 3912}, {579, 19792}, {595, 596}, {614, 4676}, {653, 7017}, {740, 32913}, {750, 32925}, {752, 32866}, {846, 24325}, {894, 3666}, {896, 32914}, {902, 32923}, {942, 7283}, {982, 3923}, {984, 3980}, {986, 1220}, {990, 4123}, {1043, 3868}, {1089, 3336}, {1150, 28605}, {1155, 7081}, {1211, 6646}, {1215, 17596}, {1219, 20070}, {1222, 14923}, {1233, 10030}, {1265, 6904}, {1266, 19796}, {1269, 19810}, {1281, 17611}, {1376, 3699}, {1429, 17760}, {1621, 4427}, {1730, 29529}, {1764, 30710}, {1770, 5015}, {1790, 18042}, {1836, 3705}, {1909, 22097}, {1992, 20043}, {2094, 34255}, {2108, 30982}, {2176, 24621}, {2308, 32924}, {2796, 29655}, {2887, 32857}, {2975, 17164}, {3006, 20292}, {3187, 17160}, {3219, 4359}, {3264, 19809}, {3305, 17336}, {3306, 18743}, {3501, 20917}, {3550, 32920}, {3596, 29551}, {3662, 32777}, {3663, 19786}, {3670, 13740}, {3683, 16823}, {3695, 24470}, {3703, 4645}, {3712, 29839}, {3715, 26038}, {3752, 17351}, {3757, 4640}, {3758, 5256}, {3770, 29508}, {3816, 17777}, {3821, 32780}, {3840, 18201}, {3846, 17767}, {3873, 32929}, {3891, 17126}, {3927, 9534}, {3928, 4659}, {3929, 4384}, {3936, 17483}, {3938, 24841}, {3967, 5205}, {3969, 17295}, {3971, 17122}, {3977, 5249}, {3993, 4038}, {4000, 26065}, {4011, 17063}, {4292, 7270}, {4357, 19808}, {4358, 27003}, {4362, 4650}, {4365, 32919}, {4383, 17350}, {4387, 4860}, {4388, 17768}, {4392, 24552}, {4393, 32005}, {4398, 19785}, {4413, 27538}, {4414, 32771}, {4416, 4886}, {4417, 5905}, {4432, 29820}, {4438, 17889}, {4488, 18228}, {4552, 17074}, {4647, 6763}, {4649, 4970}, {4655, 32778}, {4664, 5287}, {4671, 23958}, {4672, 29821}, {4699, 19732}, {4756, 9342}, {4850, 26223}, {4854, 29837}, {4858, 20919}, {4862, 25527}, {4887, 20106}, {4967, 19833}, {5224, 19822}, {5228, 25242}, {5253, 25253}, {5273, 31995}, {5294, 16706}, {5435, 28808}, {5437, 30568}, {5484, 5835}, {5695, 10453}, {5737, 17118}, {5739, 17347}, {5741, 17484}, {5743, 17334}, {5836, 9369}, {5846, 20101}, {5880, 29641}, {6147, 25650}, {6358, 20881}, {6360, 20477}, {6685, 17593}, {6703, 17246}, {6996, 21375}, {7262, 16825}, {7308, 25728}, {10436, 25507}, {11112, 16086}, {11351, 16816}, {11688, 16678}, {13735, 30117}, {13741, 24046}, {16687, 17142}, {16817, 31445}, {16831, 32090}, {17011, 20176}, {17013, 19738}, {17054, 17697}, {17080, 28968}, {17116, 31993}, {17143, 18206}, {17184, 32779}, {17234, 17776}, {17249, 19827}, {17273, 32782}, {17276, 27184}, {17297, 32858}, {17353, 24177}, {17365, 17778}, {17379, 20182}, {17495, 32911}, {17591, 25496}, {17601, 29670}, {17738, 24631}, {17770, 32861}, {18139, 26842}, {18739, 29423}, {19582, 25524}, {19731, 31036}, {19789, 24597}, {20237, 20920}, {21361, 29698}, {22011, 24047}, {22413, 24523}, {23512, 29069}, {24210, 28526}, {24248, 32773}, {24589, 27065}, {24715, 29673}, {24725, 29849}, {26040, 27549}, {29651, 31178}, {29846, 32856}, {32860, 32912}

X(32939) = anticomplement of X(4415)


X(32940) = X(2)X(18201)∩X(6)X(17155)

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

X(32940) lies on these lines: {2, 18201}, {6, 17155}, {7, 25957}, {10, 4880}, {31, 24349}, {38, 894}, {42, 32845}, {63, 32771}, {75, 32864}, {81, 726}, {86, 3989}, {88, 6686}, {171, 17165}, {190, 3720}, {238, 17140}, {239, 4722}, {244, 27064}, {320, 15523}, {321, 32913}, {329, 25960}, {354, 17351}, {518, 4418}, {527, 4683}, {537, 3920}, {545, 4854}, {596, 1203}, {748, 17350}, {896, 3757}, {940, 32925}, {982, 26223}, {1046, 4968}, {1086, 29850}, {1211, 5852}, {1215, 3218}, {1757, 4359}, {1961, 24821}, {2308, 32922}, {2887, 17483}, {2895, 17771}, {3219, 24325}, {3338, 25591}, {3662, 26061}, {3681, 3980}, {3703, 17365}, {3705, 24725}, {3729, 32915}, {3745, 28582}, {3750, 4427}, {3751, 32860}, {3758, 17017}, {3773, 32863}, {3782, 29631}, {3836, 26842}, {3846, 17484}, {3873, 3923}, {3927, 31339}, {3928, 29828}, {3952, 17122}, {3995, 4038}, {4042, 17118}, {4363, 24690}, {4388, 31300}, {4389, 29647}, {4392, 25496}, {4415, 29845}, {4432, 29817}, {4438, 31019}, {4641, 32914}, {4649, 17147}, {4650, 26227}, {4654, 29857}, {4655, 29667}, {4659, 17156}, {4672, 7191}, {4675, 29854}, {4860, 30957}, {4892, 29872}, {4914, 28570}, {4972, 32857}, {4981, 24342}, {5057, 29655}, {5220, 26037}, {5294, 24231}, {5905, 25760}, {6536, 17258}, {7081, 31161}, {7262, 31178}, {8013, 19797}, {9965, 26034}, {17116, 21020}, {17124, 27538}, {17126, 32920}, {17154, 17598}, {17184, 32780}, {17276, 32776}, {17354, 29677}, {17364, 32852}, {17600, 19717}, {17772, 20086}, {17778, 32848}, {17874, 20881}, {20292, 29673}, {24165, 32911}, {24627, 31264}, {24723, 29685}, {25557, 29851}, {26250, 31111}, {26267, 30800}, {26840, 32781}, {28605, 32853}, {31034, 32855}, {32778, 32859}


X(32941) = X(1)X(75)∩X(2)X(2177)

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

X(32941) lies on these lines: {1, 75}, {2, 2177}, {3, 23379}, {6, 519}, {8, 238}, {9, 4432}, {10, 1001}, {31, 16704}, {37, 4702}, {38, 32929}, {42, 24552}, {43, 3996}, {55, 3741}, {69, 752}, {87, 1120}, {100, 30942}, {141, 528}, {142, 20181}, {145, 4527}, {149, 25760}, {171, 10453}, {192, 4693}, {210, 4011}, {239, 27474}, {306, 4865}, {312, 3961}, {321, 3938}, {333, 8616}, {346, 4439}, {354, 3980}, {390, 3775}, {497, 3846}, {515, 21629}, {516, 1350}, {518, 3923}, {537, 3729}, {551, 3946}, {599, 28562}, {673, 17284}, {712, 9997}, {726, 3242}, {748, 4651}, {750, 29824}, {859, 23375}, {902, 1150}, {956, 20992}, {960, 4523}, {976, 3702}, {984, 3685}, {993, 8053}, {1125, 3755}, {1211, 3058}, {1215, 3870}, {1279, 3696}, {1376, 3840}, {1385, 24257}, {1386, 28581}, {1621, 5235}, {1698, 17341}, {1743, 4753}, {1757, 4676}, {1999, 17716}, {2345, 16503}, {2550, 3836}, {2796, 17276}, {2886, 3771}, {2887, 3434}, {2901, 30145}, {3187, 17469}, {3210, 17598}, {3214, 5192}, {3241, 7229}, {3244, 4133}, {3246, 17348}, {3286, 8666}, {3416, 17766}, {3476, 7175}, {3550, 14829}, {3616, 4743}, {3621, 16477}, {3632, 4535}, {3633, 28650}, {3661, 4366}, {3662, 24715}, {3663, 28580}, {3666, 29652}, {3679, 4595}, {3681, 32930}, {3689, 30818}, {3706, 3744}, {3722, 26227}, {3739, 24331}, {3746, 10479}, {3748, 29651}, {3749, 11679}, {3751, 4672}, {3752, 29668}, {3757, 17715}, {3772, 29656}, {3789, 4368}, {3791, 17156}, {3831, 5687}, {3873, 4418}, {3877, 3903}, {3891, 4365}, {3896, 17017}, {3898, 24394}, {3912, 20172}, {3914, 26128}, {3920, 32915}, {3925, 29642}, {3957, 32771}, {3966, 21085}, {3969, 32854}, {3971, 4387}, {4022, 24464}, {4096, 30568}, {4154, 23407}, {4267, 5248}, {4310, 4373}, {4361, 4709}, {4383, 4685}, {4384, 4732}, {4392, 32845}, {4407, 17257}, {4413, 4871}, {4420, 25591}, {4428, 5737}, {4429, 29637}, {4438, 4847}, {4483, 4653}, {4514, 32778}, {4669, 8692}, {4671, 32927}, {4682, 4891}, {4720, 27644}, {4759, 16885}, {4803, 16690}, {4863, 29673}, {4970, 17599}, {4972, 24943}, {4974, 7290}, {5014, 15523}, {5132, 8715}, {5156, 5255}, {5266, 17733}, {5284, 26037}, {5564, 16801}, {5772, 12630}, {5936, 8236}, {6048, 13741}, {6542, 14621}, {6682, 17594}, {7191, 32860}, {7220, 14942}, {7232, 24692}, {11680, 29846}, {12782, 24515}, {15571, 20990}, {16483, 27623}, {16487, 16833}, {16491, 16834}, {16497, 16829}, {16706, 29660}, {16817, 31327}, {17018, 32772}, {17023, 20162}, {17024, 32924}, {17116, 31178}, {17126, 32919}, {17127, 32864}, {17232, 31151}, {17233, 20179}, {17282, 25351}, {17289, 29659}, {17315, 20159}, {17345, 28534}, {17368, 20180}, {17372, 28538}, {17389, 20132}, {17450, 26627}, {17597, 24165}, {17601, 24627}, {17718, 25385}, {17764, 24248}, {17767, 24280}, {17771, 24695}, {18481, 29040}, {19804, 29820}, {20075, 26034}, {20131, 29574}, {20142, 29617}, {20153, 29622}, {20174, 30117}, {20470, 25440}, {21241, 30811}, {21282, 31017}, {24586, 31027}, {24596, 30821}, {24789, 29672}, {25694, 25697}, {26724, 29853}, {27480, 29570}, {28605, 32923}, {29674, 32850}, {29676, 32851}, {29686, 32774}, {29815, 32928}, {29832, 32848}, {29840, 32855}, {30816, 31031}, {32773, 32783}

X(32941) = anticomplement of X(4085)


X(32942) = X(1)X(312)∩X(2)X(11)

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

X(32942) lies on these lines: {1, 312}, {2, 11}, {6, 10453}, {8, 1191}, {10, 4514}, {29, 1842}, {31, 14829}, {33, 11109}, {35, 19864}, {36, 4234}, {38, 190}, {43, 3996}, {56, 4195}, {58, 29766}, {63, 4676}, {75, 614}, {81, 29824}, {86, 310}, {141, 4388}, {145, 3974}, {171, 3840}, {192, 4387}, {238, 333}, {239, 3706}, {244, 4418}, {321, 7191}, {354, 894}, {404, 23383}, {474, 25492}, {496, 17698}, {518, 27064}, {612, 18743}, {664, 24291}, {726, 17598}, {740, 29821}, {748, 2209}, {750, 30957}, {846, 4432}, {902, 32918}, {904, 7018}, {958, 17697}, {964, 3616}, {968, 29826}, {976, 25591}, {982, 3923}, {984, 4011}, {993, 13735}, {996, 1120}, {997, 4123}, {999, 11354}, {1008, 18134}, {1010, 1125}, {1015, 24275}, {1043, 1193}, {1100, 4891}, {1150, 17127}, {1279, 3757}, {1386, 1999}, {1421, 6358}, {1479, 16062}, {1616, 5793}, {1699, 13727}, {1836, 3662}, {1914, 26244}, {1978, 3112}, {2308, 32919}, {2887, 29637}, {2975, 11319}, {2999, 3886}, {3210, 5695}, {3315, 17140}, {3329, 3703}, {3583, 17677}, {3661, 3966}, {3666, 3685}, {3677, 3729}, {3698, 25965}, {3699, 3961}, {3702, 5262}, {3705, 17721}, {3744, 7081}, {3750, 6685}, {3759, 17156}, {3771, 17717}, {3773, 32866}, {3831, 5255}, {3846, 30832}, {3871, 26030}, {3873, 26223}, {3891, 4671}, {3896, 17012}, {3914, 16706}, {3920, 4358}, {3944, 26128}, {3969, 32842}, {3980, 17063}, {3993, 17600}, {3995, 29823}, {4042, 17349}, {4201, 6284}, {4203, 16678}, {4307, 18141}, {4329, 27386}, {4357, 4872}, {4359, 7292}, {4360, 17017}, {4365, 17160}, {4415, 17777}, {4438, 29676}, {4640, 24627}, {4666, 20173}, {4672, 32913}, {4683, 17273}, {4693, 4970}, {4742, 17015}, {4847, 17353}, {4850, 32929}, {4854, 17302}, {4857, 19881}, {4865, 29674}, {4871, 17122}, {4884, 17340}, {4966, 17778}, {4981, 27065}, {5014, 29679}, {5057, 17184}, {5248, 19270}, {5253, 11115}, {5259, 11110}, {5268, 30829}, {5269, 30567}, {5272, 19804}, {5293, 25079}, {5294, 26015}, {5303, 17539}, {5372, 30653}, {5550, 16454}, {5718, 29839}, {5749, 10580}, {7174, 30568}, {7244, 21443}, {7290, 11679}, {7770, 27248}, {8616, 29827}, {9668, 11359}, {10436, 10582}, {10449, 16466}, {10527, 17526}, {11108, 19853}, {11393, 17555}, {13588, 20470}, {13742, 19843}, {14007, 25512}, {14621, 31028}, {15523, 17285}, {16061, 18758}, {16067, 23304}, {16468, 32853}, {16478, 17733}, {16823, 31993}, {16828, 25542}, {17125, 26037}, {17135, 32911}, {17165, 24841}, {17279, 29641}, {17283, 25957}, {17295, 32852}, {17305, 32776}, {17351, 21342}, {17356, 21949}, {17368, 29843}, {17469, 17763}, {17536, 19874}, {17592, 29650}, {17597, 24349}, {17602, 29838}, {17682, 30110}, {17686, 27097}, {17715, 29670}, {17716, 29649}, {17719, 29656}, {17720, 29634}, {17722, 29671}, {17768, 26840}, {17783, 30824}, {17785, 29858}, {18056, 21615}, {18057, 18140}, {18064, 18152}, {19684, 29814}, {19869, 30384}, {20876, 25494}, {21334, 25898}, {24169, 24715}, {24217, 29635}, {24239, 32851}, {24295, 29655}, {24325, 29820}, {24358, 25368}, {24477, 26065}, {24549, 30545}, {24703, 27184}, {24943, 25760}, {24997, 26671}, {25385, 29672}, {25524, 26093}, {25529, 29860}, {29473, 29754}, {29666, 32774}, {29686, 32775}, {29818, 32923}, {29819, 32928}, {29832, 32862}, {29866, 30834}, {31136, 32864}, {31241, 32917}, {31359, 31435}


X(32943) = X(1)X(321)∩X(2)X(2177)

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

X(32943) lies on these lines: {1, 321}, {2, 2177}, {8, 748}, {10, 5284}, {11, 29846}, {31, 10453}, {38, 3685}, {55, 30942}, {100, 3840}, {141, 3058}, {149, 2887}, {171, 29824}, {238, 17135}, {306, 32844}, {312, 3938}, {333, 31136}, {350, 18064}, {354, 4418}, {390, 26034}, {497, 25760}, {518, 32930}, {519, 5315}, {551, 5333}, {614, 3886}, {673, 30821}, {740, 7191}, {752, 32863}, {899, 3996}, {902, 14829}, {982, 32845}, {1001, 19732}, {1043, 1201}, {1125, 26724}, {1150, 8616}, {1215, 3957}, {1279, 3706}, {1376, 30957}, {1621, 3741}, {1999, 17469}, {2321, 16488}, {2550, 25961}, {2886, 29632}, {3214, 13741}, {3219, 4432}, {3242, 4387}, {3315, 24165}, {3434, 25957}, {3452, 24709}, {3454, 4857}, {3550, 31137}, {3666, 4702}, {3681, 4011}, {3720, 5263}, {3722, 7081}, {3744, 17763}, {3745, 4891}, {3771, 11680}, {3772, 29638}, {3811, 25591}, {3831, 3871}, {3873, 3923}, {3896, 29821}, {3915, 10449}, {3924, 4673}, {3925, 29851}, {3961, 4358}, {3969, 32866}, {4359, 29820}, {4360, 29819}, {4365, 29818}, {4366, 31027}, {4420, 25079}, {4423, 26037}, {4429, 29677}, {4514, 15523}, {4649, 19743}, {4651, 17123}, {4671, 32920}, {4676, 32912}, {4693, 17147}, {4850, 29668}, {4863, 17279}, {4865, 32858}, {4914, 17229}, {4972, 29637}, {4975, 30115}, {5014, 29674}, {5278, 15485}, {5299, 21070}, {5687, 27639}, {5695, 17155}, {6057, 9053}, {7290, 17156}, {8692, 19723}, {10389, 29828}, {10707, 30831}, {11235, 30811}, {15571, 16687}, {16481, 29617}, {16823, 21020}, {16971, 24275}, {17018, 25496}, {17024, 32921}, {17061, 29836}, {17124, 30947}, {17127, 32853}, {17233, 32854}, {17289, 29685}, {17600, 27804}, {17715, 26227}, {17720, 29848}, {17721, 29849}, {19786, 29686}, {24210, 32775}, {24325, 29817}, {24387, 25645}, {24392, 29857}, {24596, 30822}, {24602, 31028}, {24789, 29853}, {24943, 32773}, {28606, 29652}, {29655, 32779}, {29660, 32774}, {29687, 32850}, {29835, 32780}, {29840, 32848}, {30837, 31031}


X(32944) = X(1)X(996)∩X(2)X(31)

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

X(32944) lies on these lines: {1, 996}, {2, 31}, {6, 30942}, {9, 29826}, {10, 5315}, {11, 2330}, {35, 20108}, {38, 27064}, {43, 24552}, {58, 19864}, {81, 3840}, {86, 799}, {141, 32843}, {149, 4085}, {244, 894}, {312, 17017}, {321, 29821}, {333, 31241}, {551, 31171}, {614, 32771}, {740, 17012}, {896, 24627}, {899, 5263}, {908, 1125}, {940, 30957}, {964, 978}, {982, 26223}, {1001, 16373}, {1010, 27627}, {1150, 16468}, {1193, 13740}, {1201, 1220}, {1215, 7191}, {1386, 17763}, {1621, 6685}, {1935, 26126}, {2163, 3624}, {2308, 14829}, {2886, 29850}, {2999, 32860}, {3006, 17722}, {3120, 16706}, {3218, 4672}, {3219, 6682}, {3454, 19881}, {3618, 11269}, {3662, 24725}, {3666, 32930}, {3681, 29652}, {3705, 26061}, {3741, 32864}, {3752, 4418}, {3757, 31264}, {3772, 29852}, {3773, 32842}, {3816, 26890}, {3821, 5057}, {3825, 25441}, {3835, 18108}, {3873, 29668}, {3923, 4850}, {3932, 17726}, {3936, 29637}, {3944, 32774}, {3952, 29823}, {3995, 17600}, {4003, 17351}, {4011, 28606}, {4038, 19717}, {4383, 31330}, {4414, 4676}, {4417, 24943}, {4427, 17593}, {4438, 29680}, {4519, 4852}, {4649, 29824}, {4657, 4679}, {4670, 9318}, {4671, 17025}, {4697, 27003}, {4865, 29679}, {5219, 29855}, {5255, 26030}, {5256, 32915}, {5294, 24239}, {5297, 24003}, {5311, 18743}, {5333, 25501}, {5718, 29632}, {5741, 32783}, {5774, 16466}, {7081, 17469}, {7290, 29828}, {7292, 24325}, {7741, 20083}, {8054, 18170}, {8167, 19701}, {9345, 17379}, {10448, 17697}, {11358, 27639}, {11680, 25453}, {15485, 29825}, {15668, 16355}, {16477, 16704}, {16484, 29822}, {16796, 17721}, {16948, 17557}, {17023, 24709}, {17024, 32920}, {17056, 29851}, {17165, 17598}, {17277, 30970}, {17279, 17723}, {17280, 32848}, {17302, 17777}, {17353, 29639}, {17445, 17477}, {17599, 32925}, {17602, 29834}, {17718, 29638}, {17719, 26230}, {17720, 29636}, {17724, 29836}, {17725, 29831}, {18134, 29677}, {19684, 26102}, {19786, 29684}, {20132, 30967}, {20292, 24169}, {21764, 26244}, {24217, 29829}, {24295, 32779}, {24342, 24589}, {24542, 29640}, {24703, 32776}, {25378, 29598}, {26128, 29666}, {27131, 29648}, {28650, 31137}, {29663, 32773}, {29819, 32926}, {29849, 32777}, {29858, 30834}

X(32944) = complement of X(33086)


X(32945) = X(1)X(3896)∩X(2)X(2177)

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

X(32945) lies on these lines: {1, 3896}, {2, 2177}, {8, 31}, {10, 1621}, {38, 32845}, {42, 3996}, {43, 24552}, {44, 4113}, {55, 5737}, {75, 3938}, {81, 519}, {100, 3741}, {149, 3846}, {171, 17135}, {210, 32930}, {238, 4651}, {239, 17469}, {321, 3961}, {333, 902}, {497, 25960}, {516, 4683}, {518, 4418}, {528, 1211}, {594, 1914}, {612, 3886}, {740, 3920}, {750, 10453}, {752, 2895}, {756, 3685}, {846, 4981}, {873, 25303}, {966, 10385}, {984, 32929}, {996, 4677}, {1001, 26037}, {1043, 10458}, {1150, 3550}, {1206, 2295}, {1215, 3935}, {1376, 30942}, {1962, 16830}, {2280, 2345}, {2321, 5276}, {2550, 25957}, {2886, 29846}, {3052, 4042}, {3058, 5743}, {3158, 29828}, {3187, 17716}, {3214, 13740}, {3240, 25496}, {3242, 17155}, {3295, 19282}, {3434, 25760}, {3679, 5278}, {3681, 3923}, {3687, 32844}, {3696, 3744}, {3702, 5293}, {3706, 17763}, {3722, 3757}, {3739, 3748}, {3745, 28581}, {3749, 5271}, {3772, 29848}, {3775, 20095}, {3826, 29851}, {3870, 32771}, {3873, 3980}, {3914, 32775}, {3915, 9534}, {3925, 29632}, {3957, 24325}, {3969, 32847}, {3979, 24342}, {3995, 4693}, {4046, 5846}, {4126, 17340}, {4360, 29816}, {4365, 32926}, {4413, 30957}, {4428, 19732}, {4429, 24943}, {4432, 27065}, {4457, 4974}, {4649, 20011}, {4660, 32782}, {4685, 32911}, {4714, 30117}, {4716, 17150}, {4850, 29652}, {4871, 9342}, {4972, 32783}, {5014, 32778}, {5015, 20653}, {5192, 6048}, {5266, 27368}, {5269, 17156}, {5695, 32925}, {8715, 10479}, {14829, 31136}, {15523, 32850}, {16706, 29686}, {17122, 29824}, {17125, 26038}, {17126, 32853}, {17163, 20045}, {17184, 24715}, {17278, 29853}, {17281, 30615}, {17284, 24596}, {17495, 17598}, {17766, 21085}, {17784, 26034}, {19808, 29685}, {20181, 30949}, {21027, 29689}, {21241, 30831}, {21282, 31037}, {21805, 27064}, {23958, 24344}, {24589, 29820}, {24602, 31027}, {24693, 27186}, {24789, 29638}, {26724, 29672}, {28562, 31143}, {28605, 32920}, {29673, 32779}, {29690, 32851}, {29815, 32921}, {29832, 32855}


X(32946) = X(1)X(1330)∩X(2)X(2308)

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

X(32946) lies on these lines: {1, 1330}, {2, 2308}, {6, 2887}, {7, 24165}, {9, 29653}, {10, 5739}, {31, 3771}, {37, 4703}, {38, 32859}, {42, 4660}, {43, 4645}, {46, 17748}, {55, 752}, {63, 17770}, {69, 3741}, {75, 32861}, {81, 25760}, {141, 25496}, {171, 4417}, {193, 21241}, {226, 4362}, {238, 18134}, {239, 17889}, {306, 3923}, {312, 32846}, {320, 982}, {321, 24725}, {329, 3971}, {345, 24695}, {516, 4028}, {518, 4865}, {519, 1478}, {524, 2886}, {540, 993}, {726, 5905}, {740, 1836}, {748, 18139}, {750, 5741}, {758, 26893}, {894, 32778}, {902, 20064}, {908, 29649}, {940, 3846}, {1215, 3416}, {1386, 26128}, {1745, 3811}, {1757, 29641}, {1999, 3944}, {2177, 4450}, {2550, 4685}, {2650, 5016}, {2895, 31330}, {2999, 24169}, {3006, 32912}, {3120, 3187}, {3178, 12514}, {3210, 32857}, {3218, 29849}, {3219, 29643}, {3550, 20101}, {3662, 29821}, {3666, 4655}, {3687, 3980}, {3705, 7779}, {3742, 17376}, {3751, 29673}, {3758, 32780}, {3769, 17719}, {3772, 3791}, {3782, 32921}, {3821, 5256}, {3836, 4383}, {3868, 25306}, {3870, 17766}, {3873, 29844}, {3879, 24210}, {3883, 29651}, {3891, 32856}, {3912, 4011}, {3966, 24325}, {4001, 29639}, {4038, 17378}, {4062, 32929}, {4090, 10327}, {4357, 29644}, {4365, 20017}, {4386, 10026}, {4389, 17600}, {4438, 4641}, {4640, 28570}, {4648, 25501}, {4649, 32773}, {4650, 32851}, {4672, 32777}, {4683, 28606}, {4851, 24703}, {4871, 18141}, {4884, 5852}, {4970, 24248}, {4972, 31134}, {4974, 24789}, {5057, 32915}, {5233, 17122}, {5249, 16825}, {5272, 17298}, {5311, 26580}, {5718, 32916}, {5846, 32920}, {6515, 26013}, {6542, 9902}, {6679, 30811}, {6682, 17723}, {6685, 26034}, {7290, 29672}, {7759, 20544}, {8167, 17313}, {8616, 29839}, {10436, 23812}, {11679, 25385}, {11680, 32919}, {12047, 17733}, {14829, 17717}, {14996, 29845}, {15523, 26223}, {16475, 25527}, {16704, 24892}, {17011, 32776}, {17017, 17184}, {17031, 30985}, {17123, 17234}, {17126, 29846}, {17127, 29632}, {17147, 17491}, {17155, 17483}, {17165, 32854}, {17275, 27798}, {17300, 26102}, {17361, 17722}, {17363, 20536}, {17484, 32925}, {17485, 32453}, {17591, 26840}, {17592, 24723}, {17718, 28498}, {17763, 31053}, {18904, 23543}, {19717, 29647}, {20011, 21282}, {20075, 28562}, {20090, 29837}, {20292, 32860}, {20539, 21093}, {21747, 29865}, {24349, 32866}, {24545, 26579}, {24943, 31017}, {25451, 25649}, {25957, 32911}, {25958, 29631}, {25959, 29850}, {26131, 31339}, {27064, 29674}, {27065, 29854}, {29834, 30991}, {29842, 32775}, {29866, 30653}, {30942, 32863}, {31019, 32914}, {32772, 32782}, {32858, 32930}


X(32947) = X(1)X(6327)∩X(2)X(902)

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

X(32947) lies on these lines: {1, 6327}, {2, 902}, {8, 4365}, {10, 3583}, {11, 32918}, {31, 29631}, {38, 4514}, {42, 4388}, {55, 25760}, {81, 752}, {100, 3846}, {141, 3058}, {149, 3741}, {171, 4450}, {192, 32854}, {238, 4972}, {497, 26034}, {516, 2941}, {518, 4683}, {519, 2895}, {528, 1211}, {536, 4914}, {540, 16474}, {748, 4429}, {756, 32850}, {846, 3006}, {894, 29685}, {968, 29643}, {984, 5014}, {1001, 25957}, {1201, 4201}, {1215, 5057}, {1376, 25960}, {1621, 2887}, {1699, 29828}, {1836, 32771}, {2177, 4417}, {2292, 5015}, {2550, 6818}, {2886, 32917}, {3120, 3757}, {3218, 29655}, {3219, 29673}, {3416, 32915}, {3434, 31330}, {3454, 3746}, {3666, 32844}, {3681, 4703}, {3685, 15523}, {3705, 4414}, {3720, 4645}, {3744, 32775}, {3745, 28566}, {3749, 29848}, {3750, 3936}, {3771, 25958}, {3782, 32923}, {3821, 7191}, {3836, 5284}, {3873, 4655}, {3877, 25308}, {3883, 3914}, {3896, 14459}, {3915, 16062}, {3920, 4425}, {3923, 29667}, {3938, 27184}, {3944, 26227}, {3961, 26580}, {3966, 32860}, {3969, 4693}, {3989, 9791}, {3995, 28599}, {4011, 29679}, {4026, 32772}, {4030, 4415}, {4085, 32911}, {4090, 26792}, {4357, 20553}, {4359, 24715}, {4392, 29844}, {4423, 25961}, {4428, 30811}, {4432, 28595}, {4512, 29857}, {4643, 4863}, {4676, 26061}, {4697, 28494}, {4799, 24357}, {4854, 5846}, {4865, 28606}, {4968, 24851}, {4970, 32842}, {4981, 24697}, {5051, 5255}, {5269, 29847}, {5278, 32865}, {5737, 31140}, {5793, 12953}, {6536, 16830}, {7290, 29852}, {7292, 24169}, {10459, 26117}, {11319, 19879}, {11359, 16483}, {11680, 32916}, {16060, 30042}, {16484, 18139}, {17126, 29635}, {17127, 25453}, {17140, 32857}, {17147, 32866}, {17155, 24248}, {17302, 29819}, {17449, 26840}, {17469, 19786}, {17594, 29849}, {17763, 24210}, {18134, 31134}, {20064, 29829}, {20101, 29837}, {20292, 24325}, {24331, 27186}, {24552, 32784}, {24692, 26842}, {25527, 29638}, {25959, 29642}, {26128, 29836}, {26223, 29659}, {29651, 31019}, {29670, 31053}, {29835, 32913}, {29864, 30652}, {29868, 30653}, {32778, 32929}


X(32948) = X(2)X(902)∩X(8)X(17155)

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

X(32948) lies on these lines: {2, 902}, {8, 17155}, {10, 191}, {31, 4429}, {38, 32850}, {42, 4645}, {43, 6327}, {55, 25957}, {81, 4085}, {100, 2887}, {149, 3840}, {165, 29857}, {171, 4972}, {210, 4683}, {238, 4450}, {244, 4514}, {321, 24715}, {497, 30957}, {516, 32930}, {519, 32863}, {612, 32776}, {750, 29845}, {752, 32911}, {756, 24723}, {899, 4388}, {968, 29854}, {982, 5014}, {986, 5300}, {1001, 25961}, {1086, 4030}, {1150, 32865}, {1215, 20292}, {1330, 3214}, {1376, 25760}, {1621, 3836}, {1647, 27002}, {1738, 32914}, {2177, 18134}, {2308, 20101}, {2550, 6817}, {2886, 32918}, {2895, 4685}, {3006, 17596}, {3120, 7081}, {3210, 32854}, {3218, 29673}, {3416, 32860}, {3434, 30942}, {3452, 9458}, {3501, 26085}, {3662, 3938}, {3681, 4655}, {3683, 3823}, {3685, 29687}, {3701, 24851}, {3703, 32845}, {3729, 17007}, {3744, 29836}, {3748, 3834}, {3749, 29638}, {3750, 18139}, {3752, 32844}, {3771, 25959}, {3782, 32927}, {3821, 3920}, {3896, 32846}, {3914, 17763}, {3923, 29679}, {3925, 32917}, {3961, 17184}, {3980, 29667}, {4090, 17484}, {4113, 17344}, {4126, 17334}, {4201, 10459}, {4202, 5255}, {4413, 25960}, {4414, 29641}, {4417, 31134}, {4421, 30811}, {4425, 5297}, {4642, 7270}, {4850, 4865}, {4894, 24046}, {5015, 24443}, {5016, 24440}, {5233, 9350}, {5263, 32781}, {5269, 29636}, {5846, 32924}, {5880, 32771}, {6057, 28530}, {6653, 31027}, {7191, 17766}, {7791, 30036}, {10327, 24248}, {11115, 19879}, {12699, 25591}, {14459, 32852}, {16468, 20064}, {16706, 17469}, {17123, 24988}, {17126, 25453}, {17147, 32847}, {17165, 32857}, {17276, 30615}, {17282, 29853}, {17291, 29686}, {17302, 29816}, {17483, 24692}, {17495, 28599}, {17591, 29832}, {17594, 29643}, {17716, 29834}, {17889, 26227}, {19998, 20290}, {20533, 30821}, {24326, 24699}, {24602, 26590}, {24627, 29690}, {25351, 26724}, {25527, 29848}, {27003, 29655}, {27186, 29651}, {28595, 32779}, {29670, 31019}, {29674, 32929}


X(32949) = X(1)X(6327)∩X(2)X(2308)

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

X(32949) lies on these lines: {1, 6327}, {2, 2308}, {6, 25957}, {7, 17155}, {9, 29854}, {10, 2895}, {31, 18134}, {37, 4683}, {38, 320}, {42, 4645}, {43, 31034}, {57, 29849}, {63, 29643}, {69, 31330}, {75, 32852}, {79, 2901}, {81, 2887}, {141, 32772}, {171, 3936}, {226, 17763}, {238, 18139}, {306, 4418}, {312, 24725}, {319, 21020}, {321, 32846}, {354, 17376}, {519, 11551}, {524, 3925}, {540, 5251}, {614, 17298}, {726, 17483}, {740, 20292}, {748, 17234}, {750, 4417}, {752, 1621}, {894, 15523}, {902, 20101}, {940, 25760}, {984, 32859}, {1086, 32924}, {1836, 4851}, {1961, 26580}, {1962, 24723}, {1999, 3120}, {2650, 7270}, {2886, 32919}, {3006, 32913}, {3187, 17889}, {3218, 29671}, {3219, 17770}, {3416, 32771}, {3662, 17017}, {3683, 28570}, {3703, 17365}, {3706, 17374}, {3720, 4388}, {3741, 32863}, {3745, 32775}, {3748, 28566}, {3750, 4450}, {3758, 26061}, {3771, 17126}, {3782, 32928}, {3821, 17011}, {3836, 32911}, {3868, 25308}, {3873, 4865}, {3879, 3914}, {3888, 5208}, {3896, 24715}, {3912, 32930}, {3923, 32858}, {3957, 17766}, {3966, 4675}, {3971, 17484}, {3989, 6646}, {3995, 17491}, {4078, 17781}, {4359, 32861}, {4362, 31019}, {4365, 6542}, {4383, 25961}, {4387, 17311}, {4423, 17313}, {4425, 17019}, {4447, 21319}, {4649, 4972}, {4655, 28606}, {4660, 17018}, {4697, 32779}, {4722, 21026}, {4854, 17390}, {4970, 24692}, {4974, 26724}, {5233, 17124}, {5247, 30055}, {5249, 5847}, {5269, 29848}, {5311, 27184}, {5712, 26034}, {5718, 32918}, {5739, 26037}, {5741, 17122}, {5846, 32923}, {5880, 14459}, {5905, 32925}, {6536, 16826}, {7184, 17187}, {7232, 17599}, {7290, 29853}, {7613, 20043}, {8616, 20064}, {10453, 17375}, {11246, 32845}, {12609, 27368}, {14996, 25958}, {16475, 29852}, {16825, 27186}, {17012, 24169}, {17056, 32917}, {17127, 29642}, {17140, 32866}, {17147, 32857}, {17165, 32847}, {17176, 30941}, {17232, 29677}, {17291, 29684}, {17364, 29641}, {17378, 31134}, {17379, 29647}, {17449, 29840}, {17469, 29836}, {17776, 24695}, {17871, 20930}, {18141, 30957}, {19684, 32784}, {19717, 29633}, {21747, 29869}, {24165, 26842}, {24349, 32854}, {24627, 29688}, {25453, 25959}, {25527, 29636}, {26098, 30942}, {26128, 29834}, {26223, 29674}, {27064, 29687}, {29649, 31053}, {29866, 30652}, {29870, 30653}, {30962, 30989}, {31017, 32783}, {32856, 32926}


X(32950) = X(1)X(4450)∩X(2)X(1155)

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

X(32950) lies on these lines: {1, 4450}, {2, 1155}, {31, 3821}, {38, 4660}, {42, 4655}, {43, 4683}, {46, 5051}, {55, 17184}, {63, 4972}, {65, 17676}, {69, 3896}, {100, 27184}, {141, 32929}, {171, 29847}, {190, 29679}, {320, 17018}, {321, 24248}, {516, 24552}, {748, 24169}, {750, 4425}, {752, 17017}, {846, 25957}, {896, 25453}, {899, 4703}, {902, 26128}, {964, 1770}, {968, 18139}, {986, 5016}, {1054, 25960}, {1150, 3914}, {1376, 26580}, {1386, 20064}, {1621, 3662}, {1738, 5278}, {2550, 4981}, {2887, 4414}, {3052, 26230}, {3120, 32916}, {3218, 32773}, {3219, 4429}, {3305, 24988}, {3416, 17147}, {3550, 32775}, {3647, 19846}, {3663, 3891}, {3666, 6327}, {3681, 6646}, {3744, 17235}, {3755, 4001}, {3782, 26227}, {3869, 4201}, {3870, 17274}, {3873, 26840}, {3920, 4389}, {3923, 32781}, {3936, 17594}, {3944, 32918}, {3966, 17495}, {3996, 17273}, {4026, 11246}, {4085, 32912}, {4138, 30834}, {4202, 12514}, {4388, 4850}, {4392, 4514}, {4418, 32784}, {4419, 10327}, {4427, 32777}, {4432, 29677}, {4442, 11679}, {4463, 18252}, {4512, 24542}, {4643, 4651}, {4645, 28606}, {4650, 29631}, {4672, 29663}, {4697, 29647}, {4741, 20012}, {4799, 25349}, {4851, 27804}, {4892, 29678}, {4970, 32852}, {5484, 14923}, {6685, 24725}, {7226, 32850}, {7262, 29850}, {11680, 24627}, {12609, 16342}, {16347, 28628}, {16706, 17127}, {17126, 19786}, {17150, 17301}, {17165, 17276}, {17211, 25581}, {17302, 20101}, {17305, 29648}, {17591, 32844}, {17593, 29849}, {17596, 25760}, {17601, 29846}, {17768, 26223}, {17889, 32917}, {24697, 26037}, {24709, 31242}, {24715, 31330}, {25958, 32851}, {29670, 32856}, {29671, 31134}, {29854, 31151}, {32771, 32857}, {32778, 32845}

leftri

Points h SB SC + f(a,b,c) on the Euler line: X(32951)-X(33063)

rightri

Centers X(32951)-X(33063) were contributed by Clark Kimberling, June 21, 2019:


X(32951) = (name pending)

Barycentrics    SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 + 5*b^4 - 2*b^2*c^2 + 5*c^4 : :
X(32951) = 3 (a^4+b^4+c^4) X[2] - S^2 X[4]

As a point on the Euler line, X(32951) has Shinagawa coefficients (2(E+F)2-2S2,-S2).

X(32951) lies on these lines: {2, 3}, {6, 32823}, {69, 7828}, {141, 10542}, {315, 7942}, {388, 30103}, {497, 30104}, {626, 7735}, {1007, 7803}, {1285, 7934}, {1992, 7856}, {2030, 5207}, {2548, 7852}, {2549, 7874}, {3589, 31404}, {3618, 7752}, {3619, 7944}, {3767, 7794}, {3788, 7738}, {3926, 7851}, {5024, 32835}, {5230, 30816}, {5254, 32817}, {5286, 7778}, {5304, 7776}, {5319, 7821}, {6337, 7790}, {6392, 7881}, {6722, 7914}, {7736, 7834}, {7739, 7888}, {7758, 7817}, {7763, 7919}, {7772, 9770}, {7774, 7932}, {7789, 32822}, {7792, 32816}, {7795, 7844}, {7800, 7886}, {7868, 18840}, {7870, 9741}, {7889, 31415}, {7912, 16989}, {7913, 31401}, {7917, 11008}, {7930, 11185}, {7935, 21843}, {7938, 17008}, {15048, 32831}, {16984, 20065}

X(32951) = complement of X(33181)
X(32951) = {X(2),X(3)}-harmonic conjugate of X(33189)
X(32951) = {X(2),X(4)}-harmonic conjugate of X(14069)
X(32951) = {X(2),X(5)}-harmonic conjugate of X(16045)
X(32951) = {X(2),X(20)}-harmonic conjugate of X(32954)
X(32951) = orthocentroidal-circle-inverse of X(14069)


X(32952) = (name pending)

Barycentrics    SB SC + 2(a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 + 7*b^4 + 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(32952) has Shinagawa coefficients (4(E+F)2-4S2,S2).

X(32952) lies on these lines: {2, 3}, {69, 7930}, {230, 18840}, {626, 1285}, {1007, 7846}, {1056, 30104}, {1058, 30103}, {1992, 7909}, {3619, 7857}, {3815, 18841}, {6680, 7896}, {7735, 7794}, {7736, 7874}, {7738, 7852}, {7792, 32818}, {7851, 32822}, {7863, 9741}, {14482, 32831}

X(32952) = complement of X(33182)
X(32952) = {X(2),X(3)}-harmonic conjugate of X(33194)
X(32952) = {X(2),X(4)}-harmonic conjugate of X(32953)
X(32952) = orthocentroidal-circle-inverse of X(32953)


X(32953) = (name pending)

Barycentrics    SB SC - 2(a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 + 9*b^4 - 2*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(32953) has Shinagawa coefficients (4(E+F)2-4S2,-S2).

X(32953) lies on these lines: {2, 3}, {69, 7942}, {1056, 30103}, {1058, 30104}, {1285, 6680}, {3618, 7899}, {6337, 7919}, {7735, 7826}, {7736, 7852}, {7738, 7874}, {7765, 9741}, {7792, 32823}, {7829, 9770}, {7851, 32817}, {18841, 31404}

X(32953) = complement of X(33183)
X(32953) = {X(2),X(3)}-harmonic conjugate of X(33195)
X(32953) = {X(2),X(4)}-harmonic conjugate of X(32952)
X(32953) = orthocentroidal-circle-inverse of X(32952)


X(32954) = (name pending)

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

As a point on the Euler line, X(32954) has Shinagawa coefficients (2(E+F)2-3S2,S2).

X(32954) lies on these lines: {2, 3}, {6, 3788}, {32, 7776}, {55, 30103}, {56, 30104}, {83, 7940}, {99, 7851}, {183, 7832}, {187, 7784}, {194, 16984}, {230, 7795}, {287, 26944}, {315, 1384}, {325, 30435}, {385, 7881}, {574, 7852}, {599, 7780}, {620, 5013}, {626, 3053}, {641, 19146}, {642, 19145}, {754, 22331}, {758, 30146}, {999, 26686}, {1078, 7868}, {1351, 20576}, {1617, 28773}, {1691, 3763}, {1975, 7828}, {1992, 32825}, {2021, 31239}, {2099, 30120}, {3094, 6683}, {3295, 26629}, {3589, 6387}, {3618, 6393}, {3734, 7886}, {3767, 7789}, {3926, 5305}, {3933, 7735}, {3972, 7773}, {4045, 15815}, {5007, 7888}, {5008, 7903}, {5023, 7761}, {5024, 7803}, {5206, 7853}, {5210, 7830}, {5286, 6390}, {5304, 32818}, {5306, 7758}, {5309, 7863}, {5346, 7813}, {5976, 7786}, {6144, 7916}, {6179, 7788}, {6337, 15048}, {7746, 7820}, {7749, 7822}, {7751, 7880}, {7752, 15484}, {7754, 7806}, {7755, 7801}, {7760, 7870}, {7762, 21309}, {7763, 7792}, {7765, 8716}, {7766, 7947}, {7769, 7846}, {7771, 7944}, {7777, 10583}, {7781, 7817}, {7782, 7919}, {7783, 7932}, {7787, 7925}, {7793, 7879}, {7794, 8667}, {7796, 14614}, {7797, 7891}, {7799, 7856}, {7804, 7862}, {7805, 7908}, {7808, 31489}, {7814, 12150}, {7816, 7844}, {7827, 11165}, {7872, 32456}, {7878, 11163}, {7889, 31274}, {7935, 15513}, {10349, 11842}, {17599, 30118}, {18841, 32871}, {18907, 32816}, {20172, 31493}, {29473, 30811}

X(32954) = midpoint of X(2) and X(33224)
X(32954) = complement of X(14064)
X(32954) = anticomplement of X(33186)
X(32954) = {X(2),X(3)}-harmonic conjugate of X(7866)
X(32954) = {X(2),X(4)}-harmonic conjugate of X(8361)
X(32954) = {X(2),X(20)}-harmonic conjugate of X(32951)
X(32954) = orthocentroidal-circle-inverse of X(8361)


X(32955) = (name pending)

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

As a point on the Euler line, X(32955) has Shinagawa coefficients (2(E+F)2-4S2,-S2).

X(32955) lies on these lines: {2, 3}, {69, 7899}, {115, 32822}, {597, 31407}, {1007, 7828}, {1285, 7773}, {1992, 7814}, {2548, 31275}, {3618, 7942}, {3767, 7813}, {3788, 32457}, {5319, 9770}, {5485, 7870}, {6722, 7795}, {7735, 7759}, {7736, 7829}, {7738, 7844}, {7797, 14482}, {7851, 32829}, {7857, 32006}, {7868, 32838}, {18840, 32832}, {10588, 30103}, {10589, 30104}, {14971, 17130}, {15048, 32835}

X(32955) = complement of X(33203)
X(32955) = {X(2),X(3)}-harmonic conjugate of X(32959)
X(32955) = {X(2),X(4)}-harmonic conjugate of X(33189)
X(32955) = {X(2),X(5)}-harmonic conjugate of X(14069)
X(32955) = orthocentroidal-circle-inverse of X(33189)


X(32956) = (name pending)

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

As a point on the Euler line, X(32956) has Shinagawa coefficients (2(E+F)2,-S2).

X(32956) lies on these lines: {2, 3}, {39, 32818}, {69, 3096}, {76, 3619}, {83, 18841}, {141, 5286}, {193, 7879}, {315, 3618}, {626, 7736}, {1007, 7786}, {1056, 26561}, {1058, 26590}, {1229, 3673}, {1285, 7750}, {1992, 7768}, {2548, 7853}, {2549, 7822}, {2896, 16989}, {3186, 31360}, {3314, 14482}, {3589, 7784}, {3620, 7754}, {3763, 5254}, {3767, 6292}, {3785, 7792}, {3926, 7868}, {4045, 7738}, {4385, 29611}, {4911, 5749}, {5015, 5222}, {5024, 32831}, {5218, 30104}, {5304, 7767}, {5305, 15589}, {5319, 7854}, {5485, 10159}, {6337, 7832}, {6704, 7825}, {7195, 17192}, {7288, 30103}, {7735, 7780}, {7737, 7889}, {7739, 7794}, {7758, 7849}, {7763, 7944}, {7774, 7938}, {7778, 31400}, {7797, 16990}, {7821, 9770}, {7823, 16987}, {7827, 21356}, {7829, 7865}, {7831, 7943}, {7846, 14907}, {7851, 32828}, {7856, 31168}, {7867, 31401}, {7875, 7928}, {7894, 11008}, {7918, 11185}, {7919, 32832}, {7923, 16986}, {7932, 17008}, {8164, 27020}, {9741, 32820}, {11174, 32816}, {13161, 17284}, {15048, 32830}, {20541, 31405}, {25914, 30825}

X(32956) = complement of X(33198)
X(32956) = {X(2),X(3)}-harmonic conjugate of X(14069)
X(32956) = {X(2),X(4)}-harmonic conjugate of X(16045)
X(32956) = {X(2),X(5)}-harmonic conjugate of X(32957)
X(32956) = {X(2),X(20)}-harmonic conjugate of X(7819)
X(32956) = orthocentroidal-circle-inverse of X(16045)


X(32957) = (name pending)

Barycentrics    SB SC + 4 S^2 + (a^4 + b^4 + c^4) : :
Barycentrics    a^4 + 8*a^2*b^2 - b^4 + 8*a^2*c^2 + 10*b^2*c^2 - c^4 : :

As a point on the Euler line, X(32957) has Shinagawa coefficients (2(E+F)2+2S2,S2).

X(32957) lies on these lines: {2, 3}, {69, 7858}, {141, 31404}, {325, 18840}, {1007, 7909}, {1056, 26959}, {1058, 27020}, {1078, 1285}, {2548, 7845}, {3618, 7856}, {3619, 7752}, {3815, 32818}, {3934, 7736}, {5013, 32822}, {5712, 29438}, {6292, 31415}, {6310, 10219}, {6392, 14482}, {6683, 7738}, {7735, 7808}, {7792, 18841}, {7794, 9770}, {7800, 7843}, {7818, 31417}, {7863, 31401}, {7936, 32006}, {7946, 16990}, {9605, 32834}, {9766, 31407}, {11174, 32828}, {15491, 31400}, {31406, 32830}, {31467, 32831}

X(32957) = {X(2),X(4)}-harmonic conjugate of X(32960)
X(32957) = {X(2),X(5)}-harmonic conjugate of X(32956)
X(32957) = orthocentroidal-circle-inverse of X(32960)


X(32958) = (name pending)

Barycentrics    SB SC + 4 S^2 - (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 8*a^2*b^2 + 9*b^4 - 8*a^2*c^2 - 10*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(32958) has Shinagawa coefficients (2(E+F)2-6S2,-S2).

X(32958) lies on these lines: {2, 3}, {230, 32823}, {1007, 7760}, {1285, 7857}, {5024, 32871}, {5485, 32820}, {6337, 14061}, {6722, 7781}, {7735, 7838}, {7736, 7886}, {7755, 9770}, {7768, 23055}, {7851, 32839}, {7868, 32867}, {13881, 32817}, {18840, 32838}

X(32958) = {X(2),X(4)}-harmonic conjugate of X(32959)
X(32958) = {X(2),X(5)}-harmonic conjugate of X(33189)
X(32958) = orthocentroidal-circle-inverse of X(32959)


X(32959) = (name pending)

Barycentrics    SB SC - 4 S^2 + (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 8*a^2*b^2 + 7*b^4 - 8*a^2*c^2 - 6*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(32959) has Shinagawa coefficients (2(E+F)2-6S2,S2).

X(32959) lies on these lines: {2, 3}, {69, 7940}, {230, 32818}, {1007, 7857}, {1285, 7752}, {3767, 31274}, {5305, 32835}, {5485, 32824}, {7735, 7764}, {7738, 7886}, {7781, 22247}, {7792, 32839}, {8164, 26686}, {13881, 32822}, {18841, 32884}, {22329, 32825}, {31406, 32871}

X(32959) = {X(2),X(3)}-harmonic conjugate of X(32955)
X(32959) = {X(2),X(4)}-harmonic conjugate of X(32958)
X(32959) = orthocentroidal-circle-inverse of X(32958)


X(32960) = (name pending)

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

As a point on the Euler line, X(32960) has Shinagawa coefficients (2(E+F)2+2S2,-S2).

X(32960) lies on these lines: {2, 3}, {69, 7786}, {83, 1285}, {141, 31400}, {599, 9606}, {1007, 3096}, {1056, 27020}, {1058, 26959}, {1078, 3618}, {2548, 7873}, {2549, 31239}, {3619, 7763}, {3785, 11174}, {3815, 32823}, {3926, 18840}, {3934, 7738}, {5013, 32817}, {5024, 32830}, {5286, 15271}, {6292, 7888}, {6683, 7736}, {7735, 7815}, {7754, 14482}, {7784, 15491}, {7795, 15482}, {7796, 21356}, {7801, 31450}, {7831, 32006}, {7851, 32838}, {7868, 32829}, {7889, 21843}, {7935, 31415}, {8164, 26561}, {9605, 15589}, {9698, 9770}, {15048, 32834}, {21358, 31492}

X(32960) = {X(2),X(3)}-harmonic conjugate of X(16045)
X(32960) = {X(2),X(4)}-harmonic conjugate of X(32957)
X(32960) = orthocentroidal-circle-inverse of X(32957)


X(32961) = (name pending)

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

As a point on the Euler line, X(32961) has Shinagawa coefficients ((E+F)2-3S2,-2S2).

X(32961) lies on these lines: {2, 3}, {32, 6722}, {69, 5031}, {83, 31415}, {115, 7763}, {148, 6337}, {193, 7941}, {194, 1007}, {230, 7773}, {315, 625}, {325, 13881}, {385, 32816}, {626, 16990}, {637, 32435}, {638, 32432}, {1506, 7803}, {2548, 7828}, {2549, 7769}, {2996, 32831}, {3314, 32828}, {3329, 31404}, {3618, 7932}, {3619, 24256}, {3767, 7752}, {3785, 7885}, {3788, 11185}, {3815, 7851}, {3926, 7925}, {4366, 10591}, {5171, 9754}, {5286, 7777}, {5304, 7921}, {5319, 7858}, {5461, 7764}, {5475, 7886}, {6392, 7906}, {6645, 10590}, {7603, 7834}, {7615, 7870}, {7617, 7869}, {7710, 10131}, {7735, 7785}, {7736, 7797}, {7737, 7857}, {7749, 7825}, {7755, 7775}, {7758, 7814}, {7779, 32823}, {7783, 32829}, {7790, 31401}, {7793, 32006}, {7795, 7899}, {7800, 7934}, {7802, 21843}, {7809, 14023}, {7810, 12815}, {7816, 18424}, {7823, 32827}, {7835, 15031}, {7861, 31455}, {7863, 18546}, {7864, 17005}, {7888, 18362}, {7891, 32815}, {7902, 9698}, {7904, 17006}, {7928, 32867}, {7939, 15589}, {7947, 32830}, {8797, 9229}, {9737, 23514}, {9770, 13571}, {9939, 23055}, {10895, 26686}, {10896, 26629}, {20081, 32818}, {22110, 32821}

X(32961) = complement of X(32964)
X(32961) = anticomplement of X(33233)
X(32961) = {X(2),X(3)}-harmonic conjugate of X(33000)
X(32961) = {X(2),X(4)}-harmonic conjugate of X(16925)
X(32961) = {X(2),X(5)}-harmonic conjugate of X(16924)
X(32961) = {X(2),X(20)}-harmonic conjugate of X(7907)
X(32961) = orthocentroidal-circle-inverse of X(16925)


X(32962) = (name pending)

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

As a point on the Euler line, X(32962) has Shinagawa coefficients ((E+F)2+3S2,4S2).

X(32962) lies on these lines: {2, 3}, {76, 31415}, {148, 31400}, {194, 31404}, {1007, 17128}, {1506, 7781}, {2548, 7760}, {2549, 15031}, {2896, 32827}, {3620, 24256}, {3767, 7878}, {4366, 10588}, {5475, 7780}, {6337, 17005}, {6645, 10589}, {6683, 18424}, {7603, 7763}, {7617, 7755}, {7745, 17008}, {7773, 16990}, {7779, 32834}, {7785, 32828}, {7793, 32838}, {7821, 8176}, {7829, 18362}, {7858, 31417}, {7900, 15589}, {9698, 18546}, {10352, 23514}, {11184, 32820}, {13881, 16989}, {20080, 32872}, {31276, 32816}, {31489, 32819}

X(32962) = anticomplement of X(33001)
X(32962) = {X(2),X(3)}-harmonic conjugate of X(33188)
X(32962) = {X(2),X(4)}-harmonic conjugate of X(32965)
X(32962) = {X(2),X(5)}-harmonic conjugate of X(32963)
X(32962) = {X(2),X(20)}-harmonic conjugate of X(33012)
X(32962) = orthocentroidal-circle-inverse of X(32965)


X(32963) = (name pending)

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

As a point on the Euler line, X(32963) has Shinagawa coefficients ((E+F)2-5S2,-4S2).

X(32963) lies on these lines: {2, 3}, {148, 32829}, {625, 7854}, {1506, 7902}, {2548, 7856}, {2896, 32838}, {3620, 5031}, {3767, 7858}, {5007, 8176}, {5461, 7772}, {7603, 7803}, {7617, 7794}, {7738, 17005}, {7746, 7843}, {7752, 7758}, {7764, 18362}, {7773, 17008}, {7774, 13881}, {7793, 32827}, {7797, 31404}, {7828, 31415}, {7862, 7863}, {7878, 31417}, {7897, 32834}, {7912, 32828}, {7946, 32816}, {17004, 32006}, {17129, 32823}

X(32963) = anticomplement of X(33000)
X(32963) = {X(2),X(3)}-harmonic conjugate of X(33204)
X(32963) = {X(2),X(4)}-harmonic conjugate of X(32964)
X(32963) = {X(2),X(5)}-harmonic conjugate of X(32962)
X(32963) = {X(2),X(20)}-harmonic conjugate of X(33206)
X(32963) = orthocentroidal-circle-inverse of X(32964)


X(32964) = (name pending)

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

As a point on the Euler line, X(32964) has Shinagawa coefficients ((E+F)2-5S2,4S2).

X(32964) lies on these lines: {2, 3}, {69, 7891}, {76, 21843}, {187, 7759}, {193, 1691}, {194, 2021}, {315, 620}, {325, 5023}, {385, 6337}, {574, 7829}, {598, 31417}, {626, 8588}, {1007, 7823}, {1285, 7921}, {1975, 17008}, {2482, 7751}, {2549, 7857}, {3053, 7774}, {3767, 7782}, {3785, 7836}, {3788, 7873}, {3926, 4027}, {3972, 31401}, {4366, 7288}, {5013, 16989}, {5131, 30123}, {5171, 10352}, {5204, 26629}, {5210, 7750}, {5217, 26686}, {5218, 6645}, {5319, 7618}, {5976, 20081}, {6179, 26613}, {6393, 20080}, {6680, 15515}, {6781, 7862}, {7622, 9698}, {7735, 7783}, {7737, 7769}, {7738, 7806}, {7746, 32456}, {7749, 11185}, {7771, 7795}, {7776, 15655}, {7779, 32831}, {7780, 32833}, {7785, 32829}, {7787, 31400}, {7789, 16990}, {7792, 15815}, {7799, 14023}, {7800, 7835}, {7816, 32832}, {7825, 31274}, {7834, 8589}, {7870, 8182}, {7893, 32818}, {7925, 32006}, {7946, 32825}, {8667, 32820}, {8722, 10350}, {8787, 11160}, {8859, 11147}, {14712, 32816}, {17129, 32817}

X(32964) = complement of X(32996)
X(32964) = anticomplement of X(32961)
X(32964) = {X(2),X(3)}-harmonic conjugate of X(32965)
X(32964) = {X(2),X(4)}-harmonic conjugate of X(32963)
X(32964) = {X(2),X(20)}-harmonic conjugate of X(14063)
X(32964) = orthocentroidal-circle-inverse of X(32963)


X(32965) = (name pending)

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

As a point on the Euler line, X(32965) has Shinagawa coefficients ((E+F)2+3S2,-4S2).

X(32965) lies on these lines: {2, 3}, {39, 14907}, {69, 7783}, {99, 7800}, {148, 32828}, {187, 7803}, {193, 3094}, {194, 3785}, {315, 574}, {316, 31401}, {325, 15815}, {385, 7738}, {599, 32820}, {620, 7935}, {626, 15515}, {1007, 7885}, {1078, 2549}, {1975, 16990}, {2021, 14712}, {2482, 7869}, {2548, 7802}, {2896, 3926}, {3053, 16989}, {3314, 6337}, {3767, 7771}, {3788, 8589}, {3819, 14135}, {4045, 5206}, {4299, 27020}, {4302, 26959}, {5013, 7750}, {5023, 7792}, {5024, 7762}, {5131, 30119}, {5204, 26590}, {5217, 26561}, {5254, 17008}, {5286, 7793}, {5976, 20094}, {6179, 7739}, {6390, 7879}, {6393, 32840}, {6680, 8588}, {6776, 32522}, {6781, 7808}, {7618, 7883}, {7735, 7864}, {7736, 7823}, {7737, 7786}, {7747, 15482}, {7748, 32832}, {7749, 7872}, {7756, 7815}, {7757, 14023}, {7758, 7811}, {7759, 31652}, {7761, 7763}, {7767, 31859}, {7769, 7910}, {7777, 32006}, {7781, 7810}, {7782, 7795}, {7785, 31400}, {7799, 7936}, {7822, 32456}, {7827, 8182}, {7828, 21843}, {7834, 15513}, {7842, 31455}, {7854, 32833}, {7858, 11057}, {7863, 7865}, {7891, 7928}, {7897, 32831}, {7898, 32816}, {7912, 32829}, {7939, 32818}, {9607, 14614}, {9744, 32152}, {9939, 13571}, {15271, 32819}, {15589, 20081}, {31276, 32815}

X(32965) = complement of X(14068)
X(32965) = anticomplement of X(16924)
X(32965) = {X(2),X(3)}-harmonic conjugate of X(32964)
X(32965) = {X(2),X(4)}-harmonic conjugate of X(32962)
X(32965) = {X(2),X(20)}-harmonic conjugate of X(14035)
X(32965) = orthocentroidal-circle-inverse of X(32962)


X(32966) = (name pending)

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

As a point on the Euler line, X(32966) has Shinagawa coefficients ((E+F)2-3S2,-4S2).

X(32966) lies on these lines: {2, 3}, {32, 14061}, {69, 5103}, {76, 625}, {83, 7844}, {99, 7862}, {115, 194}, {148, 7763}, {183, 7885}, {230, 7823}, {316, 7746}, {325, 20081}, {385, 7773}, {538, 7814}, {626, 31276}, {671, 7781}, {1078, 7825}, {1506, 7790}, {1975, 7925}, {2548, 7797}, {2896, 32832}, {3329, 7851}, {3614, 26590}, {3734, 7899}, {3767, 7766}, {3788, 18424}, {3815, 7864}, {3934, 7934}, {3972, 7886}, {4366, 10896}, {5013, 17005}, {5031, 18906}, {5254, 7777}, {5305, 7921}, {5309, 7858}, {5461, 7755}, {5475, 7787}, {5552, 6653}, {6179, 7843}, {6337, 20094}, {6645, 10895}, {6683, 7918}, {6722, 7747}, {7173, 26561}, {7603, 7786}, {7617, 7883}, {7620, 32824}, {7735, 9478}, {7745, 7806}, {7748, 7769}, {7749, 7802}, {7750, 17004}, {7751, 7809}, {7753, 7856}, {7754, 7941}, {7758, 19570}, {7759, 14568}, {7760, 7775}, {7771, 7842}, {7776, 17129}, {7778, 17128}, {7779, 32816}, {7780, 7860}, {7803, 31415}, {7804, 7942}, {7805, 7926}, {7808, 7919}, {7815, 7911}, {7816, 7940}, {7817, 7878}, {7827, 8176}, {7836, 11185}, {7847, 31455}, {7888, 18546}, {7891, 32819}, {7906, 20105}, {7909, 17130}, {7917, 17131}, {7922, 9466}, {7923, 11174}, {7928, 15271}, {7937, 31239}, {9737, 14639}, {11002, 27374}, {14881, 15092}, {17008, 32006}, {20065, 32827}, {20158, 24883}, {22110, 32820}

X(32966) = complement of X(33014)
X(32966) = anticomplement of X(7907)
X(32966) = {X(2),X(4)}-harmonic conjugate of X(3552)
X(32966) = {X(2),X(5)}-harmonic conjugate of X(33002)
X(32966) = {X(2),X(20)}-harmonic conjugate of X(33259)
X(32966) = orthocentroidal-circle-inverse of X(3552)


X(32967) = (name pending)

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

As a point on the Euler line, X(32967) has Shinagawa coefficients ((E+F)2-5S2,-2S2).

X(32967) lies on these lines: {2, 3}, {39, 14061}, {76, 7862}, {83, 7603}, {115, 7769}, {141, 15514}, {183, 7912}, {194, 13881}, {230, 7785}, {315, 17004}, {316, 7749}, {325, 17129}, {385, 7746}, {625, 1078}, {629, 14904}, {630, 14905}, {1007, 7906}, {1506, 3329}, {2548, 7806}, {2996, 32835}, {3054, 7750}, {3314, 32832}, {3614, 26686}, {3620, 32870}, {3734, 7940}, {3767, 7777}, {3788, 17128}, {3815, 7797}, {3934, 7899}, {4366, 7741}, {5182, 18553}, {5461, 7765}, {5475, 7857}, {6179, 7775}, {6645, 7951}, {6683, 7919}, {7173, 26629}, {7617, 7870}, {7735, 7921}, {7736, 7920}, {7751, 7814}, {7755, 7858}, {7764, 14568}, {7768, 12815}, {7771, 7825}, {7773, 7793}, {7778, 31276}, {7780, 7809}, {7781, 18362}, {7786, 7844}, {7790, 31455}, {7808, 7942}, {7815, 7928}, {7816, 15031}, {7827, 9698}, {7851, 31489}, {7852, 16987}, {7864, 31401}, {7867, 18806}, {7871, 17131}, {7891, 11185}, {7893, 17008}, {7909, 9466}, {7918, 15482}, {7932, 11174}, {7938, 15271}, {7944, 16988}, {7946, 8667}, {8860, 9939}, {9607, 9771}, {15079, 30139}, {15850, 23235}, {16819, 31262}, {16989, 31404}, {16990, 32838}, {24726, 25341}

X(32967) = complement of X(33259)
X(32967) = {X(2),X(3)}-harmonic conjugate of X(16923)
X(32967) = {X(2),X(4)}-harmonic conjugate of X(7907)
X(32967) = {X(2),X(5)}-harmonic conjugate of X(384)
X(32967) = {X(2),X(20)}-harmonic conjugate of X(33000)
X(32967) = {X(2),X(384)}-harmonic conjugate of X(33245)
X(32967) = orthocentroidal-circle-inverse of X(7907)


X(32968) = (name pending)

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

As a point on the Euler line, X(32968) has Shinagawa coefficients ((E+F)2+S2,S2).

X(32968) lies on these lines: {2, 3}, {6, 32828}, {69, 2548}, {76, 7736}, {83, 7735}, {141, 32816}, {230, 32838}, {325, 31404}, {350, 31402}, {388, 26959}, {497, 27020}, {626, 3619}, {1007, 1506}, {1285, 7793}, {1975, 31400}, {1992, 7751}, {2549, 6683}, {2550, 27091}, {2551, 17030}, {2996, 15048}, {3054, 32883}, {3055, 32839}, {3314, 18840}, {3421, 26801}, {3589, 13881}, {3618, 3767}, {3620, 7776}, {3734, 6337}, {3785, 7745}, {3815, 3926}, {5013, 15491}, {5082, 26752}, {5182, 11623}, {5286, 11174}, {5306, 32885}, {5319, 14762}, {5395, 18907}, {5475, 7800}, {6310, 6688}, {6376, 31405}, {6390, 31467}, {6392, 9605}, {6704, 7844}, {7603, 7822}, {7618, 31457}, {7737, 7815}, {7738, 7786}, {7753, 14023}, {7754, 32834}, {7758, 9466}, {7762, 15589}, {7767, 15484}, {7774, 31276}, {7775, 21356}, {7777, 32818}, {7783, 32822}, {7784, 32827}, {7785, 16990}, {7787, 17008}, {7789, 31489}, {7796, 9770}, {7838, 11008}, {7875, 18841}, {9698, 17130}, {10349, 16989}, {10352, 14651}, {10590, 26561}, {10591, 26590}, {11163, 31407}, {14930, 32872}, {17128, 32817}, {19843, 26687}, {26105, 27255}, {26582, 31418}, {27076, 31416}

X(32968) = complement of X(32990)
X(32968) = {X(2),X(3)}-harmonic conjugate of X(32978)
X(32968) = {X(2),X(4)}-harmonic conjugate of X(16043)
X(32968) = {X(2),X(5)}-harmonic conjugate of X(14064)
X(32968) = {X(2),X(20)}-harmonic conjugate of X(11285)
X(32968) = {X(2),X(384)}-harmonic conjugate of X(631)
X(32968) = orthocentroidal-circle-inverse of X(16043)


X(32969) = (name pending)

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

As a point on the Euler line, X(32969) has Shinagawa coefficients ((E+F)2-3S2,-S2).

X(32969) lies on these lines: {2, 3}, {69, 1570}, {115, 6337}, {141, 32838}, {230, 32816}, {315, 2031}, {385, 32823}, {625, 32006}, {966, 25687}, {1007, 3767}, {1504, 32806}, {1505, 32805}, {1506, 3618}, {1992, 7755}, {2548, 7886}, {3053, 32827}, {3054, 7784}, {3619, 7867}, {3926, 13881}, {5013, 32839}, {5254, 32829}, {5461, 7781}, {6566, 12323}, {6567, 12322}, {6680, 31415}, {7735, 7752}, {7736, 7828}, {7738, 7769}, {7760, 9770}, {7763, 14061}, {7778, 32828}, {7780, 23055}, {7792, 31404}, {7810, 23053}, {7825, 21843}, {7844, 31401}, {7851, 31400}, {7863, 18362}, {7881, 32834}, {7891, 32822}, {7899, 32832}, {7903, 11008}, {7912, 17008}, {7925, 32818}, {7931, 18840}, {7940, 11185}, {10590, 26686}, {10591, 26629}, {12815, 21356}, {15271, 32867}, {22110, 32825}, {31859, 32835}

X(32969) = complement of X(32989)
X(32969) = {X(2),X(3)}-harmonic conjugate of X(32977)
X(32969) = {X(2),X(4)}-harmonic conjugate of X(32970)
X(32969) = {X(2),X(5)}-harmonic conjugate of X(14001)
X(32969) = {X(2),X(20)}-harmonic conjugate of X(33233)
X(32969) = {X(2),X(384)}-harmonic conjugate of X(33189)
X(32969) = orthocentroidal-circle-inverse of X(32970)


X(32970) = (name pending)

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

As a point on the Euler line, X(32970) has Shinagawa coefficients ((E+F)2-3S2,S2).

X(32970) lies on these lines: {2, 3}, {6, 10008}, {32, 1007}, {69, 1692}, {187, 32006}, {230, 3926}, {315, 7940}, {385, 32818}, {524, 32825}, {620, 3767}, {626, 21843}, {1285, 7785}, {1992, 7764}, {2549, 7886}, {3053, 32816}, {3054, 32838}, {3055, 32884}, {3085, 26686}, {3086, 26629}, {3618, 5028}, {3619, 5033}, {3785, 7778}, {3815, 32839}, {5182, 20399}, {5215, 7821}, {5304, 32835}, {6390, 6392}, {6645, 8164}, {7735, 7760}, {7736, 7769}, {7737, 7862}, {7738, 7828}, {7749, 7795}, {7754, 32831}, {7755, 9167}, {7789, 32828}, {7792, 31400}, {7793, 10349}, {7800, 7874}, {7801, 23055}, {7835, 32832}, {7836, 17008}, {7860, 26613}, {7869, 21356}, {7881, 15589}, {7888, 14023}, {7891, 32817}, {7899, 14907}, {7920, 14482}, {7925, 20065}, {7945, 16990}, {9752, 10256}, {13881, 32815}, {22329, 32821}, {31411, 32806}

X(32970) = complement of X(32972)
X(32970) = {X(2),X(3)}-harmonic conjugate of X(14064)
X(32970) = {X(2),X(4)}-harmonic conjugate of X(32969)
X(32970) = {X(2),X(5)}-harmonic conjugate of X(32976)
X(32970) = {X(2),X(20)}-harmonic conjugate of X(7887)
X(32970) = {X(2),X(384)}-harmonic conjugate of X(3090)
X(32970) = orthocentroidal-circle-inverse of X(32969)


X(32971) = (name pending)

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

As a point on the Euler line, X(32971) has Shinagawa coefficients ((E+F)2,2S2).

X(32971) lies on these lines: {2, 3}, {6, 6392}, {32, 32828}, {39, 32815}, {69, 7745}, {76, 193}, {83, 2996}, {99, 31400}, {141, 32006}, {148, 10352}, {264, 26164}, {315, 3620}, {385, 32834}, {598, 7768}, {620, 32839}, {626, 32827}, {1007, 7789}, {1506, 32829}, {1975, 7736}, {2548, 3734}, {2549, 7808}, {2550, 26687}, {2551, 20172}, {3087, 26214}, {3618, 5254}, {3619, 7784}, {3767, 7804}, {3785, 3934}, {3788, 31415}, {3815, 6337}, {3933, 15484}, {3972, 32832}, {4293, 26959}, {4294, 27020}, {5032, 7760}, {5140, 32529}, {5225, 26590}, {5229, 26561}, {5304, 7787}, {5475, 7795}, {5819, 25994}, {6248, 6776}, {6462, 31403}, {6645, 14986}, {6688, 14135}, {6704, 7872}, {7620, 7827}, {7738, 11174}, {7747, 7800}, {7749, 32867}, {7753, 7758}, {7762, 20080}, {7763, 31404}, {7774, 17128}, {7777, 32831}, {7801, 32825}, {7812, 11160}, {7816, 31401}, {7823, 16990}, {7829, 18546}, {7837, 32869}, {7839, 14930}, {7846, 15031}, {7852, 18424}, {7854, 14537}, {7858, 32833}, {7863, 32837}, {7879, 18840}, {7881, 32823}, {7883, 23334}, {7890, 32878}, {7891, 32835}, {7906, 32840}, {8716, 9606}, {9466, 14023}, {9770, 32821}, {10358, 14853}, {10588, 26629}, {10589, 26686}, {11163, 32820}, {13161, 26626}, {13468, 22331}, {15491, 15815}, {15589, 20065}, {17004, 32870}, {17131, 32868}, {17784, 26752}, {31859, 32822}

X(32971) = complement of X(33023)
X(32971) = anticomplement of X(16043)
X(32971) = {X(2),X(4)}-harmonic conjugate of X(32974)
X(32971) = {X(2),X(5)}-harmonic conjugate of X(32988)
X(32971) = {X(2),X(20)}-harmonic conjugate of X(32990)
X(32971) = orthocentroidal-circle-inverse of X(32974)


X(32972) = (name pending)

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

As a point on the Euler line, X(32972) has Shinagawa coefficients ((E+F)2-2S2,-2S2).

X(32972) lies on these lines: {2, 3}, {32, 32827}, {69, 13881}, {115, 2996}, {193, 625}, {230, 32006}, {315, 14061}, {325, 6392}, {538, 32825}, {574, 32839}, {626, 3620}, {1007, 5254}, {2031, 20065}, {2548, 7829}, {2549, 7862}, {2899, 30763}, {3314, 32834}, {3785, 7746}, {3788, 32815}, {5032, 5319}, {5139, 30558}, {5225, 26629}, {5229, 26686}, {5286, 7752}, {5304, 7785}, {5395, 5475}, {5461, 7751}, {6340, 6342}, {6722, 7825}, {7615, 17130}, {7620, 7870}, {7735, 7773}, {7736, 7851}, {7737, 7886}, {7748, 31275}, {7754, 32823}, {7776, 20080}, {7781, 32837}, {7783, 32835}, {7790, 31400}, {7794, 18362}, {7796, 9166}, {7800, 32838}, {7803, 31404}, {7815, 32867}, {7834, 31415}, {7842, 21843}, {7861, 31401}, {7874, 18424}, {7885, 17008}, {7899, 11185}, {7920, 14930}, {7925, 32831}, {7934, 32832}, {7935, 32883}, {7947, 32840}, {8176, 31417}, {9607, 11184}, {9771, 31492}, {10513, 17129}, {10588, 26590}, {10589, 26561}, {14148, 32876}

X(32972) = complement of X(439)
X(32972) = anticomplement of X(32970)
X(32972) = {X(2),X(4)}-harmonic conjugate of X(32973)
X(32972) = {X(2),X(5)}-harmonic conjugate of X(32987)
X(32972) = {X(2),X(20)}-harmonic conjugate of X(32989)
X(32972) = orthocentroidal-circle-inverse of X(32973)


X(32973) = (name pending)

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

As a point on the Euler line, X(32973) has Shinagawa coefficients ((E+F)2-2S2,2S2).

X(32973) lies on these lines: {2, 3}, {6, 6337}, {32, 193}, {69, 3053}, {83, 31400}, {99, 5286}, {115, 32826}, {141, 5023}, {187, 3620}, {194, 5304}, {287, 18913}, {315, 7835}, {385, 32830}, {388, 26629}, {497, 26686}, {524, 22331}, {538, 32824}, {597, 22332}, {620, 2548}, {988, 26626}, {1007, 7745}, {1196, 18287}, {1285, 7762}, {1384, 3933}, {1506, 32839}, {1975, 6392}, {2482, 7772}, {2549, 6680}, {3767, 7816}, {3491, 9292}, {3589, 15815}, {3618, 5013}, {3619, 5210}, {3734, 32828}, {3788, 7737}, {3934, 21843}, {3972, 7763}, {4299, 30104}, {4302, 30103}, {4366, 14986}, {5007, 5032}, {5171, 10519}, {5206, 7800}, {5266, 29585}, {5319, 7781}, {6179, 32833}, {6292, 8588}, {6390, 30435}, {6776, 13335}, {6781, 7867}, {7738, 7792}, {7747, 32827}, {7749, 32838}, {7751, 32836}, {7754, 32817}, {7759, 32825}, {7764, 32837}, {7769, 31404}, {7774, 7891}, {7777, 32835}, {7778, 32006}, {7782, 7803}, {7783, 16989}, {7787, 10352}, {7793, 15589}, {7801, 11160}, {7804, 31401}, {7822, 15513}, {7832, 7936}, {7834, 32456}, {7836, 7946}, {7857, 11185}, {7889, 15515}, {7893, 10513}, {7906, 32841}, {7945, 14712}, {9737, 14853}, {10349, 10788}, {14614, 32820}, {17005, 32871}, {17008, 17128}, {19758, 19783}, {20172, 30478}

X(32973) = midpoint of X(37172) and X(37173)
X(32973) = reflection of X(2) in X(33224)
X(32973) = complement of X(32982)
X(32973) = anticomplement of X(14064)
X(32973) = pole of Brocard axis wrt conic {{X(13),X(14),X(15),X(16),X(69)}}
X(32973) = {X(2),X(3)}-harmonic conjugate of X(32990)
X(32973) = {X(2),X(4)}-harmonic conjugate of X(32972)
X(32973) = {X(2),X(20)}-harmonic conjugate of X(32974)
X(32973) = orthocentroidal-circle-inverse of X(32972)


X(32974) = (name pending)

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

As a point on the Euler line, X(32974) has Shinagawa coefficients ((E+F)2,-2S2).

X(32974) lies on these lines: {2, 3}, {6, 32006}, {39, 32816}, {69, 5254}, {76, 2996}, {83, 5033}, {115, 7800}, {148, 7938}, {193, 315}, {253, 9229}, {264, 26214}, {287, 18945}, {316, 1692}, {325, 7738}, {388, 26590}, {491, 6462}, {497, 26561}, {543, 7869}, {574, 32829}, {625, 31401}, {626, 2549}, {754, 5319}, {1007, 5013}, {2207, 26206}, {2548, 4045}, {2550, 26558}, {2551, 26582}, {2896, 15589}, {3096, 11185}, {3314, 32830}, {3618, 7745}, {3734, 32826}, {3767, 3785}, {4299, 30103}, {4302, 30104}, {5032, 7827}, {5171, 9752}, {5304, 7797}, {5309, 7873}, {6337, 7778}, {6683, 31415}, {7709, 9742}, {7735, 7750}, {7736, 7773}, {7737, 7834}, {7739, 7759}, {7747, 7913}, {7748, 7795}, {7752, 31400}, {7754, 20080}, {7756, 7867}, {7758, 7765}, {7763, 7847}, {7768, 11160}, {7774, 7864}, {7776, 15048}, {7783, 32831}, {7786, 31404}, {7794, 11648}, {7801, 32824}, {7802, 7919}, {7815, 32838}, {7821, 32825}, {7823, 7923}, {7828, 7910}, {7830, 7844}, {7831, 32832}, {7862, 32839}, {7868, 32819}, {7881, 32817}, {7886, 21843}, {7888, 32837}, {7904, 17008}, {7921, 14930}, {7922, 32833}, {7925, 32835}, {7928, 16990}, {7932, 14712}, {7936, 14568}, {7939, 10513}, {7947, 32841}, {9607, 9766}, {10590, 27020}, {10591, 26959}, {13161, 17316}, {17030, 31418}, {18424, 31239}, {18841, 18845}, {19562, 20023}, {31859, 32818}

X(32974) = reflection of X(2) in X(33223)
X(32974) = complement of X(32981)
X(32974) = anticomplement of X(14001)
X(32974) = {X(2),X(3)}-harmonic conjugate of X(32989)
X(32974) = {X(2),X(4)}-harmonic conjugate of X(32971)
X(32974) = {X(2),X(20)}-harmonic conjugate of X(32973)
X(32974) = orthocentroidal-circle-inverse of X(32971)


X(32975) = (name pending)

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

As a point on the Euler line, X(32975) has Shinagawa coefficients ((E+F)2+3S2,S2).

X(32975) lies on these lines: {2, 3}, {6, 32838}, {69, 1506}, {183, 31404}, {230, 32867}, {754, 31417}, {1007, 3934}, {1384, 5395}, {2548, 7780}, {3055, 32829}, {3095, 14494}, {3398, 7612}, {3618, 7746}, {3619, 31239}, {3815, 32828}, {3926, 31489}, {3974, 30152}, {6337, 31455}, {6392, 31406}, {7603, 7800}, {7735, 7878}, {7736, 7760}, {7781, 31401}, {7789, 32839}, {7815, 31415}, {7821, 21356}, {10349, 18841}, {10588, 26959}, {10589, 27020}, {11184, 32825}, {13881, 15491}, {15271, 32816}, {15815, 32826}, {16990, 32823}, {31276, 32818}

X(32975) = {X(2),X(4)}-harmonic conjugate of X(32978)
X(32975) = {X(2),X(5)}-harmonic conjugate of X(16043)
X(32975) = orthocentroidal-circle-inverse of X(32978)


X(32976) = (name pending)

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

As a point on the Euler line, X(32976) has Shinagawa coefficients ((E+F)2-5S2,-S2).

X(32976) lies on these lines: {2, 3}, {69, 7862}, {141, 32867}, {1007, 7746}, {3054, 3785}, {3618, 7886}, {3619, 5107}, {5254, 32839}, {6337, 15301}, {6722, 7902}, {7735, 7858}, {7736, 7856}, {7738, 14061}, {7749, 32006}, {7778, 32838}, {7800, 31275}, {7888, 12815}, {7909, 32832}, {7946, 17008}, {13881, 32829}, {14023, 23055}, {15271, 32883}

X(32976) = {X(2),X(4)}-harmonic conjugate of X(32977)
X(32976) = {X(2),X(5)}-harmonic conjugate of X(32970)
X(32976) = orthocentroidal-circle-inverse of X(32977)


X(32977) = (name pending)

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

As a point on the Euler line, X(32977) has Shinagawa coefficients ((E+F)2-5S2,S2).

X(32977) lies on these lines: {2, 3}, {6, 32839}, {69, 7749}, {230, 32829}, {1007, 7759}, {1570, 3618}, {3054, 32828}, {3619, 7874}, {5023, 32827}, {5058, 32805}, {5062, 32806}, {5304, 32871}, {6179, 9770}, {6337, 7746}, {7735, 7769}, {7736, 7857}, {7751, 23055}, {7754, 32835}, {7789, 32838}, {7793, 32823}, {7795, 31274}, {7801, 23053}, {7817, 31450}, {7829, 31401}, {7862, 21843}, {7945, 18840}, {8667, 32825}, {9167, 17130}, {17008, 32818}, {31489, 32884}, {32459, 32826}

X(32977) = complement of X(32988)
X(32977) = {X(2),X(3)}-harmonic conjugate of X(32969)
X(32977) = {X(2),X(4)}-harmonic conjugate of X(32976)
X(32977) = {X(2),X(20)}-harmonic conjugate of X(33249)
X(32977) = orthocentroidal-circle-inverse of X(32976)


X(32978) = (name pending)

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

As a point on the Euler line, X(32978) has Shinagawa coefficients ((E+F)2+3S2,-S2).

X(32978) lies on these lines: {2, 3}, {69, 5034}, {141, 32829}, {183, 31400}, {193, 31406}, {538, 31450}, {599, 32825}, {1007, 7800}, {1078, 7736}, {1506, 32006}, {1992, 7780}, {2896, 32823}, {3053, 15491}, {3055, 7784}, {3618, 5052}, {3619, 3788}, {3767, 15482}, {3785, 3815}, {3926, 15271}, {3934, 6337}, {5013, 32828}, {5024, 6392}, {5218, 26959}, {5254, 32838}, {7288, 27020}, {7735, 7786}, {7738, 32832}, {7750, 31404}, {7755, 23055}, {7767, 31467}, {7768, 9770}, {7778, 32839}, {7808, 21843}, {7817, 23053}, {7830, 31415}, {7836, 18840}, {7881, 32835}, {8556, 31492}, {8667, 9606}, {9466, 31457}, {9698, 14023}, {10104, 14912}, {10159, 11172}, {10583, 18841}, {13881, 32867}, {15815, 32815}, {16990, 32818}, {27091, 30478}, {31276, 32817}, {31489, 32816}, {31859, 32834}

X(32978) = complement of X(32987)
X(32978) = {X(2),X(3)}-harmonic conjugate of X(32968)
X(32978) = {X(2),X(4)}-harmonic conjugate of X(32975)
X(32978) = {X(2),X(20)}-harmonic conjugate of X(32992)
X(32978) = orthocentroidal-circle-inverse of X(32975)


X(32979) = (name pending)

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

As a point on the Euler line, X(32979) has Shinagawa coefficients ((E+F)2,4S2).

X(32979) lies on these lines: {2, 3}, {6, 2996}, {39, 32826}, {76, 18845}, {99, 31404}, {187, 32838}, {193, 7745}, {263, 6310}, {2548, 7781}, {3620, 32006}, {3734, 32816}, {3785, 7747}, {3926, 5475}, {4366, 5261}, {5274, 6645}, {5286, 7878}, {5319, 18546}, {5921, 6248}, {6392, 7760}, {7603, 32839}, {7615, 7755}, {7736, 32819}, {7737, 7780}, {7759, 32836}, {7764, 32824}, {7775, 32825}, {7785, 32830}, {7795, 32827}, {7816, 31415}, {7823, 15589}, {7860, 23334}, {7900, 10513}, {9770, 32820}, {14023, 14537}, {20065, 32834}, {21843, 32867}

X(32979) = anticomplement of X(32990)
X(32979) = {X(2),X(4)}-harmonic conjugate of X(32982)
X(32979) = orthocentroidal-circle-inverse of X(32982)


X(32980) = (name pending)

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

As a point on the Euler line, X(32980) has Shinagawa coefficients ((E+F)2-2S2,-4S2).

X(32980) lies on these lines: {2, 3}, {115, 6392}, {148, 8781}, {193, 7773}, {325, 2996}, {625, 3926}, {2548, 7902}, {3767, 7843}, {3785, 7825}, {3788, 32826}, {5107, 7946}, {5286, 7858}, {5395, 7792}, {6653, 27525}, {7615, 7794}, {7748, 32829}, {7761, 32838}, {7790, 31404}, {7795, 18424}, {7821, 32836}, {7854, 32828}, {7861, 31415}, {7863, 32815}, {7885, 15589}, {7888, 32824}, {7909, 11185}, {7912, 32830}, {7936, 32832}, {13881, 32006}, {14023, 31173}

X(32980) = anticomplement of X(32989)
X(32980) = {X(2),X(4)}-harmonic conjugate of X(32981)
X(32980) = orthocentroidal-circle-inverse of X(32981)


X(32981) = (name pending)

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

As a point on the Euler line, X(32981) has Shinagawa coefficients ((E+F)2-2S2,4S2).

X(32981) lies on these lines: {2, 3}, {32, 6392}, {187, 32828}, {193, 1975}, {194, 5052}, {390, 6645}, {543, 5319}, {1285, 7754}, {2549, 7829}, {2996, 7735}, {3600, 4366}, {3620, 7750}, {3734, 3785}, {3767, 32826}, {3788, 32827}, {3926, 7737}, {3972, 5286}, {4027, 20094}, {4339, 29585}, {5032, 11164}, {5034, 7787}, {5182, 10992}, {5225, 26686}, {5229, 26629}, {5395, 7736}, {5475, 32829}, {5866, 9608}, {6337, 7745}, {6781, 7800}, {7618, 9698}, {7747, 7888}, {7758, 32824}, {7762, 32817}, {7779, 32840}, {7782, 31400}, {7785, 32831}, {7789, 32006}, {7793, 32834}, {7795, 7873}, {7863, 32825}, {7870, 23334}, {18845, 32835}, {14023, 32836}, {14537, 32837}, {15589, 17128}, {20065, 20080}, {21843, 32838}, {31401, 32456}, {31415, 32839}

X(32981) = anticomplement of X(32974)
X(32981) = {X(2),X(4)}-harmonic conjugate of X(32980)
X(32981) = {X(2),X(20)}-harmonic conjugate of X(33023)
X(32981) = orthocentroidal-circle-inverse of X(32980)


X(32982) = (name pending)

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

As a point on the Euler line, X(32982) has Shinagawa coefficients ((E+F)2,-4S2).

X(32982) lies on these lines: {2, 3}, {39, 32827}, {69, 2996}, {83, 18845}, {115, 3785}, {148, 32458}, {193, 5254}, {315, 6392}, {316, 1570}, {543, 32824}, {625, 32829}, {626, 32815}, {2548, 7872}, {2549, 7764}, {2896, 32834}, {3618, 5395}, {3620, 7784}, {3767, 7842}, {3926, 7748}, {5225, 26561}, {5229, 26590}, {5304, 7823}, {7620, 7883}, {7737, 7861}, {7738, 7773}, {7739, 7843}, {7758, 11648}, {7761, 32828}, {7781, 32825}, {7795, 32826}, {7827, 23334}, {7847, 31400}, {7881, 32822}, {7897, 32840}, {7910, 32832}, {7911, 11185}, {7912, 32831}, {10513, 20081}, {13161, 29585}, {31859, 32823}

X(32982) = anticomplement of X(32973)
X(32982) = {X(2),X(4)}-harmonic conjugate of X(32979)
X(32982) = orthocentroidal-circle-inverse of X(32979)


X(32983) = (name pending)

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

As a point on the Euler line, X(32983) has Shinagawa coefficients ((E+F)2+S2,3S2).

X(32983) lies on these lines: {2, 3}, {69, 5475}, {115, 3618}, {141, 32827}, {193, 15484}, {538, 2548}, {1007, 3734}, {1285, 17008}, {1506, 6337}, {1975, 31404}, {1992, 7753}, {2996, 9605}, {3053, 32838}, {3785, 8556}, {3815, 8716}, {3934, 32006}, {4366, 8164}, {5013, 32826}, {5225, 27020}, {5229, 26959}, {5309, 7615}, {5395, 30435}, {7735, 12150}, {7736, 7757}, {7739, 18546}, {7745, 8667}, {7758, 14711}, {7762, 32834}, {7764, 31417}, {7777, 32817}, {7803, 15031}, {7818, 21356}, {7880, 8176}, {9740, 32893}, {9766, 32836}, {9770, 32833}, {11008, 17131}, {11184, 32837}, {13468, 32885}, {17128, 32818}, {26687, 31418}, {31400, 32819}

X(32983) = reflection of X(33215) in X(2)
X(32983) = {X(2),X(4)}-harmonic conjugate of X(32986)
X(32983) = orthocentroidal-circle-inverse of X(32986)


X(32984) = (name pending)

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

As a point on the Euler line, X(32984) has Shinagawa coefficients ((E+F)2-3S2,-3S2).

X(32984) lies on these lines: {2, 3}, {32, 14971}, {69, 625}, {115, 1007}, {230, 32827}, {524, 13881}, {543, 6337}, {576, 19662}, {599, 32828}, {626, 7617}, {671, 7763}, {1975, 7620}, {1992, 3767}, {2548, 7817}, {3589, 18584}, {3618, 7844}, {3785, 7610}, {3926, 22110}, {5013, 9771}, {5032, 5305}, {5254, 11184}, {5286, 11163}, {5485, 32818}, {5569, 7842}, {6722, 7737}, {7615, 7801}, {7618, 7748}, {7735, 7812}, {7736, 7827}, {7746, 23055}, {7749, 8182}, {7750, 8860}, {7752, 9166}, {7773, 22329}, {7776, 11160}, {7784, 11168}, {7789, 20112}, {7814, 11054}, {7816, 10150}, {7825, 23053}, {7829, 31417}, {7840, 32823}, {7851, 31404}, {7870, 11185}, {7883, 32832}, {7925, 32817}, {8859, 20065}, {9939, 17008}, {11147, 32479}, {11161, 11623}, {18424, 31275}

X(32984) = reflection of X(33216) in X(2)
X(32984) = {X(2),X(4)}-harmonic conjugate of X(32985)
X(32984) = orthocentroidal-circle-inverse of X(32985)


X(32985) = (name pending)

Barycentrics    6 SB SC - 4 S^2 + (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 4*a^2*b^2 + b^4 - 4*a^2*c^2 + 2*b^2*c^2 + c^4 : :

As a point on the Euler line, X(32985) has Shinagawa coefficients ((E+F)2-3S2,3S2).

X(32985) lies on these lines: {2, 3}, {6, 32459}, {32, 1992}, {39, 7618}, {69, 187}, {76, 26613}, {99, 7735}, {141, 5210}, {193, 1384}, {194, 9741}, {230, 32815}, {287, 18931}, {315, 7870}, {385, 32817}, {524, 3053}, {543, 3767}, {574, 3618}, {597, 5013}, {598, 7769}, {599, 3785}, {620, 1007}, {671, 7857}, {1285, 7774}, {1501, 4176}, {1975, 22329}, {2021, 13085}, {2549, 7817}, {3619, 7820}, {3620, 15655}, {3734, 21843}, {3763, 5585}, {3788, 3849}, {3793, 20080}, {3933, 11160}, {3934, 5569}, {3972, 7736}, {4293, 26629}, {4294, 26686}, {5032, 11165}, {5206, 7795}, {5215, 7615}, {5304, 31859}, {5306, 8716}, {5485, 8859}, {7610, 32828}, {7620, 11164}, {7622, 31401}, {7665, 9486}, {7738, 7782}, {7745, 11184}, {7747, 9167}, {7749, 23053}, {7755, 15300}, {7757, 13357}, {7762, 32831}, {7763, 7812}, {7773, 23334}, {7797, 32480}, {7800, 15513}, {7813, 11008}, {7816, 23055}, {7822, 15810}, {7823, 32823}, {7835, 7883}, {7836, 9939}, {7840, 7891}, {7862, 22247}, {7863, 14023}, {7886, 32479}, {8593, 14981}, {8667, 32836}, {8721, 11156}, {9177, 19663}, {9734, 14561}, {9737, 20423}, {9740, 32830}, {9753, 21166}, {9766, 32837}, {9771, 32839}, {10352, 10788}, {10991, 11161}, {11179, 13335}, {12150, 13356}, {13663, 32497}, {13783, 32494}, {13881, 32826}, {15534, 22331}, {15597, 32838}, {22110, 32816}

X(32985) = reflection of X(2) in X(11288)
X(32985) = reflection of X(16041) in X(2)
X(32985) = anticomplement of X(11318)
X(32985) = orthocentroidal-circle-inverse of X(32984)
X(32985) = {X(2),X(3)}-harmonic conjugate of X(33215)
X(32985) = {X(2),X(4)}-harmonic conjugate of X(32984)
X(32985) = {X(2),X(20)}-harmonic conjugate of X(7841)
X(32985) = {X(35305),X(35306)}-harmonic conjugate of X(2)
X(32985) = {X(35942),X(35943)}-harmonic conjugate of X(35955)
X(32985) = {X(37172),X(37173)}-harmonic conjugate of X(4)


X(32986) = (name pending)

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

As a point on the Euler line, X(32986) has Shinagawa coefficients ((E+F)2+S2,-3S2).

X(32986) lies on these lines: {2, 3}, {39, 32006}, {69, 538}, {141, 32815}, {148, 16990}, {193, 15048}, {315, 7738}, {316, 7736}, {543, 7865}, {574, 1007}, {599, 10008}, {626, 6337}, {754, 1992}, {1285, 14712}, {1692, 3849}, {2548, 7842}, {2794, 5182}, {3314, 32817}, {3618, 4045}, {3619, 3734}, {3767, 7830}, {3785, 5254}, {3815, 32827}, {3926, 7784}, {4293, 26590}, {4294, 26561}, {5013, 32816}, {5225, 26959}, {5229, 27020}, {5286, 7750}, {5461, 23053}, {6392, 7767}, {6781, 7913}, {7615, 15810}, {7694, 21163}, {7735, 7790}, {7748, 7800}, {7756, 7795}, {7758, 7873}, {7763, 7911}, {7765, 14023}, {7768, 11055}, {7773, 31400}, {7774, 7898}, {7783, 32818}, {7798, 11008}, {7802, 7803}, {7809, 9770}, {7810, 11648}, {7825, 31401}, {7827, 11057}, {7831, 11185}, {7844, 21843}, {7854, 14711}, {7864, 20065}, {7879, 32830}, {7883, 32833}, {7885, 32823}, {7928, 32822}, {8556, 32828}, {8596, 11606}, {9741, 32480}, {11168, 32885}, {14929, 20080}, {15482, 31415}, {15815, 32829}, {17128, 18840}, {24296, 30828}

X(32986) = reflection of X(2) in X(11287)
X(32986) = reflection of X(14033) in X(2)
X(32986) = anticomplement of X(11286)
X(32986) = {X(2),X(3)}-harmonic conjugate of X(33216)
X(32986) = {X(2),X(4)}-harmonic conjugate of X(32983)
X(32986) = {X(2),X(20)}-harmonic conjugate of X(1003)
X(32986) = orthocentroidal-circle-inverse of X(32983)


X(32987) = (name pending)

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

As a point on the Euler line, X(32987) has Shinagawa coefficients ((E+F)2+2S2,2S2).

X(32987) lies on these lines: {2, 3}, {32, 5395}, {39, 2996}, {76, 31404}, {193, 2548}, {543, 31450}, {574, 32826}, {1506, 3926}, {3618, 13881}, {3619, 18584}, {3620, 3934}, {3734, 32829}, {3785, 5475}, {5182, 20398}, {6179, 32832}, {6337, 31489}, {6392, 7736}, {6462, 31463}, {7603, 7795}, {7615, 7765}, {7617, 7829}, {7697, 9742}, {7749, 32883}, {7753, 32885}, {7759, 11160}, {7764, 32836}, {7774, 32834}, {7777, 32830}, {7785, 15589}, {7800, 32827}, {7837, 32893}, {7849, 8176}, {7941, 10513}, {9752, 10358}, {10590, 26959}, {10591, 27020}, {10983, 14494}, {11185, 31400}, {15271, 32006}, {17005, 32835}, {17008, 32870}, {17128, 32831}, {17129, 32872}, {17131, 32886}, {27091, 31418}, {31401, 32815}

X(32987) = anticomplement of X(32978)
X(32987) = {X(2),X(4)}-harmonic conjugate of X(32990)
X(32987) = {X(2),X(5)}-harmonic conjugate of X(32972)
X(32987) = orthocentroidal-circle-inverse of X(32990)


X(32988) = (name pending)

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

As a point on the Euler line, X(32988) has Shinagawa coefficients ((E+F)2-4S2,-2S2).

X(32988) lies on these lines: {2, 3}, {115, 32829}, {193, 7752}, {620, 32826}, {625, 3785}, {626, 32838}, {1007, 6392}, {2548, 6722}, {2549, 32839}, {3620, 5107}, {3926, 7862}, {5032, 7858}, {5286, 14061}, {7615, 7863}, {7746, 7845}, {7772, 14971}, {7794, 32828}, {7795, 31275}, {7800, 32867}, {7815, 32883}, {7818, 12815}, {7828, 31404}, {7886, 31415}, {7888, 32836}, {7912, 15589}, {7925, 32830}, {7946, 9740}, {9771, 22332}, {16990, 32870}, {18362, 32837}, {19662, 22234}, {20080, 32823}

X(32988) = anticomplement of X(32977)
X(32988) = {X(2),X(4)}-harmonic conjugate of X(32989)
X(32988) = {X(2),X(5)}-harmonic conjugate of X(32971)
X(32988) = orthocentroidal-circle-inverse of X(32989)


X(32989) = (name pending)

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

As a point on the Euler line, X(32989) has Shinagawa coefficients ((E+F)2-4S2,2S2).

X(32989) lies on these lines: {2, 3}, {32, 32829}, {99, 2996}, {187, 32816}, {193, 1692}, {230, 6337}, {385, 32831}, {597, 31492}, {620, 3926}, {1007, 3053}, {1078, 3620}, {2548, 32839}, {3734, 32838}, {3785, 3788}, {3972, 5395}, {5028, 31400}, {5206, 31274}, {5218, 26686}, {5286, 7857}, {5569, 7849}, {7288, 26629}, {7618, 7765}, {7622, 7829}, {7746, 32815}, {7749, 17130}, {7758, 32837}, {7774, 32835}, {7793, 10352}, {7796, 11160}, {7814, 26613}, {7836, 15589}, {7838, 32887}, {7862, 32827}, {7863, 32836}, {7873, 8182}, {7888, 9167}, {7891, 17008}, {7940, 14907}, {7947, 10513}, {9737, 9752}, {9742, 21445}, {13881, 32459}, {14023, 32825}, {17004, 32834}, {17006, 32870}, {17129, 32840}, {20080, 32818}

X(32989) = complement of X(32980)
X(32989) = anticomplement of X(32969)
X(32989) = {X(2),X(3)}-harmonic conjugate of X(32974)
X(32989) = {X(2),X(4)}-harmonic conjugate of X(32988)
X(32989) = {X(2),X(20)}-harmonic conjugate of X(32972)
X(32989) = orthocentroidal-circle-inverse of X(32988)


X(32990) = (name pending)

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

As a point on the Euler line, X(32990) has Shinagawa coefficients ((E+F)2+2S2,-2S2).

X(32990) lies on these lines: {2, 3}, {39, 193}, {69, 5013}, {115, 32838}, {141, 6337}, {183, 6392}, {194, 15589}, {315, 31400}, {316, 31404}, {524, 22332}, {574, 3620}, {597, 22331}, {626, 32829}, {988, 17316}, {1007, 7784}, {1078, 5286}, {1506, 32827}, {2548, 7830}, {2549, 2996}, {3053, 3618}, {3314, 32831}, {3589, 5023}, {3619, 7789}, {3815, 32006}, {3934, 32815}, {4293, 27020}, {4294, 26959}, {5024, 7767}, {5032, 7772}, {5171, 14853}, {5218, 26561}, {5304, 7793}, {5395, 6683}, {6292, 15515}, {6776, 13334}, {7288, 26590}, {7618, 7863}, {7736, 7750}, {7739, 7780}, {7756, 32826}, {7758, 7810}, {7761, 31401}, {7763, 7831}, {7764, 31450}, {7771, 7803}, {7774, 7904}, {7781, 32836}, {7783, 16990}, {7786, 14907}, {7821, 31457}, {7822, 8589}, {7834, 21843}, {7842, 31415}, {7847, 32832}, {7854, 15810}, {7864, 17008}, {7865, 32837}, {7872, 32867}, {7879, 32818}, {7889, 8588}, {7906, 10513}, {7928, 32835}, {7935, 32839}, {8667, 9607}, {9737, 10519}, {11648, 32885}, {13357, 20065}, {14148, 32875}, {17784, 26801}, {19761, 19783}, {26582, 30478}, {32494, 32805}, {32497, 32806}

X(32990) = complement of X(32979)
X(32990) = anticomplement of X(32968)
X(32990) = {X(2),X(3)}-harmonic conjugate of X(32973)
X(32990) = {X(2),X(4)}-harmonic conjugate of X(32987)
X(32990) = {X(2),X(20)}-harmonic conjugate of X(32971)
X(32990) = orthocentroidal-circle-inverse of X(32987)


X(32991) = (name pending)

Barycentrics    4 SB SC + S^2 + (b^2 c^2 + c^2 a^2 + a^2 b^2) : :
Barycentrics    3*a^4 + 6*a^2*b^2 - 5*b^4 + 6*a^2*c^2 + 14*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(32991) has Shinagawa coefficients ((E+F)2+2S2,4S2).

X(32991) lies on these lines: {2, 3}, {187, 32867}, {538, 31417}, {1506, 32815}, {2548, 6392}, {2996, 7736}, {3620, 7773}, {3926, 31415}, {3934, 32827}, {5395, 7735}, {5475, 14023}, {7603, 32829}, {7615, 7772}, {7737, 32838}, {7757, 31407}, {7780, 32885}, {7785, 20080}, {7789, 18584}, {7793, 18845}, {7794, 32816}, {7816, 32839}, {7855, 32868}, {11185, 31404}, {17130, 32825}, {21843, 32883}, {22331, 23055}, {31401, 32826}

X(32991) = {X(2),X(4)}-harmonic conjugate of X(33023)
X(32991) = orthocentroidal-circle-inverse of X(33023)


X(32992) = (name pending)

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

As a point on the Euler line, X(32992) has Shinagawa coefficients ((E+F)2+2S2,S2).

X(32992) lies on these lines: {2, 3}, {6, 32832}, {11, 27020}, {12, 26959}, {69, 31404}, {76, 3815}, {83, 230}, {115, 6683}, {141, 7752}, {183, 2548}, {194, 31406}, {315, 15271}, {325, 1506}, {350, 31460}, {524, 7858}, {538, 9698}, {543, 31652}, {574, 32819}, {597, 7856}, {625, 6292}, {626, 7603}, {1007, 7881}, {1078, 7745}, {1285, 5395}, {1329, 17030}, {1975, 31401}, {2886, 27091}, {3054, 7857}, {3055, 7769}, {3329, 5305}, {3589, 5038}, {3619, 11173}, {3620, 32823}, {3630, 7949}, {3631, 7917}, {3703, 30152}, {3734, 31455}, {3767, 11174}, {3793, 20088}, {3814, 26558}, {3816, 27255}, {3933, 7777}, {4884, 24080}, {5007, 22329}, {5013, 11185}, {5103, 5104}, {5254, 7786}, {5304, 32870}, {5306, 7878}, {5475, 7750}, {5939, 6704}, {5943, 27374}, {6179, 13468}, {6376, 31466}, {6390, 17128}, {6393, 24256}, {6645, 15325}, {7617, 7902}, {7735, 32838}, {7736, 7754}, {7741, 26590}, {7746, 7792}, {7748, 15482}, {7749, 7804}, {7753, 7780}, {7757, 9606}, {7758, 11163}, {7760, 9300}, {7763, 31489}, {7764, 9466}, {7767, 7785}, {7773, 7800}, {7775, 7854}, {7776, 16990}, {7787, 17004}, {7793, 18907}, {7803, 13881}, {7810, 7843}, {7812, 11168}, {7822, 7862}, {7836, 17005}, {7847, 15031}, {7859, 14061}, {7870, 9771}, {7872, 18424}, {7879, 32816}, {7886, 7889}, {7900, 14929}, {7909, 22110}, {7912, 16986}, {7926, 15598}, {7951, 26561}, {8716, 31492}, {10350, 20576}, {10950, 30140}, {15079, 30119}, {15484, 20065}, {15950, 30136}, {16829, 21031}, {17008, 30435}, {17130, 32820}, {17602, 30134}, {17757, 26801}, {18061, 21965}, {20172, 26364}, {24390, 26752}, {24988, 27117}, {25639, 26582}, {26363, 26687}, {27076, 31488}, {31400, 31859}

X(32992) = complement of X(7824)
X(32992) = {X(2),X(4)}-harmonic conjugate of X(11285)
X(32992) = {X(2),X(5)}-harmonic conjugate of X(6656)
X(32992) = {X(2),X(20)}-harmonic conjugate of X(32978)
X(32992) = orthocentroidal-circle-inverse of X(11285)


X(32993) = (name pending)

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

As a point on the Euler line, X(32993) has Shinagawa coefficients ((E+F)2-3S2,-8S2).

X(32993) lies on these lines: {2, 3}, {76, 18424}, {115, 7760}, {148, 7752}, {316, 7780}, {625, 7836}, {626, 15031}, {671, 7764}, {2896, 7825}, {2996, 20105}, {3767, 20088}, {5475, 7797}, {6653, 11681}, {7603, 7847}, {7620, 32825}, {7746, 14712}, {7747, 14061}, {7755, 9166}, {7759, 19570}, {7763, 20094}, {7768, 31173}, {7773, 7779}, {7775, 13571}, {7796, 18546}, {7823, 13881}, {7843, 14568}, {7844, 10583}, {7898, 32832}, {7900, 32827}, {7905, 32457}, {7912, 11185}, {7920, 15484}, {7925, 32819}, {7929, 32828}, {12110, 23514}, {20081, 32816}

X(32993) = anticomplement of X(33259)
X(32993) = {X(2),X(4)}-harmonic conjugate of X(6658)
X(32993) = orthocentroidal-circle-inverse of X(6658)


X(32994) = (name pending)

Barycentrics    12 SB SC + 12 S^2 + (b^2 c^2 + c^2 a^2 + a^2 b^2) : :
Barycentrics    7*a^2*b^2 - 6*b^4 + 7*a^2*c^2 + 13*b^2*c^2 - 6*c^4 : :

As a point on the Euler line, X(32994) has Shinagawa coefficients ((E+F)2+13S2,12S2).

X(32994) lies on these lines: {2, 3}, {385, 18584}, {625, 22564}, {7603, 7757}, {7766, 31415}, {7897, 9466}, {7929, 8556}, {8716, 17005}, {14162, 22712}


X(32995) = (name pending)

Barycentrics    8 SB SC + 2 S^2 + (b^2 c^2 + c^2 a^2 + a^2 b^2) : :
Barycentrics    3*a^4 + 4*a^2*b^2 - 5*b^4 + 4*a^2*c^2 + 12*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(32995) has Shinagawa coefficients ((E+F)2+3S2,8S2).

X(32995) lies on these lines: {2, 3}, {148, 31404}, {2548, 15031}, {5475, 7805}, {7615, 7760}, {7757, 31417}, {7764, 11185}, {7803, 18424}, {7900, 32834}, {14712, 32838}, {31276, 32827}

X(32995) = anticomplement of X(33012)
X(32995) = {X(2),X(4)}-harmonic conjugate of X(32997)
X(32995) = orthocentroidal-circle-inverse of X(32997)


X(32996) = (name pending)

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

As a point on the Euler line, X(32996) has Shinagawa coefficients ((E+F)2-S2,-8S2).

X(32996) lies on these lines: {2, 3}, {115, 20065}, {148, 32816}, {194, 32827}, {315, 17131}, {316, 14023}, {671, 7758}, {1916, 20105}, {3407, 18845}, {5207, 8586}, {6392, 7900}, {7794, 7825}, {7800, 15031}, {7836, 32826}, {7842, 18424}, {7847, 31415}, {7898, 32828}, {7912, 32815}, {7929, 32834}, {7947, 32822}, {8176, 31652}, {9988, 16635}, {9989, 16634}, {20094, 32831}

X(32996) = complement of X(33214)
X(32996) = anticomplement of X(32964)
X(32996) = {X(2),X(4)}-harmonic conjugate of X(14068)
X(32996) = orthocentroidal-circle-inverse of X(14068)


X(32997) = (name pending)

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

As a point on the Euler line, X(32997) has Shinagawa coefficients ((E+F)2+3S2,-8S2).

X(32997) lies on these lines: {2, 3}, {148, 3785}, {315, 7756}, {732, 20080}, {1285, 7920}, {2549, 7760}, {2896, 32815}, {3926, 7898}, {5286, 14712}, {6337, 7885}, {6781, 7872}, {7737, 7847}, {7738, 7823}, {7748, 7780}, {7763, 7842}, {7783, 32006}, {7795, 7910}, {7830, 11185}, {7873, 32833}, {7929, 20094}, {7939, 32817}, {8591, 32824}, {11057, 14023}, {13571, 32480}, {16990, 32819}, {31276, 32826}

X(32997) = reflection of X(2) in X(33263)
X(32997) = anticomplement of X(14035)
X(32997) = {X(2),X(4)}-harmonic conjugate of X(32995)
X(32997) = {X(2),X(20)}-harmonic conjugate of X(33244)
X(32997) = orthocentroidal-circle-inverse of X(32995)


X(32998) = (name pending)

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

As a point on the Euler line, X(32998) has Shinagawa coefficients ((E+F)2-7S2,-2S2).

X(32998) lies on these lines: {2, 3}, {1506, 16989}, {3054, 7773}, {3055, 7851}, {3314, 32838}, {3619, 8586}, {3785, 17006}, {5286, 17005}, {6722, 7803}, {7617, 7863}, {7746, 7774}, {7751, 12815}, {7752, 14023}, {7763, 14148}, {7783, 32839}, {7794, 7862}, {7806, 31404}, {7857, 31415}, {7902, 14971}, {7922, 16990}, {7925, 32828}, {7947, 32834}, {9939, 23053}, {12150, 31417}, {14061, 31401}, {17004, 32816}

X(32998) = complement of X(33206)
X(32998) = {X(2),X(4)}-harmonic conjugate of X(33000)
X(32998) = {X(2),X(5)}-harmonic conjugate of X(16925)
X(32998) = {X(2),X(20)}-harmonic conjugate of X(16923)
X(32998) = orthocentroidal-circle-inverse of X(33000)


X(32999) = (name pending)

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

As a point on the Euler line, X(32999) has Shinagawa coefficients ((E+F)2+5S2,2S2).

X(32999) lies on these lines: {2, 3}, {193, 32870}, {315, 7603}, {385, 31404}, {1007, 31276}, {1078, 31415}, {1506, 7751}, {1975, 3055}, {2548, 6179}, {3926, 17005}, {6722, 10352}, {7615, 31450}, {7617, 7765}, {7746, 16989}, {7752, 16990}, {7763, 17130}, {7777, 32828}, {7812, 31417}, {7851, 15491}, {7873, 8176}, {7891, 32839}, {7904, 32827}, {7906, 32834}, {7941, 15589}, {9754, 10358}, {11185, 31455}, {17004, 32867}, {17006, 32883}, {17128, 32829}

X(32999) = complement of X(33012)
X(32999) = {X(2),X(3)}-harmonic conjugate of X(33003)
X(32999) = {X(2),X(4)}-harmonic conjugate of X(33001)
X(32999) = {X(2),X(5)}-harmonic conjugate of X(7791)
X(32999) = {X(2),X(20)}-harmonic conjugate of X(33015)
X(32999) = orthocentroidal-circle-inverse of X(33001)


X(33000) = (name pending)

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

As a point on the Euler line, X(33000) has Shinagawa coefficients ((E+F)2-7S2,2S2).

X(33000) lies on these lines: {2, 3}, {385, 32829}, {620, 17130}, {1007, 7793}, {1153, 7849}, {1975, 3054}, {3618, 5111}, {3785, 7925}, {3788, 16990}, {3926, 17004}, {5569, 7873}, {6179, 7769}, {6722, 15515}, {7619, 7829}, {7622, 7765}, {7746, 32457}, {7749, 7751}, {7752, 21843}, {7777, 32839}, {7800, 7940}, {7806, 31400}, {7815, 10352}, {7817, 31457}, {7827, 31450}, {7857, 16989}, {7862, 14907}, {7891, 17006}, {7906, 32835}, {7947, 15589}, {9737, 9754}, {12815, 18546}, {13468, 32821}, {17128, 32838}, {17129, 32831}, {31404, 32884}

X(33000) = complement of X(32963)
X(33000) = {X(2),X(3)}-harmonic conjugate of X(32961)
X(33000) = {X(2),X(4)}-harmonic conjugate of X(32998)
X(33000) = {X(2),X(20)}-harmonic conjugate of X(32967)
X(33000) = orthocentroidal-circle-inverse of X(32998)


X(33001) = (name pending)

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

As a point on the Euler line, X(33001) has Shinagawa coefficients ((E+F)2+5S2,-2S2).

X(33001) lies on these lines: {2, 3}, {39, 17008}, {69, 5038}, {83, 21843}, {315, 31455}, {385, 31400}, {538, 31457}, {574, 32832}, {1007, 2896}, {1078, 7774}, {1506, 14907}, {2548, 7771}, {3054, 7851}, {3055, 7773}, {3314, 32829}, {3618, 10007}, {3619, 7945}, {3620, 7947}, {3785, 7777}, {3815, 20065}, {5286, 17004}, {6337, 31276}, {7610, 22332}, {7622, 7863}, {7736, 7793}, {7749, 7803}, {7750, 31489}, {7757, 31450}, {7762, 31467}, {7763, 7794}, {7769, 7800}, {7783, 32828}, {7786, 16989}, {7802, 31415}, {7823, 31404}, {7864, 17006}, {7904, 17005}, {7906, 15589}, {7914, 31274}, {7925, 32839}, {7929, 32823}, {7946, 9770}, {8667, 31492}, {9606, 14614}

X(33001) = complement of X(32962)
X(33001) = {X(2),X(3)}-harmonic conjugate of X(16924)
X(33001) = {X(2),X(4)}-harmonic conjugate of X(32999)
X(33001) = {X(2),X(20)}-harmonic conjugate of X(16921)
X(33001) = orthocentroidal-circle-inverse of X(32999)


X(33002) = (name pending)

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

As a point on the Euler line, X(33002) has Shinagawa coefficients ((E+F)2+5S2,4S2).

X(33002) lies on these lines: {2, 3}, {76, 7603}, {148, 31401}, {183, 7900}, {194, 1506}, {574, 15031}, {625, 7938}, {1975, 17005}, {2548, 7766}, {3053, 17006}, {3055, 32819}, {3329, 13881}, {3619, 5103}, {3934, 7912}, {4027, 7808}, {5475, 7793}, {6722, 7846}, {7617, 7772}, {7745, 17004}, {7746, 7787}, {7752, 7794}, {7773, 7929}, {7775, 7946}, {7777, 20081}, {7779, 32828}, {7783, 31489}, {7785, 14023}, {7814, 9466}, {7815, 7898}, {7843, 9939}, {7847, 18424}, {7854, 8176}, {7862, 7945}, {7885, 15271}, {7902, 9166}, {7930, 31275}, {7934, 31239}, {7936, 31173}, {8860, 22331}, {17008, 20088}, {20065, 32838}, {31652, 32480}

X(33002) = complement of X(33022)
X(33002) = anticomplement of X(33015)
X(33002) = {X(2),X(4)}-harmonic conjugate of X(33004)
X(33002) = {X(2),X(5)}-harmonic conjugate of X(32966)
X(33002) = orthocentroidal-circle-inverse of X(33004)


X(33003) = (name pending)

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

As a point on the Euler line, X(33003) has Shinagawa coefficients ((E+F)2+9S2,-2S2).

X(33003) lies on these lines: {2, 3}, {3314, 32839}, {3620, 32871}, {3785, 17005}, {5286, 17006}, {7749, 16989}, {7760, 17008}, {7769, 16990}, {7774, 7780}, {7781, 32832}, {7783, 32838}, {11168, 32821}, {14568, 31450}, {17004, 31400}, {20065, 31489}

X(33003) = complement of X(33009)
X(33003) = {X(2),X(3)}-harmonic conjugate of X(32999)
X(33003) = {X(2),X(20)}-harmonic conjugate of X(16922)


X(33004) = (name pending)

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

As a point on the Euler line, X(33004) has Shinagawa coefficients ((E+F)2+5S2,-4S2).

X(33004) lies on these lines: {2, 3}, {39, 6179}, {69, 5116}, {83, 5206}, {98, 32522}, {99, 7815}, {141, 7891}, {148, 32832}, {183, 7783}, {187, 7786}, {194, 574}, {230, 7864}, {316, 31455}, {325, 7904}, {385, 5013}, {484, 30140}, {620, 3096}, {625, 7910}, {1506, 7802}, {2076, 3618}, {2548, 14712}, {2896, 7763}, {3053, 3329}, {3336, 30135}, {3619, 4048}, {3620, 12215}, {3785, 7779}, {3788, 7831}, {3815, 7823}, {3934, 7782}, {3972, 6683}, {4045, 7857}, {4366, 5217}, {4396, 32107}, {4400, 32005}, {5010, 26959}, {5023, 11174}, {5024, 7839}, {5152, 7795}, {5204, 6645}, {5254, 17004}, {5267, 27091}, {5569, 7827}, {6194, 9737}, {6292, 7835}, {6337, 16990}, {6653, 10527}, {7280, 27020}, {7622, 7883}, {7709, 10104}, {7736, 20088}, {7738, 17008}, {7746, 7847}, {7749, 7790}, {7750, 7777}, {7752, 7830}, {7757, 7780}, {7759, 9939}, {7761, 7769}, {7764, 7811}, {7767, 7906}, {7773, 17005}, {7778, 7928}, {7784, 7925}, {7785, 14907}, {7789, 16986}, {7796, 7810}, {7799, 7854}, {7800, 7836}, {7803, 21843}, {7808, 8588}, {7812, 9698}, {7814, 7873}, {7821, 7936}, {7843, 11057}, {7848, 7871}, {7849, 7870}, {7853, 7940}, {7862, 7911}, {7865, 7909}, {7869, 31168}, {7872, 14061}, {7874, 7937}, {7879, 7947}, {7886, 7918}, {7899, 7935}, {7908, 32027}, {7921, 31406}, {9607, 22329}, {10788, 11272}, {11059, 15822}, {11163, 31492}, {13571, 14023}, {13881, 17006}, {14614, 22332}, {15271, 17128}, {17129, 20105}, {20065, 31400}, {31239, 32456}

X(33004) = complement of X(33018)
X(33004) = anticomplement of X(16921)
X(33004) = {X(2),X(3)}-harmonic conjugate of X(3552)
X(33004) = {X(2),X(4)}-harmonic conjugate of X(33002)
X(33004) = {X(2),X(20)}-harmonic conjugate of X(16044)
X(33004) = orthocentroidal-circle-inverse of X(33002)


X(33005) = (name pending)

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

As a point on the Euler line, X(33005) has Shinagawa coefficients ((E+F)2+5S2,6S2).

X(33005) lies on these lines: {2, 3}, {325, 18584}, {754, 32832}, {1506, 18546}, {2023, 11152}, {2548, 7894}, {3618, 11646}, {5475, 17008}, {7603, 11185}, {7615, 7757}, {7617, 7753}, {7760, 31417}, {7774, 31415}, {7818, 16990}, {7823, 32838}, {7941, 32834}, {8176, 9466}, {11160, 32893}, {13468, 20065}, {15031, 31401}, {17005, 32815}, {21356, 24256}

X(33005) = {X(2),X(4)}-harmonic conjugate of X(33008)
X(33005) = orthocentroidal-circle-inverse of X(33008)


X(33006) = (name pending)

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

As a point on the Euler line, X(33006) has Shinagawa coefficients ((E+F)2-3S2,-6S2).

X(33006) lies on these lines: lines: {2, 3}, {32, 5461}, {39, 8176}, {69, 8586}, {76, 7615}, {115, 7774}, {148, 1007}, {194, 9770}, {315, 31173}, {316, 17008}, {385, 32827}, {524, 7773}, {543, 7763}, {597, 7851}, {598, 7828}, {625, 7801}, {671, 7752}, {754, 18362}, {1975, 22110}, {1992, 6034}, {2482, 7862}, {2548, 7827}, {3618, 10485}, {3767, 7812}, {3849, 7746}, {3926, 7620}, {5032, 7921}, {5254, 11163}, {5475, 7817}, {5485, 20081}, {5978, 16635}, {5979, 16634}, {6337, 8591}, {6392, 7941}, {7610, 7750}, {7617, 7810}, {7618, 7769}, {7619, 15515}, {7622, 7756}, {7737, 14061}, {7747, 14971}, {7758, 11054}, {7767, 16509}, {7790, 31415}, {7793, 23055}, {7795, 15031}, {7802, 8182}, {7823, 8859}, {7840, 32816}, {7864, 31404}, {7883, 16990}, {7885, 32828}, {7891, 32826}, {7893, 9740}, {7904, 32838}, {7925, 32815}, {7939, 32834}, {9737, 9880}, {9753, 23514}, {9939, 32006}, {11160, 17129}, {12962, 13637}, {12969, 13757}, {13881, 20065}, {18546, 32833}, {21356, 31276}

X(33006) = complement of X(33208)
X(33006) = {X(2),X(4)}-harmonic conjugate of X(33007)
X(33006) = {X(2),X(20)}-harmonic conjugate of X(33274)
X(33006) = orthocentroidal-circle-inverse of X(33007)


X(33007) = (name pending)

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

As a point on the Euler line, X(33007) has Shinagawa coefficients ((E+F)2-3S2,6S2).

X(33007) lies on these lines: {2, 3}, {32, 543}, {61, 12155}, {62, 12154}, {69, 5104}, {99, 7737}, {148, 5939}, {187, 11185}, {193, 11173}, {194, 1992}, {315, 3849}, {316, 7870}, {385, 32815}, {524, 1975}, {576, 10992}, {598, 2548}, {599, 7750}, {671, 3767}, {754, 32833}, {1078, 8182}, {1285, 7766}, {1383, 14360}, {1506, 7622}, {2482, 7747}, {2549, 3972}, {2896, 21356}, {3053, 22329}, {3734, 6781}, {3785, 17128}, {3788, 31173}, {3926, 7823}, {4027, 10788}, {4293, 4366}, {4294, 6645}, {5032, 7839}, {5038, 7738}, {5182, 12110}, {5206, 32832}, {5305, 19661}, {5475, 32456}, {5569, 15513}, {6179, 11054}, {7785, 9770}, {7615, 26613}, {7617, 7749}, {7620, 8859}, {7739, 12150}, {7745, 11163}, {7748, 7817}, {7756, 7803}, {7773, 22110}, {7779, 32817}, {7781, 15300}, {7795, 7802}, {7836, 32006}, {7857, 9166}, {7862, 9167}, {7891, 23334}, {7893, 11160}, {7900, 32818}, {7925, 32827}, {7941, 32831}, {8593, 23235}, {9740, 17129}, {9741, 20088}, {9753, 23698}, {9863, 11180}, {10350, 19924}, {11178, 32152}, {11179, 11257}, {12251, 22564}, {12943, 26629}, {12953, 26686}, {16118, 30123}, {18907, 31859}, {20081, 32822}

X(33007) = midpoint of X(2) and X(33193)
X(33007) = reflection of X(2) in X(1003)
X(33007) = reflection of X(33017) in X(2)
X(33007) = complement of X(33192)
X(33007) = anticomplement of X(7841)
X(33007) = {X(2),X(4)}-harmonic conjugate of X(33006)
X(33007) = {X(2),X(20)}-harmonic conjugate of X(7833)
X(33007) = orthocentroidal-circle-inverse of X(33006)


X(33008) = (name pending)

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

As a point on the Euler line, X(33008) has Shinagawa coefficients ((E+F)2+5S2,-6S2).

X(33008) lies on these lines: {2, 3}, {99, 16990}, {187, 16989}, {574, 754}, {1007, 7898}, {1992, 3094}, {2482, 7865}, {2549, 7771}, {2896, 6337}, {3448, 14605}, {3785, 7783}, {3926, 7904}, {4045, 8588}, {5013, 20065}, {5206, 7803}, {5210, 7792}, {5976, 8591}, {6781, 15482}, {7618, 7799}, {7620, 32885}, {7736, 14712}, {7738, 7793}, {7739, 8182}, {7750, 9766}, {7756, 18546}, {7761, 8589}, {7763, 7818}, {7782, 7800}, {7785, 14976}, {7790, 21843}, {7795, 31168}, {7802, 31401}, {7810, 32833}, {7823, 31400}, {7843, 31457}, {7845, 15602}, {7858, 31450}, {7868, 32459}, {7884, 26613}, {7885, 32829}, {7929, 32818}, {7939, 32831}, {9830, 21356}, {11152, 11177}, {17005, 32827}, {19570, 32480}

X(33008) = midpoint of X(2) and X(33207)
X(33008) = reflection of X(33016) in X(2)
X(33008) = {X(2),X(4)}-harmonic conjugate of X(33005)
X(33008) = {X(2),X(20)}-harmonic conjugate of X(11361)
X(33008) = orthocentroidal-circle-inverse of X(33005)


X(33009) = (name pending)

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

As a point on the Euler line, X(33009) has Shinagawa coefficients ((E+F)2+7S2,4S2).

X(33009) lies on these lines: {2, 3}, {671, 31450}, {1506, 7798}, {6179, 31417}, {7603, 7759}, {7617, 9698}, {7750, 18584}, {7785, 32838}, {7793, 32867}, {20065, 31415}

X(33009) = anticomplement of X(33003)
X(33009) = {X(2),X(4)}-harmonic conjugate of X(33012)
X(33009) = {X(2),X(5)}-harmonic conjugate of X(14063)
X(33009) = {X(2),X(20)}-harmonic conjugate of X(33188)
X(33009) = orthocentroidal-circle-inverse of X(33012)


X(33010) = (name pending)

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

As a point on the Euler line, X(33010) has Shinagawa coefficients ((E+F)2+9S2,8S2).

X(33010) lies on these lines: {2, 3}, {194, 7603}, {7617, 7760}, {7764, 20081}, {7768, 8176}, {7777, 20105}, {7821, 31276}, {7900, 32832}

X(33010) = {X(2),X(4)}-harmonic conjugate of X(33022)
X(33010) = {X(2),X(5)}-harmonic conjugate of X(33011)
X(33010) = orthocentroidal-circle-inverse of X(33022)


X(33011) = (name pending)

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

As a point on the Euler line, X(33011) has Shinagawa coefficients ((E+F)2-7S2,-8S2).

X(33011) lies on these lines: {2, 3}, {194, 32457}, {625, 7922}, {3620, 5103}, {5461, 7856}, {7752, 7813}, {7760, 18362}, {7766, 13881}, {7769, 18424}, {7772, 9166}, {7787, 14061}, {7794, 7912}, {7797, 31415}, {7851, 18584}, {7858, 8176}, {7862, 15031}, {7900, 14023}, {7929, 32832}, {11161, 22234}, {20094, 32829}

X(33011) = {X(2),X(4)}-harmonic conjugate of X(33014)
X(33011) = {X(2),X(5)}-harmonic conjugate of X(33010)
X(33011) = orthocentroidal-circle-inverse of X(33014)


X(33012) = (name pending)

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

As a point on the Euler line, X(33012) has Shinagawa coefficients ((E+F)2+7S2,-4S2).

X(33012) lies on these lines: {2, 3}, {148, 32838}, {193, 5038}, {1007, 7904}, {1078, 7758}, {2896, 32829}, {3785, 7946}, {5007, 5569}, {5013, 17008}, {7622, 7794}, {7738, 17004}, {7749, 7902}, {7760, 31450}, {7763, 7854}, {7769, 7936}, {7771, 7858}, {7780, 31457}, {7786, 21843}, {7793, 31400}, {7800, 7909}, {7815, 7863}, {7843, 14907}, {7897, 32835}, {7912, 32839}, {8556, 32820}, {11185, 15515}, {14712, 31404}, {17005, 32006}, {22329, 22332}

X(33012) = complement of X(32995)
X(33012) = anticomplement of X(32999)
X(33012) = {X(2),X(3)}-harmonic conjugate of X(14035)
X(33012) = {X(2),X(4)}-harmonic conjugate of X(33009)
X(33012) = {X(2),X(20)}-harmonic conjugate of X(32962)
X(33012) = orthocentroidal-circle-inverse of X(33009)


X(33013) = (name pending)

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

As a point on the Euler line, X(33013) has Shinagawa coefficients ((E+F)2+3S2,6S2).

X(33013) lies on these lines: {2, 3}, {17, 10809}, {18, 10808}, {32, 598}, {39, 671}, {76, 7775}, {83, 7817}, {99, 7603}, {111, 23297}, {115, 3329}, {148, 3815}, {183, 9939}, {187, 17006}, {194, 11163}, {316, 7810}, {385, 5475}, {524, 7785}, {543, 1506}, {575, 8593}, {597, 7797}, {599, 7773}, {625, 7931}, {1078, 3849}, {1153, 15513}, {1975, 11184}, {1992, 7921}, {2482, 7769}, {2548, 7615}, {3053, 8860}, {3734, 7870}, {3785, 23334}, {3934, 7883}, {4366, 7951}, {5013, 32480}, {5038, 9830}, {5254, 20112}, {5395, 11172}, {5461, 7828}, {6054, 6248}, {6287, 10810}, {6645, 7741}, {6680, 14971}, {7610, 7793}, {7620, 31404}, {7622, 7782}, {7737, 17004}, {7745, 22329}, {7749, 26613}, {7750, 11168}, {7752, 7801}, {7753, 14568}, {7757, 18546}, {7766, 15484}, {7777, 11185}, {7787, 10807}, {7790, 18424}, {7804, 14061}, {7808, 7923}, {7809, 9466}, {7814, 17130}, {7818, 18806}, {7823, 32832}, {7825, 7928}, {7836, 22110}, {7842, 15810}, {7853, 16988}, {7858, 11054}, {7861, 14762}, {7893, 32828}, {7898, 15271}, {7906, 9770}, {7911, 31239}, {7919, 16987}, {7926, 17131}, {7938, 21358}, {7946, 15533}, {8591, 32819}, {11002, 12525}, {11160, 32834}, {11161, 18553}, {11178, 22486}, {14160, 15819}, {16509, 20088}, {16829, 31160}, {16990, 32827}, {18800, 25555}, {22679, 22712}

X(33013) = reflection of X(33273) in X(2)
X(33013) = {X(2),X(4)}-harmonic conjugate of X(7833)
X(33013) = orthocentroidal-circle-inverse of X(7833)


X(33014) = (name pending)

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

As a point on the Euler line, X(33014) has Shinagawa coefficients ((E+F)2-7S2,8S2).

X(33014) lies on these lines: {2, 3}, {76, 15513}, {83, 15515}, {99, 5206}, {187, 194}, {193, 2076}, {385, 5023}, {574, 7787}, {620, 7802}, {1078, 8588}, {1384, 7839}, {1975, 5210}, {2080, 10131}, {2482, 7796}, {3053, 7766}, {3231, 3360}, {3329, 15815}, {3620, 4048}, {3788, 7898}, {3849, 7814}, {4027, 5171}, {4366, 5204}, {5131, 30139}, {5152, 20094}, {5162, 20065}, {5217, 6645}, {6390, 7893}, {6781, 7752}, {7750, 7891}, {7756, 7857}, {7761, 7945}, {7763, 7900}, {7765, 32480}, {7771, 7816}, {7786, 8589}, {7789, 7904}, {7799, 7946}, {7811, 7863}, {7821, 11057}, {7830, 7835}, {7836, 7929}, {7842, 7940}, {7843, 19569}, {7847, 7932}, {7860, 14976}, {7870, 7873}, {7874, 7910}, {7878, 31652}, {7880, 7936}, {9734, 12110}, {10353, 30270}, {10987, 31999}, {12215, 20080}, {13335, 32522}, {16948, 20158}, {17004, 32819}, {20190, 22486}, {23208, 32517}

X(33014) = anticomplement of X(32966)
X(33014) = {X(2),X(3)}-harmonic conjugate of X(33022)
X(33014) = {X(2),X(4)}-harmonic conjugate of X(33011)
X(33014) = {X(2),X(20)}-harmonic conjugate of X(33019)
X(33014) = orthocentroidal-circle-inverse of X(33011)


X(33015) = (name pending)

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

As a point on the Euler line, X(33015) has Shinagawa coefficients ((E+F)2+7S2,-2S2).

X(33015) lies on these lines: {2, 3}, {39, 17004}, {76, 14148}, {148, 15815}, {183, 7906}, {230, 7920}, {315, 17005}, {385, 31401}, {1007, 7939}, {1078, 7759}, {1506, 7771}, {3055, 7750}, {3314, 7769}, {3767, 17006}, {3785, 7941}, {3788, 16986}, {3815, 7793}, {3934, 7891}, {5319, 8859}, {5326, 26561}, {5444, 30136}, {5445, 30140}, {6179, 9698}, {6292, 7940}, {6681, 27255}, {6683, 7857}, {6722, 7918}, {7294, 26590}, {7603, 7802}, {7610, 31492}, {7619, 7870}, {7622, 17130}, {7746, 7864}, {7749, 7786}, {7752, 7873}, {7766, 31406}, {7780, 7837}, {7783, 32832}, {7785, 31489}, {7800, 7925}, {7810, 7814}, {7828, 15482}, {7831, 7862}, {7835, 31239}, {7836, 15271}, {7839, 17008}, {7930, 31274}, {7947, 16990}, {8182, 31417}, {8556, 32821}, {8667, 13571}, {9606, 22329}, {9607, 15597}, {10335, 32189}, {11152, 11623}

X(33015) = complement of X(33002)
X(33015) = {X(2),X(3)}-harmonic conjugate of X(16921)
X(33015) = {X(2),X(4)}-harmonic conjugate of X(16922)
X(33015) = {X(2),X(20)}-harmonic conjugate of X(32999)
X(33015) = orthocentroidal-circle-inverse of X(16922)


X(33016) = (name pending)

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

As a point on the Euler line, X(33016) has Shinagawa coefficients ((E+F)2+S2,6S2).

X(33016) lies on these lines: {2, 3}, {99, 31415}, {115, 16989}, {148, 7736}, {315, 9466}, {316, 16990}, {538, 5475}, {598, 7615}, {671, 7739}, {1352, 22486}, {1992, 19570}, {2548, 7757}, {3314, 32827}, {3767, 12150}, {4366, 10590}, {5182, 14561}, {6034, 9830}, {6310, 21849}, {6392, 7921}, {6645, 10591}, {7737, 17008}, {7745, 14614}, {7747, 32832}, {7750, 8556}, {7753, 18546}, {7759, 14711}, {7775, 32833}, {7777, 32815}, {7783, 31404}, {7804, 18424}, {7823, 32828}, {7840, 32836}, {7858, 11055}, {7893, 32834}, {7941, 32830}, {8667, 20065}, {8716, 32819}, {9771, 11164}, {11160, 32874}, {11606, 18842}, {12154, 16267}, {12155, 16268}, {17128, 32816}, {31276, 32006}

X(33016) = reflection of X(33008) in X(2)
X(33016) = complement of X(33207)
X(33016) = {X(2),X(4)}-harmonic conjugate of X(33017)
X(33016) = {X(2),X(20)}-harmonic conjugate of X(33273)
X(33016) = orthocentroidal-circle-inverse of X(33017)


X(33017) = (name pending)

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

As a point on the Euler line, X(33017) has Shinagawa coefficients ((E+F)2+S2,-6S2).

X(33017) lies on these lines: {2, 3}, {69, 148}, {115, 14907}, {147, 11152}, {194, 32006}, {315, 538}, {316, 2549}, {325, 8716}, {543, 7818}, {671, 7811}, {754, 11648}, {1992, 5111}, {2548, 7847}, {2996, 17129}, {3314, 32815}, {3421, 6653}, {3767, 7802}, {3849, 5309}, {3926, 7885}, {5182, 10722}, {5254, 14614}, {5286, 7823}, {5485, 11606}, {6337, 7912}, {6392, 7893}, {6722, 8588}, {6781, 7844}, {7735, 14712}, {7737, 7790}, {7738, 7785}, {7739, 7812}, {7747, 7803}, {7750, 8667}, {7756, 7763}, {7758, 7860}, {7761, 9466}, {7777, 32827}, {7783, 32816}, {7784, 32819}, {7795, 7911}, {7800, 7910}, {7810, 18546}, {7830, 32832}, {7873, 14711}, {7880, 32479}, {7897, 20094}, {7904, 32828}, {7939, 32830}, {8182, 9166}, {8591, 32528}, {9744, 13449}, {9754, 23514}, {9770, 32480}, {9865, 32474}, {9939, 19570}, {10242, 11171}, {11057, 14568}, {12943, 26590}, {12953, 26561}, {14061, 21843}, {16118, 30119}, {17128, 32826}, {22486, 31670}

X(33017) = midpoint of X(2) and X(33192)
X(33017) = reflection of X(2) in X(7841)
X(33017) = reflection of X(33007) in X(2)
X(33017) = complement of X(33193)
X(33017) = anticomplement of X(1003)
X(33017) = {X(2),X(4)}-harmonic conjugate of X(33016)
X(33017) = {X(2),X(20)}-harmonic conjugate of X(13586)
X(33017) = orthocentroidal-circle-inverse of X(33016)


X(33018) = (name pending)

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

As a point on the Euler line, X(33018) has Shinagawa coefficients ((E+F)2+S2,8S2).

X(33018) lies on these lines: {2, 3}, {32, 15031}, {76, 7843}, {83, 7902}, {115, 7787}, {148, 1569}, {194, 5475}, {316, 7854}, {598, 5007}, {625, 7945}, {671, 7772}, {3060, 6310}, {3734, 7909}, {3934, 7898}, {4027, 10358}, {4366, 10895}, {5286, 32528}, {5395, 11606}, {6179, 14537}, {6645, 10896}, {7603, 7782}, {7615, 10807}, {7745, 7766}, {7747, 7793}, {7752, 7863}, {7758, 7785}, {7760, 18546}, {7773, 7897}, {7774, 20105}, {7777, 32819}, {7804, 7932}, {7809, 17130}, {7825, 7938}, {7828, 18424}, {7839, 15484}, {7860, 9466}, {7894, 32457}, {7910, 31239}, {7922, 31173}, {8593, 22234}, {8859, 22331}, {14712, 32832}, {18513, 26959}, {18514, 27020}, {18553, 22486}, {20094, 32826}

X(33018) = anticomplement of X(33004)
X(33018) = {X(2),X(4)}-harmonic conjugate of X(33019)
X(33018) = {X(2),X(20)}-harmonic conjugate of X(33022)
X(33018) = orthocentroidal-circle-inverse of X(33019)


X(33019) = (name pending)

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

As a point on the Euler line, X(33019) has Shinagawa coefficients ((E+F)2+S2,-8S2).

X(33019) lies on these lines: {2, 3}, {76, 7842}, {83, 7872}, {99, 7825}, {115, 7793}, {148, 315}, {193, 15514}, {194, 316}, {538, 7860}, {543, 7796}, {625, 7782}, {671, 7751}, {1975, 7885}, {2549, 7785}, {2896, 11185}, {2979, 6310}, {3314, 32819}, {3436, 6653}, {3734, 7911}, {3767, 10631}, {3849, 6179}, {3926, 20094}, {3934, 7910}, {3972, 7861}, {4027, 10722}, {4366, 12953}, {5171, 14639}, {5206, 14061}, {5254, 7766}, {5286, 20088}, {5309, 19569}, {5475, 7847}, {6321, 12251}, {6645, 12943}, {6781, 7857}, {7709, 10242}, {7737, 7797}, {7745, 7864}, {7747, 7787}, {7752, 7756}, {7757, 7843}, {7760, 11648}, {7761, 31276}, {7765, 7812}, {7773, 7783}, {7775, 32480}, {7779, 20105}, {7780, 11057}, {7781, 7809}, {7784, 17128}, {7804, 7918}, {7814, 31173}, {7815, 15031}, {7816, 7934}, {7870, 32479}, {7878, 14537}, {7883, 17130}, {7902, 12150}, {7920, 18907}, {7921, 15048}, {7926, 32450}, {7936, 9466}, {7940, 32456}, {7941, 31859}, {8176, 31457}, {9821, 22515}, {9988, 31710}, {9989, 31709}, {10723, 30270}, {11257, 13449}, {14023, 19570}, {14568, 14976}, {15815, 17005}, {18513, 27020}, {18514, 26959}, {20553, 21219}

X(33019) = anticomplement of X(3552)
X(33019) = {X(2),X(4)}-harmonic conjugate of X(33018)
X(33019) = {X(2),X(20)}-harmonic conjugate of X(33014)
X(33019) = orthocentroidal-circle-inverse of X(33018)


X(33020) = (name pending)

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

As a point on the Euler line, X(33020) has Shinagawa coefficients (3(E+F)2+3S2,4S2).

X(33020) lies on these lines: {2, 3}, {76, 13571}, {83, 7755}, {148, 7786}, {183, 20088}, {316, 31239}, {373, 6310}, {626, 10159}, {1506, 7836}, {2548, 7779}, {2896, 5475}, {3618, 13196}, {3815, 17128}, {3934, 7768}, {4027, 11623}, {4045, 15031}, {4857, 27020}, {5013, 20094}, {5270, 26959}, {6680, 12815}, {6704, 7919}, {7603, 7832}, {7736, 20081}, {7746, 10583}, {7752, 7869}, {7766, 32828}, {7772, 19570}, {7773, 16986}, {7777, 32821}, {7787, 32832}, {7789, 17005}, {7797, 7808}, {7815, 14712}, {7823, 15271}, {7827, 14762}, {7834, 11606}, {7858, 9466}, {7875, 13881}, {7889, 14061}, {7891, 31489}, {7893, 15484}, {7900, 16990}, {7912, 31415}, {7918, 18424}, {9596, 30998}, {10353, 14651}, {15491, 32819}, {31404, 32825}, {31407, 32836}

X(33020) = {X(2),X(4)}-harmonic conjugate of X(33021)
X(33020) = orthocentroidal-circle-inverse of X(33021)


X(33021) = (name pending)

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

As a point on the Euler line, X(33021) has Shinagawa coefficients (3(E+F)2+3S2,-4S2).

X(33021) lies on these lines: {2, 3}, {6, 7904}, {39, 2896}, {69, 32449}, {83, 7830}, {99, 6292}, {110, 14133}, {141, 7783}, {147, 13334}, {148, 3934}, {183, 7864}, {187, 7859}, {194, 7800}, {230, 7923}, {287, 10619}, {316, 6683}, {325, 7928}, {574, 3096}, {620, 7944}, {633, 3106}, {634, 3107}, {695, 8041}, {1078, 4045}, {1352, 32522}, {1506, 7911}, {1691, 10346}, {1975, 16986}, {2548, 7898}, {2549, 31276}, {3053, 7875}, {3314, 5013}, {3329, 7750}, {3785, 7766}, {3788, 7937}, {3815, 7885}, {4027, 10991}, {4857, 26959}, {5024, 7879}, {5206, 7846}, {5207, 10007}, {5270, 27020}, {5475, 7910}, {5650, 6310}, {6646, 33299}, {6653, 26801}, {6704, 6781}, {7736, 7900}, {7738, 10335}, {7746, 7918}, {7749, 7919}, {7752, 7935}, {7757, 7854}, {7759, 7936}, {7760, 7810}, {7761, 7785}, {7763, 7938}, {7764, 7883}, {7765, 19570}, {7767, 7839}, {7769, 7853}, {7771, 7834}, {7772, 7811}, {7774, 7929}, {7777, 7784}, {7780, 7827}, {7782, 7822}, {7787, 14907}, {7788, 22332}, {7790, 7815}, {7793, 7803}, {7794, 31168}, {7796, 7865}, {7799, 7849}, {7802, 7808}, {7809, 9698}, {7813, 32027}, {7823, 11174}, {7835, 7914}, {7851, 17004}, {7857, 7913}, {7858, 7873}, {7868, 7891}, {7893, 9605}, {7897, 32825}, {7912, 31401}, {7915, 8589}, {7934, 31455}, {7941, 31406}, {9598, 30998}, {9862, 10333}, {10130, 19577}, {12815, 14061}, {15048, 17129}, {17128, 20094}

X(33021) = {X(2),X(3)}-harmonic conjugate of X(33225)
X(33021) = {X(2),X(4)}-harmonic conjugate of X(33020)
X(33021) = orthocentroidal-circle-inverse of X(33020)


X(33022) = (name pending)

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

As a point on the Euler line, X(33022) has Shinagawa coefficients ((E+F)2+9S2,-8S2).

X(33022) lies on these lines: {2, 3}, {76, 8589}, {83, 8588}, {187, 7878}, {193, 5116}, {194, 7771}, {385, 15815}, {574, 7760}, {620, 7938}, {1078, 7781}, {3329, 5023}, {5013, 7766}, {5131, 30135}, {5206, 7787}, {6179, 31652}, {7763, 7929}, {7764, 9939}, {7769, 7898}, {7782, 31276}, {7783, 20105}, {7786, 15513}, {7797, 21843}, {7830, 7912}, {7831, 7945}, {7843, 14976}, {7858, 31457}, {7897, 7904}, {7900, 14907}, {14712, 31401}, {15602, 32450}, {15822, 30793}, {20088, 31400}, {20094, 32828}

X(33022) = anticomplement of X(33002)
X(33022) = {X(2),X(3)}-harmonic conjugate of X(33014)
X(33022) = {X(2),X(4)}-harmonic conjugate of X(33010)
X(33022) = {X(2),X(20)}-harmonic conjugate of X(33018)
X(33022) = orthocentroidal-circle-inverse of X(33010)


X(33023) = (name pending)

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

As a point on the Euler line, X(33023) has Shinagawa coefficients ((E+F)2+2S2,-4S2).

X(33023) lies on these lines: {2, 3}, {148, 32834}, {183, 2996}, {193, 7738}, {194, 20080}, {316, 31400}, {574, 32816}, {625, 32839}, {1007, 15815}, {1692, 14712}, {1975, 3620}, {1992, 9607}, {2549, 3785}, {2896, 10008}, {3926, 7761}, {3934, 32826}, {5013, 32006}, {5028, 20065}, {5033, 7787}, {5286, 6179}, {5304, 7864}, {5395, 11174}, {5921, 11257}, {6337, 7784}, {6776, 32152}, {7618, 7888}, {7748, 32828}, {7756, 7800}, {7763, 7910}, {7775, 31450}, {7794, 32824}, {7818, 32825}, {7821, 32837}, {7842, 31401}, {7854, 32836}, {7861, 21843}, {7879, 32817}, {7897, 32841}, {7904, 15589}, {7912, 32835}, {7929, 10513}, {7936, 32833}, {9983, 20105}, {14930, 20088}, {23334, 31407}, {31173, 31457}

X(33023) = anticomplement of X(32971)
X(33023) = {X(2),X(4)}-harmonic conjugate of X(32991)
X(33023) = {X(2),X(20)}-harmonic conjugate of X(32981)
X(33023) = orthocentroidal-circle-inverse of X(32991)


X(33024) = (name pending)

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

As a point on the Euler line, X(33024) has Shinagawa coefficients ((E+F)2+5S2,8S2).

X(33024) lies on these lines: {2, 3}, {148, 1506}, {194, 31415}, {671, 9698}, {1975, 18584}, {3614, 4366}, {4027, 23514}, {5475, 6179}, {6645, 7173}, {7603, 20094}, {7751, 7785}, {7752, 7908}, {7786, 18424}, {7814, 8176}, {7829, 9166}, {7856, 18362}, {7858, 19570}, {7900, 32828}, {7929, 32827}, {9606, 20112}, {10583, 14061}, {17005, 32819}, {31450, 32480}

X(33024) = {X(2),X(4)}-harmonic conjugate of X(33260)
X(33024) = orthocentroidal-circle-inverse of X(33260)


X(33025) = (name pending)

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

As a point on the Euler line, X(33025) has Shinagawa coefficients (2(E+F)2+S2,-4S2).

X(33025) lies on these lines: {2, 3}, {193, 7864}, {194, 10513}, {390, 26561}, {574, 32835}, {626, 32831}, {2549, 7794}, {2896, 6392}, {2996, 16990}, {3096, 32815}, {3314, 32840}, {3600, 26590}, {3619, 32819}, {3620, 7928}, {3785, 7790}, {3926, 7847}, {5024, 32823}, {5254, 15589}, {5286, 7761}, {5304, 7750}, {7738, 7784}, {7739, 7873}, {7783, 32841}, {7786, 32827}, {7800, 7872}, {7803, 7910}, {7815, 32870}, {7825, 31404}, {7831, 32828}, {7865, 32869}, {7898, 14930}, {7911, 32816}, {7918, 14907}, {7925, 32873}, {7929, 20080}, {7934, 32829}, {9770, 22332}, {11648, 32874}, {14994, 20081}

X(33025) = anticomplement of X(33198)


X(33026) = (name pending)

Barycentrics    SB SC + (b c + c a + a b)^2 : :
As a point on the Euler line, X(33026) has Shinagawa coefficients ((E+F)2+S2+2abc$a$,S2).

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

X(33026) lies on these lines: {2, 3}, {6, 32022}, {387, 20131}, {388, 16819}, {497, 31996}, {966, 17499}, {1834, 20135}, {2550, 27255}, {4648, 17034}, {10436, 26036}, {16994, 20065}, {26040, 27020}, {31405, 31997}

X(33026) = complement of X(33040)
X(33026) = {X(2),X(3)}-harmonic conjugate of X(33044)
X(33026) = {X(2),X(5)}-harmonic conjugate of X(33042)
X(33026) = {X(2),X(20)}-harmonic conjugate of X(33036)


X(33027) = (name pending)

Barycentrics    SB SC - 2 (b c + c a + a b)^2 : :
As a point on the Euler line, X(33027) has Shinagawa coefficients (2(E+F)2+2S2+4abc$a$,-S2).

Barycentrics    a^4 - 8*a^2*b^2 - b^4 - 16*a^2*b*c - 16*a*b^2*c - 8*a^2*c^2 - 16*a*b*c^2 - 6*b^2*c^2 - c^4 : :

X(33027) lies on these lines: {2, 3}, {387, 20156}, {1056, 31996}, {1058, 16819}


X(33028) = (name pending)

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

As a point on the Euler line, X(33028) has Shinagawa coefficients ((E+F)2+S2+2abc$a$,2S2).

X(33028) lies on these lines: {2, 3}, {274, 7774}, {330, 31405}, {387, 20132}, {894, 26036}, {1478, 16819}, {1479, 31996}, {1834, 20131}, {3826, 26687}, {5277, 17008}, {5800, 20139}, {6625, 17349}, {6645, 19843}, {7736, 27318}, {7823, 16994}, {11185, 16589}, {16827, 26098}, {16992, 20065}, {16999, 32828}, {20172, 25466}, {26686, 31245}

X(33028) = complement of X(33059)
X(33028) = anticomplement of X(33036)
X(33028) = {X(2),X(3)}-harmonic conjugate of X(33055)
X(33028) = {X(2),X(4)}-harmonic conjugate of X(33029)
X(33028) = {X(2),X(5)}-harmonic conjugate of X(33053)
X(33028) = {X(2),X(20)}-harmonic conjugate of X(33047)
X(33028) = orthocentroidal-circle-inverse of X(33029)


X(33029) = (name pending)

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

As a point on the Euler line, X(33029) has Shinagawa coefficients ((E+F)2+S2+2abc$a$,-2S2).

X(33029) lies on these lines: {2, 3}, {69, 27269}, {315, 16589}, {387, 20142}, {1001, 26558}, {1478, 31996}, {1479, 16819}, {1834, 20154}, {3785, 16999}, {4423, 26561}, {4660, 30063}, {5275, 20065}, {5283, 7774}, {5286, 17000}, {7738, 27318}, {7823, 16993}, {16990, 18140}, {17260, 26036}, {26101, 31004}

X(33029) = complement of X(33058)
X(33029) = anticomplement of X(33035)
X(33029) = {X(2),X(3)}-harmonic conjugate of X(33054)
X(33029) = {X(2),X(4)}-harmonic conjugate of X(33028)
X(33029) = {X(2),X(5)}-harmonic conjugate of X(33052)
X(33029) = {X(2),X(20)}-harmonic conjugate of X(16917)
X(33029) = orthocentroidal-circle-inverse of X(33028)


X(33030) = (name pending)

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

As a point on the Euler line, X(33030) has Shinagawa coefficients ((E+F)2+S2+2abc$a$,4S2).

X(33030) lies on these lines: {2, 3}, {6, 6625}, {148, 5283}, {274, 7785}, {387, 20145}, {986, 6650}, {1834, 20132}, {2548, 27318}, {2886, 6645}, {3583, 31996}, {3585, 16819}, {4366, 25466}, {5270, 16829}, {7745, 17000}, {7823, 16992}, {11185, 27269}, {16996, 20065}, {16998, 20088}, {17350, 26036}, {17752, 33109}, {25385, 27954}

X(33030) = anticomplement of X(33047)
X(33030) = {X(2),X(4)}-harmonic conjugate of X(17685)
X(33030) = {X(2),X(20)}-harmonic conjugate of X(33063)
X(33030) = orthocentroidal-circle-inverse of X(17685)


X(33031) = (name pending)

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

As a point on the Euler line, X(33031) has Shinagawa coefficients ((E+F)2+S2+2abc$a$,6S2).

X(33031) lies on these lines: {2, 3}, {1478, 16829}, {6645, 31418}

X(33031) = {X(2),X(4)}-harmonic conjugate of X(33032)
X(33031) = orthocentroidal-circle-inverse of X(33032)


X(33032) = (name pending)

Barycentrics    6 SB SC - (b c + c a + a b)^2 : :
As a point on the Euler line, X(33032) has Shinagawa coefficients ((E+F)2+S2+2abc$a$,-6S2).

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

X(33032) lies on these lines: {2, 3}, {1479, 16829}, {27269, 32006}

X(33032) = {X(2),X(4)}-harmonic conjugate of X(33031)
X(33032) = orthocentroidal-circle-inverse of X(33031)


X(33033) = (name pending)

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

As a point on the Euler line, X(33033) has Shinagawa coefficients ((E+F)2+2S2+2abc$a$,S2).

X(33033) lies on these lines: {2, 3}, {11, 31996}, {12, 16819}, {2886, 27255}, {3822, 26558}, {3826, 27091}, {3841, 26582}, {3925, 27020}, {4972, 27048}, {5292, 20131}, {7762, 16992}, {7785, 16994}, {10198, 20172}, {15888, 16829}, {17030, 25466}, {17034, 17056}, {27318, 31406}, {31466, 31997}

X(33033) = complement of X(33047)
X(33033) = {X(2),X(4)}-harmonic conjugate of X(33036)
X(33033) = {X(2),X(5)}-harmonic conjugate of X(33034)
X(33033) = {X(2),X(20)}-harmonic conjugate of X(33044)
X(33033) = orthocentroidal-circle-inverse of X(33036)


X(33034) = (name pending)

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

As a point on the Euler line, X(33034) has Shinagawa coefficients ((E+F)2+2abc$a$,-S2).

X(33034) lies on these lines: {2, 3}, {11, 16819}, {12, 31996}, {325, 16589}, {1125, 26558}, {1329, 27255}, {1698, 26590}, {3291, 16735}, {3624, 26561}, {3634, 26582}, {3816, 17030}, {3846, 29968}, {3933, 27269}, {4026, 27324}, {5251, 26686}, {5259, 26629}, {5275, 7762}, {5292, 20154}, {5305, 17000}, {7767, 16999}, {7785, 16993}, {15048, 27318}, {25542, 30104}, {25960, 29966}

X(33034) = complement of X(16917)
X(33034) = {X(2),X(4)}-harmonic conjugate of X(33035)
X(33034) = {X(2),X(5)}-harmonic conjugate of X(33033)
X(33034) = {X(2),X(20)}-harmonic conjugate of X(33043)
X(33034) = orthocentroidal-circle-inverse of X(33035)


X(33035) = (name pending)

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

As a point on the Euler line, X(33035) has Shinagawa coefficients ((E+F)2+2abc$a$,S2).

X(33035) lies on these lines: {2, 3}, {6, 1509}, {55, 31996}, {56, 16819}, {58, 20154}, {86, 2271}, {194, 16993}, {274, 5275}, {386, 20131}, {966, 17206}, {1125, 20172}, {1376, 27255}, {1724, 29460}, {1975, 16589}, {3304, 16829}, {3634, 26687}, {4252, 20156}, {4255, 20135}, {4256, 20152}, {4413, 27020}, {5021, 17277}, {5277, 16992}, {5283, 31859}, {5711, 16827}, {6645, 9708}, {7793, 16994}, {9605, 27318}, {15668, 18755}, {17000, 30435}, {17030, 25524}, {19854, 26686}, {24602, 31339}

X(33035) = complement of X(33029)
X(33035) = {X(2),X(3)}-harmonic conjugate of X(33036)
X(33035) = {X(2),X(4)}-harmonic conjugate of X(33034)
X(33035) = orthocentroidal-circle-inverse of X(33034)


X(33036) = (name pending)

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

As a point on the Euler line, X(33036) has Shinagawa coefficients ((E+F)2+2S2+2abc$a$,-S2).

X(33036) lies on these lines: {2, 3}, {55, 16819}, {56, 31996}, {58, 20131}, {86, 5021}, {183, 16589}, {194, 16994}, {274, 31859}, {330, 31468}, {386, 20154}, {958, 27255}, {1001, 17030}, {2271, 17277}, {3303, 16829}, {4252, 20135}, {4255, 20156}, {4257, 20152}, {4357, 25500}, {4423, 26959}, {4648, 17206}, {5024, 27318}, {5248, 20172}, {5283, 7754}, {6626, 17234}, {7793, 16993}, {9605, 17000}, {10198, 26558}, {17259, 18755}, {19854, 26590}, {29966, 32917}, {29968, 32916}, {31449, 31997}

X(33036) = complement of X(33028)
X(33036) = {X(2),X(3)}-harmonic conjugate of X(33035)
X(33036) = {X(2),X(4)}-harmonic conjugate of X(33033)
X(33036) = {X(2),X(20)}-harmonic conjugate of X(33026)
X(33036) = orthocentroidal-circle-inverse of X(33033)


X(33037) = (name pending)

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

As a point on the Euler line, X(33037) has Shinagawa coefficients ((E+F)2+2S2+2abc$a$,2S2).

X(33037) lies on these lines: {2, 3}, {10590, 16819}, {10591, 31996}, {27255, 31418}

X(33037) = anticomplement of X(33044)
X(33037) = {X(2),X(4)}-harmonic conjugate of X(33040)
X(33037) = orthocentroidal-circle-inverse of X(33040)


X(33038) = (name pending)

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

As a point on the Euler line, X(33038) has Shinagawa coefficients ((E+F)2+2abc$a$,-2S2).

X(33038) lies on these lines: {2, 3}, {274, 2996}, {3620, 18140}, {10590, 31996}, {10591, 16819}, {16589, 32816}, {26105, 26558}

X(33038) = anticomplement of X(33043)
X(33038) = {X(2),X(4)}-harmonic conjugate of X(33039)
X(33038) = orthocentroidal-circle-inverse of X(33039)


X(33039) = (name pending)

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

As a point on the Euler line, X(33039) has Shinagawa coefficients ((E+F)2+2abc$a$,2S2).

X(33039) lies on these lines: {2, 3}, {193, 274}, {4277, 16745}, {4293, 16819}, {4294, 31996}, {4307, 16827}, {5021, 32022}, {5275, 6392}, {16589, 32815}, {16999, 32834}, {24178, 26626}

X(33039) = complement of X(33051)
X(33039) = {X(2),X(4)}-harmonic conjugate of X(33038)
X(33039) = {X(2),X(20)}-harmonic conjugate of X(33040)
X(33039) = orthocentroidal-circle-inverse of X(33038)


X(33040) = (name pending)

Barycentrics    2 SB SC - S^2 - (b c + c a + a b)^2 : :
As a point on the Euler line, X(33040) has Shinagawa coefficients ((E+F)2+2S2+2abc$a$,-2S2).

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

X(33040) lies on these lines: {2, 3}, {193, 5283}, {3785, 16589}, {4293, 31996}, {4294, 16819}, {6392, 16992}, {15589, 27269}

X(33040) = anticomplement of X(33026)
X(33040) = {X(2),X(4)}-harmonic conjugate of X(33037)
X(33040) = {X(2),X(20)}-harmonic conjugate of X(33039)
X(33040) = orthocentroidal-circle-inverse of X(33037)


X(33041) = (name pending)

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

As a point on the Euler line, X(33041) has Shinagawa coefficients ((E+F)2+3S2+2abc$a$,S2).

X(33041) lies on these lines: {2, 3}, {10588, 16819}, {10589, 31996}

X(33041) = {X(2),X(4)}-harmonic conjugate of X(33044)
X(33041) = orthocentroidal-circle-inverse of X(33044)


X(33042) = (name pending)

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

As a point on the Euler line, X(33042) has Shinagawa coefficients ((E+F)2-S2+2abc$a$,-S2).

X(33042) lies on these lines: {2, 3}, {1007, 16589}, {10588, 31996}, {10589, 16819}, {27269, 32818}

X(33042) = {X(2),X(3)}-harmonic conjugate of X(33049)
X(33042) = {X(2),X(4)}-harmonic conjugate of X(33043)
X(33042) = {X(2),X(5)}-harmonic conjugate of X(33026)
X(33042) = orthocentroidal-circle-inverse of X(33043)


X(33043) = (name pending)

Barycentrics    SB SC - 2 S^2 + (b c + c a + a b)^2 : :
As a point on the Euler line, X(33043) has Shinagawa coefficients ((E+F)2-S2+2abc$a$,S2).

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

X(33043) lies on these lines: {2, 3}, {5218, 31996}, {6337, 16589}, {7288, 16819}, {19855, 26686}, {27269, 32817}

X(33043) = complement of X(33038)
X(33043) = {X(2),X(4)}-harmonic conjugate of X(33042)
X(33043) = {X(2),X(5)}-harmonic conjugate of X(33048)
X(33043) = {X(2),X(20)}-harmonic conjugate of X(33034)
X(33043) = orthocentroidal-circle-inverse of X(33042)


X(33044) = (name pending)

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

As a point on the Euler line, X(33044) has Shinagawa coefficients ((E+F)2+3S2+2abc$a$,-S2).

X(33044) lies on these lines: {2, 3}, {5218, 16819}, {7288, 31996}, {18755, 32022}, {27255, 30478}

X(33044) = complement of X(33037)
X(33044) = {X(2),X(3)}-harmonic conjugate of X(33026)
X(33044) = {X(2),X(4)}-harmonic conjugate of X(33041)
X(33044) = {X(2),X(20)}-harmonic conjugate of X(33033)
X(33044) = orthocentroidal-circle-inverse of X(33041)


X(33045) = (name pending)

Barycentrics    2 SB SC + 2 S^2 + (b c + c a + a b)^2 : :
As a point on the Euler line, X(33045) has Shinagawa coefficients ((E+F)2+3S2+2abc$a$,2S2).

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

X(33045) lies on these lines: {2, 3}, {274, 7777}, {330, 31466}, {2548, 17000}, {3815, 27318}, {3822, 17030}, {3841, 27091}, {4366, 10198}, {4692, 30154}, {5021, 6625}, {5277, 17004}, {5292, 20132}, {6645, 26363}, {7741, 31996}, {7762, 16996}, {7785, 16992}, {7921, 16998}, {7951, 16819}, {16827, 17717}, {16999, 32832}, {17033, 33105}, {25639, 27255}, {26725, 30139}, {26752, 33108}

X(33045) = complement of X(33063)
X(33045) = {X(2),X(4)}-harmonic conjugate of X(33047)
X(33045) = {X(2),X(5)}-harmonic conjugate of X(33046)
X(33045) = {X(2),X(20)}-harmonic conjugate of X(33055)
X(33045) = orthocentroidal-circle-inverse of X(33047)


X(33046) = (name pending)

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

As a point on the Euler line, X(33046) has Shinagawa coefficients ((E+F)2-S2+2abc$a$,-2S2).

X(33046) lies on these lines: {2, 3}, {315, 16999}, {325, 27269}, {1211, 30863}, {1655, 7906}, {3314, 18140}, {3767, 17000}, {3814, 27255}, {3816, 26558}, {3825, 17030}, {5254, 27318}, {5275, 7785}, {5276, 7921}, {5277, 7823}, {5283, 7777}, {5292, 20142}, {6506, 26068}, {6653, 9709}, {7741, 16819}, {7752, 16589}, {7762, 16995}, {7794, 18146}, {7893, 16997}, {7951, 31996}, {25079, 30177}, {26010, 26531}

X(33046) = complement of X(33062)
X(33046) = {X(2),X(4)}-harmonic conjugate of X(16917)
X(33046) = {X(2),X(5)}-harmonic conjugate of X(33045)
X(33046) = {X(2),X(20)}-harmonic conjugate of X(33054)
X(33046) = orthocentroidal-circle-inverse of X(16917)


X(33047) = (name pending)

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

As a point on the Euler line, X(33047) has Shinagawa coefficients ((E+F)2+3S2+2abc$a$,-2S2).

X(33047) lies on these lines: {2, 3}, {35, 16819}, {36, 31996}, {39, 17000}, {58, 20132}, {141, 6626}, {183, 27269}, {194, 16992}, {274, 7783}, {330, 31449}, {385, 5283}, {386, 20142}, {993, 6645}, {1078, 16589}, {1333, 20136}, {1468, 17032}, {1621, 26801}, {1655, 17129}, {2271, 17349}, {3286, 20133}, {3662, 25500}, {3746, 16829}, {4252, 20131}, {4253, 20147}, {4255, 20154}, {4256, 20138}, {4257, 20137}, {4259, 20149}, {4366, 5248}, {4653, 17034}, {4894, 30154}, {5013, 27318}, {5021, 17379}, {5120, 20146}, {5124, 25508}, {5251, 27020}, {5259, 26959}, {5260, 26752}, {5275, 7793}, {5277, 16993}, {5293, 31323}, {5692, 30135}, {6653, 31419}, {6690, 26558}, {7754, 16996}, {7839, 16998}, {8720, 27478}, {10448, 17033}, {17206, 17300}, {17277, 18755}, {24726, 25359}, {24953, 26590}

X(33047) = complement of X(33030)
X(33047) = anticomplement of X(33033)
X(33047) = {X(2),X(3)}-harmonic conjugate of X(16917)
X(33047) = {X(2),X(4)}-harmonic conjugate of X(33045)
X(33047) = {X(2),X(20)}-harmonic conjugate of X(33028)
X(33047) = orthocentroidal-circle-inverse of X(33045)


X(33048) = (name pending)

Barycentrics    SB SC + 4 S^2 - (b c + c a + a b)^2 : :
As a point on the Euler line, X(33048) has Shinagawa coefficients ((E+F)2-3S2+2abc$a$,-S2).

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

X(33048) lies on these lines: {2, 3}, {16999, 32823}

X(33048) = {X(2),X(4)}-harmonic conjugate of X(33049)
X(33048) = {X(2),X(5)}-harmonic conjugate of X(33043)
X(33048) = orthocentroidal-circle-inverse of X(33049)


X(33049) = (name pending)

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

As a point on the Euler line, X(33049) has Shinagawa coefficients ((E+F)2-3S2+2abc$a$,S2).

X(33049) lies on these lines: {2, 3}, {16999, 32818}

X(33049) = {X(2),X(3)}-harmonic conjugate of X(33042)
X(33049) = {X(2),X(4)}-harmonic conjugate of X(33048)
X(33049) = orthocentroidal-circle-inverse of X(33048)


X(33050) = (name pending)

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

As a point on the Euler line, X(33050) has Shinagawa coefficients ((E+F)2+2abc$a$,-4S2).

X(33050) lies on these lines: {2, 3}, {16589, 32827}

X(33050) = {X(2),X(17685)}-harmonic conjugate of X(33051)


X(33051) = (name pending)

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

As a point on the Euler line, X(33051) has Shinagawa coefficients ((E+F)2+2S2+2abc$a$,-4S2).

X(33051) lies on these lines: {2, 3}, {1655, 20080}

X(33051) = anticomplement of X(33039)
X(33051) = {X(2),X(17685)}-harmonic conjugate of X(33050)


X(33052) = (name pending)

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

As a point on the Euler line, X(33052) has Shinagawa coefficients ((E+F)2+5S2+2abc$a$,2S2).

X(33052) lies on these lines: {2, 3}, {6668, 20172}, {10585, 26801}, {16999, 32838}, {17000, 31404}

X(33052) = {X(2),X(4)}-harmonic conjugate of X(33055)
X(33052) = {X(2),X(5)}-harmonic conjugate of X(33029)
X(33052) = orthocentroidal-circle-inverse of X(33055)


X(33053) = (name pending)

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

As a point on the Euler line, X(33053) has Shinagawa coefficients ((E+F)2-3S2+2abc$a$,-2S2).

X(33053) lies on these lines: {2, 3}, {1007, 27269}, {3847, 20172}, {10584, 26801}, {16999, 32816}, {26590, 31246}

X(33053) = {X(2),X(4)}-harmonic conjugate of X(33054)
X(33053) = {X(2),X(5)}-harmonic conjugate of X(33028)
X(33053) = orthocentroidal-circle-inverse of X(33054)


X(33054) = (name pending)

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

As a point on the Euler line, X(33054) has Shinagawa coefficients ((E+F)2-3S2+2abc$a$,2S2).

X(33054) lies on these lines: {2, 3}, {274, 17008}, {3926, 16999}, {4413, 26686}, {5277, 7774}, {6337, 27269}, {6691, 20172}, {7735, 27318}

X(33054) = complement of X(33057)
X(33054) = {X(2),X(3)}-harmonic conjugate of X(33029)
X(33054) = {X(2),X(4)}-harmonic conjugate of X(33053)
X(33054) = {X(2),X(20)}-harmonic conjugate of X(33046)
X(33054) = orthocentroidal-circle-inverse of X(33053)


X(33055) = (name pending)

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

As a point on the Euler line, X(33055) has Shinagawa coefficients ((E+F)2+5S2+2abc$a$,-2S2).

X(33055) lies on these lines: {2, 3}, {5283, 17008}, {16829, 31452}, {17000, 31400}

X(33055) = complement of X(33056)
X(33055) = {X(2),X(3)}-harmonic conjugate of X(33028)
X(33055) = {X(2),X(4)}-harmonic conjugate of X(33052)
X(33055) = {X(2),X(20)}-harmonic conjugate of X(33045)
X(33055) = orthocentroidal-circle-inverse of X(33052)


X(33056) = (name pending)

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

As a point on the Euler line, X(33056) has Shinagawa coefficients ((E+F)2+3S2+2abc$a$,4S2).

X(33056) lies on these lines: {2, 3}, {27318, 31404}

X(33056) = anticomplement of X(33055)
X(33056) = {X(2),X(4)}-harmonic conjugate of X(33059)
X(33056) = orthocentroidal-circle-inverse of X(33059)


X(33057) = (name pending)

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

As a point on the Euler line, X(33057) has Shinagawa coefficients ((E+F)2-S2+2abc$a$,-4S2).

X(33057) lies on these lines: {2, 3}, {2899, 30179}, {16999, 32006}, {27269, 32816}

X(33057) = anticomplement of X(33054)
X(33057) = {X(2),X(4)}-harmonic conjugate of X(33058)
X(33057) = orthocentroidal-circle-inverse of X(33058)


X(33058) = (name pending)

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

As a point on the Euler line, X(33058) has Shinagawa coefficients ((E+F)2-S2+2abc$a$,4S2).

X(33058) lies on these lines: {2, 3}, {274, 20065}, {2550, 6645}, {4299, 16819}, {4302, 31996}, {4317, 16829}, {6392, 16995}, {27269, 32815}

X(33058) = anticomplement of X(33029)
X(33058) = {X(2),X(4)}-harmonic conjugate of X(33057)
X(33058) = {X(2),X(20)}-harmonic conjugate of X(33059)
X(33058) = orthocentroidal-circle-inverse of X(33057)


X(33059) = (name pending)

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

As a point on the Euler line, X(33059) has Shinagawa coefficients ((E+F)2+3S2+2abc$a$,-4S2).

X(33059) lies on these lines: {2, 3}, {3785, 27269}, {4299, 31996}, {4302, 16819}, {4309, 16829}, {5283, 20065}, {6392, 16996}, {7738, 17000}, {14907, 16589}

X(33059) = anticomplement of X(33028)
X(33059) = {X(2),X(4)}-harmonic conjugate of X(33056)
X(33059) = {X(2),X(20)}-harmonic conjugate of X(33058)
X(33059) = orthocentroidal-circle-inverse of X(33056)


X(33060) = (name pending)

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

As a point on the Euler line, X(33060) has Shinagawa coefficients ((E+F)2+5S2+2abc$a$,4S2).

X(33060) lies on these lines: {2, 3}, {1506, 27318}, {5292, 20145}, {6653, 31418}, {7785, 16996}

X(33060) = {X(2),X(4)}-harmonic conjugate of X(33063)
X(33060) = {X(2),X(5)}-harmonic conjugate of X(33061)
X(33060) = orthocentroidal-circle-inverse of X(33063)


X(33061) = (name pending)

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

As a point on the Euler line, X(33061) has Shinagawa coefficients ((E+F)2-3S2+2abc$a$,-4S2).

X(33061) lies on these lines: {2, 3}, {115, 27318}, {3847, 26558}, {5292, 20158}, {7752, 27269}, {7773, 16999}, {7785, 16995}, {7821, 18146}, {7897, 18135}, {7900, 16997}, {7912, 18140}, {13881, 17000}

X(33061) = {X(2),X(4)}-harmonic conjugate of X(33062)
X(33061) = {X(2),X(5)}-harmonic conjugate of X(33060)
X(33061) = orthocentroidal-circle-inverse of X(33062)


X(33062) = (name pending)

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

As a point on the Euler line, X(33062) has Shinagawa coefficients ((E+F)2-3S2+2abc$a$,4S2).

X(33062) lies on these lines: {2, 3}, {32, 27318}, {58, 20158}, {99, 27269}, {194, 5277}, {274, 7793}, {330, 4386}, {386, 20145}, {1376, 6645}, {1975, 16999}, {3053, 17000}, {3980, 27954}, {4252, 20142}, {4255, 20132}, {4258, 20147}, {4366, 25524}, {5010, 31996}, {5096, 20139}, {5132, 20134}, {5275, 7783}, {7280, 16819}, {7782, 16589}, {8720, 27481}, {15015, 30135}, {16997, 20081}, {17206, 17343}, {17379, 18755}, {24271, 30863}

X(33062) = anticomplement of X(33046)
X(33062) = {X(2),X(3)}-harmonic conjugate of X(33063)
X(33062) = {X(2),X(4)}-harmonic conjugate of X(33061)
X(33062) = {X(2),X(20)}-harmonic conjugate of X(17685)
X(33062) = orthocentroidal-circle-inverse of X(33061)


X(33063) = (name pending)

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

As a point on the Euler line, X(33063) has Shinagawa coefficients ((E+F)2+5S2+2abc$a$,-4S2).

X(33063) lies on these lines: {2, 3}, {58, 20145}, {191, 30135}, {194, 16996}, {386, 20158}, {574, 27318}, {1078, 27269}, {3286, 20134}, {4252, 20132}, {4255, 20142}, {4265, 20139}, {5010, 16819}, {5013, 17000}, {5022, 20147}, {5267, 27255}, {5283, 7793}, {5426, 30139}, {6626, 17238}, {6653, 19843}, {7280, 31996}, {7771, 16589}, {7783, 16992}, {8669, 27481}, {17206, 17375}, {17349, 18755}, {18758, 23407}

X(33063) = anticomplement of X(33045)
X(33063) = {X(2),X(3)}-harmonic conjugate of X(33062)
X(33063) = {X(2),X(4)}-harmonic conjugate of X(33060)
X(33063) = {X(2),X(20)}-harmonic conjugate of X(33030)
X(33063) = orthocentroidal-circle-inverse of X(33060)

leftri

Centers of degree 3 with coefficients in {-1,0,1}: X(33064)-X(33175)

rightri

Centers X(33064)-X(33175) were contributed by Peter Moses, June 20, 2019:

Each center in this section has barycentrics of the form p(a,b,c) : : , where p(a,b,c) is a polynomial homogeneous of degree 3 in a,b,c, with coefficents in the set {-1, 0 , 1}. For more of these, see also X(32711)-X(32784), X(32842)-X(32866), and X(32911)-X(32950).


X(33064) = X(1)X(1330)∩X(2)X(1757)

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

X(33064) lies on these lines: {1, 1330}, {2, 1757}, {6, 26128}, {7, 3980}, {8, 17889}, {9, 29642}, {10, 3681}, {31, 17770}, {38, 3936}, {42, 3821}, {43, 3662}, {55, 4655}, {63, 3771}, {69, 4362}, {75, 21085}, {81, 29645}, {141, 1215}, {142, 4104}, {171, 320}, {210, 3836}, {226, 1469}, {238, 29672}, {244, 5741}, {306, 726}, {312, 21093}, {321, 32856}, {329, 4011}, {354, 3846}, {518, 2887}, {519, 3891}, {524, 3791}, {527, 4376}, {537, 3703}, {668, 30631}, {740, 3782}, {748, 1125}, {752, 3744}, {756, 18139}, {846, 6646}, {894, 32783}, {908, 3840}, {982, 4417}, {984, 18134}, {1001, 4703}, {1211, 24325}, {1376, 7232}, {1621, 4683}, {1738, 4685}, {1836, 32941}, {1961, 17300}, {2177, 32950}, {2308, 26230}, {2796, 32929}, {2886, 4892}, {2895, 32914}, {3011, 4001}, {3120, 17135}, {3218, 29846}, {3219, 29632}, {3242, 4865}, {3416, 32920}, {3452, 4871}, {3454, 3874}, {3475, 29651}, {3663, 4028}, {3670, 17748}, {3687, 24165}, {3720, 26580}, {3722, 4450}, {3726, 22200}, {3740, 3834}, {3750, 24723}, {3751, 25453}, {3769, 17361}, {3772, 32853}, {3775, 31993}, {3831, 21077}, {3838, 21242}, {3870, 4660}, {3873, 25760}, {3912, 3971}, {3920, 32949}, {3923, 5905}, {3935, 32948}, {3938, 6327}, {3944, 10453}, {3952, 29687}, {3957, 32947}, {3961, 4645}, {3967, 17231}, {3981, 4109}, {3996, 24715}, {4039, 17137}, {4062, 17147}, {4101, 23536}, {4138, 4847}, {4364, 10180}, {4386, 4987}, {4389, 17592}, {4392, 29849}, {4415, 4966}, {4416, 16998}, {4418, 17483}, {4430, 25958}, {4438, 30811}, {4640, 17345}, {4641, 6679}, {4649, 19786}, {4661, 25959}, {4682, 17376}, {4684, 24210}, {4697, 17365}, {4716, 19796}, {4741, 29675}, {4942, 17269}, {5057, 32943}, {5233, 17063}, {5268, 17298}, {5712, 29644}, {5718, 6682}, {5739, 16825}, {5743, 25557}, {5850, 20106}, {6541, 32858}, {6763, 25645}, {7081, 17288}, {7191, 32843}, {7226, 29643}, {7262, 17347}, {11814, 27131}, {14829, 17719}, {14996, 29847}, {15523, 17165}, {17017, 31034}, {17018, 32776}, {17126, 29848}, {17127, 29638}, {17140, 31037}, {17203, 24241}, {17232, 27538}, {17274, 17594}, {17276, 32934}, {17364, 29634}, {17484, 32930}, {17490, 24200}, {17596, 26840}, {17718, 32916}, {17763, 32863}, {18904, 22199}, {20045, 20290}, {20072, 29860}, {20292, 32945}, {20347, 24259}, {21060, 21255}, {22008, 22024}, {24239, 31120}, {24295, 24943}, {24318, 24691}, {24349, 32778}, {24552, 24725}, {24690, 25353}, {26034, 29670}, {26037, 27186}, {26098, 29652}, {27064, 29637}, {27065, 29851}, {29674, 32937}, {30942, 31053}, {31019, 31330}, {32777, 32935}, {32779, 32940}, {32846, 32926}, {32857, 32932}, {32861, 32922}

X(33064) = complement of X(32912)


X(33065) = X(1)X(26580)∩X(2)X(1757)

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

X(33065) lies on these lines: {1, 26580}, {2, 1757}, {6, 29636}, {8, 3120}, {9, 29632}, {10, 3901}, {31, 29848}, {38, 4417}, {42, 27184}, {43, 17184}, {55, 4683}, {63, 29846}, {69, 17763}, {75, 32856}, {81, 29847}, {100, 4655}, {141, 32931}, {171, 32859}, {192, 4062}, {200, 32948}, {210, 3823}, {226, 31330}, {238, 29638}, {244, 5233}, {306, 32925}, {320, 750}, {329, 32930}, {354, 25960}, {518, 25760}, {524, 17602}, {551, 31172}, {612, 32949}, {668, 30632}, {748, 29853}, {756, 18134}, {896, 17347}, {899, 3662}, {908, 30942}, {976, 1330}, {982, 5741}, {984, 3936}, {1086, 4023}, {1150, 17719}, {1155, 17345}, {1211, 32771}, {1215, 32782}, {1621, 4703}, {1647, 31056}, {1743, 29855}, {1836, 32945}, {2177, 24723}, {2308, 29634}, {2887, 3681}, {2895, 4362}, {3011, 4416}, {3061, 20974}, {3219, 3771}, {3240, 3821}, {3242, 32844}, {3305, 29851}, {3416, 32927}, {3452, 30957}, {3454, 5904}, {3617, 21027}, {3687, 17155}, {3712, 17334}, {3740, 25961}, {3741, 31053}, {3751, 29631}, {3772, 32864}, {3782, 32860}, {3786, 30984}, {3789, 30969}, {3840, 27131}, {3846, 3873}, {3870, 32947}, {3875, 14459}, {3891, 32861}, {3920, 32946}, {3923, 17484}, {3935, 4660}, {3938, 4388}, {3944, 17135}, {3952, 29674}, {3961, 6327}, {3966, 32923}, {3971, 32858}, {3980, 17483}, {3994, 17233}, {4009, 17231}, {4011, 26792}, {4090, 29679}, {4101, 13161}, {4104, 5249}, {4113, 21949}, {4138, 25006}, {4407, 26738}, {4413, 7232}, {4414, 6646}, {4415, 32915}, {4418, 5905}, {4425, 17018}, {4429, 21805}, {4430, 29655}, {4438, 30831}, {4643, 17718}, {4651, 17889}, {4661, 25958}, {4671, 21093}, {4937, 29577}, {4938, 17377}, {5057, 32941}, {5205, 17288}, {5220, 30811}, {5223, 29857}, {5241, 25557}, {5263, 24725}, {5311, 17778}, {5739, 32914}, {7226, 29671}, {7290, 29836}, {10129, 21242}, {13407, 31339}, {15523, 32937}, {16468, 26230}, {16475, 29834}, {16704, 29658}, {17126, 17770}, {17127, 29656}, {17154, 26758}, {17165, 31037}, {17272, 29828}, {17276, 32845}, {17720, 32919}, {21085, 28605}, {24703, 32943}, {24943, 27064}, {25527, 29850}, {25568, 26034}, {26128, 29852}, {26223, 32783}, {27065, 29642}, {27538, 29687}, {27812, 31030}, {28650, 29833}, {29649, 32863}, {31134, 32850}, {32777, 32938}, {32779, 32935}, {32852, 32926}


X(33066) = X(1)X(4703)∩X(2)X(44)

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

X(33066) lies on these lines: {1, 4703}, {2, 44}, {6, 19786}, {7, 14555}, {8, 1836}, {9, 18134}, {31, 29848}, {37, 17778}, {38, 32843}, {42, 4683}, {43, 4655}, {57, 5233}, {63, 4417}, {69, 189}, {72, 1330}, {75, 4886}, {81, 26580}, {92, 317}, {141, 27064}, {144, 345}, {171, 17770}, {190, 306}, {210, 4645}, {222, 28920}, {226, 333}, {238, 29672}, {239, 3782}, {307, 27398}, {319, 321}, {322, 26872}, {514, 22022}, {516, 3996}, {518, 4388}, {524, 1999}, {527, 3687}, {537, 32866}, {540, 30115}, {651, 1812}, {668, 30713}, {726, 32861}, {752, 3961}, {756, 32949}, {894, 1211}, {896, 29846}, {908, 4001}, {940, 17364}, {984, 32946}, {1043, 4101}, {1150, 31053}, {1427, 17950}, {1654, 31993}, {1730, 29788}, {1743, 25527}, {1757, 2887}, {2308, 32775}, {2999, 17274}, {3120, 32864}, {3175, 6542}, {3210, 17276}, {3218, 5741}, {3219, 3936}, {3240, 32950}, {3305, 17234}, {3416, 32937}, {3649, 16824}, {3662, 4383}, {3666, 6646}, {3681, 6327}, {3683, 29839}, {3699, 21060}, {3751, 32773}, {3752, 17345}, {3759, 19785}, {3771, 7262}, {3846, 17771}, {3879, 4656}, {3902, 5180}, {3912, 32024}, {3935, 4450}, {3944, 32853}, {3952, 20290}, {3966, 24349}, {3971, 32846}, {3975, 17137}, {3982, 24199}, {3995, 17315}, {4023, 11246}, {4062, 32936}, {4358, 26792}, {4359, 7321}, {4361, 19820}, {4363, 19797}, {4384, 4654}, {4389, 5256}, {4425, 4649}, {4651, 17491}, {4661, 5014}, {4672, 32783}, {4673, 11415}, {4685, 24715}, {4714, 11552}, {4722, 29631}, {5015, 5904}, {5057, 17135}, {5211, 21342}, {5220, 29641}, {5249, 17277}, {5257, 25507}, {5271, 17346}, {5273, 30828}, {5278, 31019}, {5287, 17378}, {5564, 28605}, {5712, 17257}, {5743, 17365}, {5839, 30699}, {5847, 32926}, {6147, 16817}, {6703, 7277}, {7055, 31627}, {7282, 31623}, {7308, 17298}, {8896, 11683}, {10381, 29958}, {10453, 24703}, {11679, 24694}, {13461, 31548}, {15523, 32938}, {16468, 26128}, {16477, 29654}, {16574, 21361}, {16603, 17739}, {16706, 17184}, {17011, 17320}, {17056, 17332}, {17095, 17206}, {17116, 19833}, {17120, 19832}, {17121, 19829}, {17167, 29767}, {17182, 29766}, {17247, 20182}, {17248, 19701}, {17258, 28606}, {17263, 18139}, {17264, 32858}, {17289, 26223}, {17296, 30568}, {17322, 19684}, {17331, 19732}, {17336, 17776}, {17349, 24789}, {17350, 32777}, {17361, 18743}, {17372, 22034}, {17397, 19722}, {17740, 20078}, {17768, 32932}, {18037, 22275}, {18141, 18228}, {18746, 28950}, {19810, 27792}, {20101, 28570}, {21805, 32948}, {22020, 29508}, {22053, 27391}, {24589, 26842}, {24725, 31330}, {25650, 31445}, {25760, 32912}, {30567, 31142}, {31037, 32779}, {32778, 32935}, {32852, 32925}, {32856, 32914}


X(33067) = X(1)X(4450)∩X(2)X(896)

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

X(33067) lies on these lines: {1, 4450}, {2, 896}, {7, 26034}, {9, 25961}, {10, 4880}, {31, 3662}, {38, 4645}, {42, 320}, {43, 32859}, {55, 7232}, {57, 25760}, {63, 25957}, {69, 32860}, {81, 3821}, {89, 29864}, {141, 4418}, {171, 17184}, {190, 29687}, {210, 17345}, {226, 32918}, {244, 4388}, {306, 32845}, {321, 32857}, {354, 32947}, {516, 32943}, {518, 32948}, {527, 32938}, {545, 6057}, {612, 17274}, {740, 32863}, {750, 27184}, {752, 7191}, {756, 6646}, {799, 30631}, {846, 18139}, {894, 32781}, {940, 32776}, {968, 17298}, {982, 6327}, {1046, 4202}, {1054, 5741}, {1086, 32914}, {1150, 17889}, {1155, 29846}, {1215, 17483}, {1330, 24443}, {1738, 4001}, {1836, 30942}, {1962, 17300}, {2206, 18209}, {2308, 16706}, {2650, 4201}, {2792, 19649}, {2887, 3218}, {3052, 29638}, {3120, 14829}, {3210, 32852}, {3219, 3836}, {3306, 25960}, {3336, 3454}, {3416, 17155}, {3631, 4046}, {3663, 32928}, {3666, 32949}, {3683, 3834}, {3705, 31134}, {3720, 24723}, {3741, 20292}, {3745, 17235}, {3752, 32843}, {3758, 29663}, {3782, 17763}, {3840, 5057}, {3846, 27003}, {3873, 4660}, {3912, 32936}, {3914, 32919}, {3928, 29857}, {3936, 17596}, {3980, 32782}, {4389, 5311}, {4392, 4865}, {4414, 18134}, {4429, 32912}, {4438, 25959}, {4514, 17449}, {4640, 29632}, {4641, 29850}, {4643, 26037}, {4654, 29828}, {4676, 29677}, {4799, 24691}, {4850, 32946}, {4972, 32913}, {4987, 5276}, {5249, 32917}, {5847, 32924}, {5880, 31330}, {5905, 32931}, {7081, 32856}, {7613, 14552}, {8013, 17271}, {9782, 26064}, {15523, 32939}, {17122, 26580}, {17126, 26128}, {17135, 24715}, {17147, 32846}, {17154, 28599}, {17227, 24943}, {17276, 32925}, {17288, 32932}, {17290, 29852}, {17469, 20101}, {17495, 20290}, {17595, 29849}, {17768, 32930}, {17770, 24169}, {23958, 25958}, {24003, 26792}, {24231, 32923}, {24248, 32915}, {24259, 30965}, {24325, 26842}, {24465, 26942}, {24690, 24699}, {24703, 24709}, {29674, 32933}, {29679, 32935}, {31019, 32916}, {32858, 32934}


X(33068) = X(2)X(1155)∩X(10)X(17678)

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

X(33068) lies on these lines: {2, 1155}, {10, 17678}, {31, 16706}, {38, 32850}, {42, 320}, {43, 4655}, {46, 16062}, {55, 3662}, {57, 32773}, {63, 4429}, {65, 4201}, {75, 26034}, {100, 17184}, {141, 32932}, {165, 25527}, {171, 3821}, {200, 17274}, {210, 6646}, {238, 24169}, {244, 32947}, {312, 24248}, {319, 32860}, {333, 1738}, {443, 31359}, {516, 32942}, {518, 26840}, {612, 4389}, {750, 32776}, {752, 29821}, {756, 17258}, {846, 3836}, {894, 11246}, {896, 29850}, {899, 4683}, {968, 17234}, {982, 4514}, {986, 7270}, {1054, 3846}, {1086, 3757}, {1215, 32857}, {1220, 4292}, {1376, 27184}, {1386, 20101}, {1737, 17677}, {1770, 13740}, {1962, 17317}, {2194, 21997}, {2352, 24678}, {2886, 24627}, {2887, 17596}, {3052, 17290}, {3120, 32918}, {3210, 3416}, {3218, 4972}, {3240, 32859}, {3550, 26128}, {3663, 32926}, {3666, 4645}, {3670, 5015}, {3705, 17595}, {3715, 17333}, {3740, 26073}, {3741, 24715}, {3745, 17302}, {3752, 4388}, {3769, 19785}, {3771, 17601}, {3782, 7081}, {3812, 26117}, {3816, 27002}, {3831, 24851}, {3883, 24177}, {3896, 32863}, {3914, 14829}, {3966, 17490}, {3980, 19808}, {4003, 29840}, {4046, 17287}, {4085, 32913}, {4234, 19869}, {4346, 7172}, {4362, 19796}, {4392, 5014}, {4414, 25957}, {4415, 5205}, {4418, 17289}, {4425, 17122}, {4450, 7191}, {4512, 17282}, {4650, 25453}, {4689, 29839}, {4697, 29633}, {4703, 16569}, {4849, 17345}, {4850, 6327}, {4860, 29843}, {4865, 17591}, {4970, 32846}, {5218, 26132}, {5269, 17304}, {5311, 17320}, {5484, 5836}, {6172, 26047}, {6685, 24692}, {7321, 32771}, {12609, 19270}, {15523, 32845}, {17126, 32774}, {17256, 26037}, {17257, 26040}, {17263, 25961}, {17264, 29687}, {17276, 32937}, {17593, 29671}, {17594, 18134}, {17598, 17766}, {17768, 27064}, {17889, 32916}, {18201, 29655}, {19278, 28628}, {24699, 25349}, {24988, 27065}, {29653, 31151}, {29669, 31178}, {29674, 32934}, {29679, 32933}, {29849, 31134}, {30615, 31302}


X(33069) = X(1)X(6327)∩X(2)X(1757)

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

X(33069) lies on these lines: {1, 6327}, {2, 1757}, {6, 29852}, {7, 4418}, {9, 29851}, {10, 3894}, {31, 320}, {38, 18134}, {42, 3662}, {55, 7232}, {57, 29846}, {63, 29632}, {69, 32914}, {81, 26128}, {141, 32771}, {142, 26037}, {171, 29848}, {210, 3834}, {226, 30942}, {238, 29853}, {244, 4417}, {306, 17155}, {312, 32856}, {354, 25760}, {518, 25957}, {537, 32862}, {612, 17298}, {614, 32843}, {726, 32858}, {756, 17234}, {846, 29830}, {894, 24943}, {908, 30957}, {940, 29847}, {968, 17274}, {982, 3936}, {984, 18139}, {1001, 4683}, {1086, 32860}, {1211, 25557}, {1330, 28082}, {1621, 4655}, {1836, 32943}, {1962, 4389}, {2308, 17364}, {2887, 3873}, {2895, 16825}, {3120, 10453}, {3210, 4062}, {3218, 3771}, {3219, 29642}, {3240, 24169}, {3416, 32923}, {3454, 18398}, {3475, 26034}, {3616, 5429}, {3681, 3836}, {3683, 17345}, {3705, 17449}, {3715, 17265}, {3720, 27184}, {3741, 31019}, {3742, 25960}, {3745, 17376}, {3750, 32950}, {3751, 29850}, {3757, 17288}, {3772, 32919}, {3782, 4966}, {3821, 17018}, {3840, 31053}, {3870, 32948}, {3891, 32846}, {3912, 32925}, {3914, 4684}, {3923, 17483}, {3938, 4645}, {3944, 29824}, {3957, 4660}, {3980, 26842}, {4011, 17484}, {4046, 7263}, {4101, 24178}, {4138, 26015}, {4362, 32863}, {4392, 29671}, {4414, 26840}, {4425, 29814}, {4430, 25959}, {4450, 17715}, {4514, 31134}, {4649, 32774}, {4699, 8013}, {4703, 5284}, {4851, 32928}, {4871, 27131}, {4892, 11680}, {5208, 30984}, {5249, 31330}, {5311, 17300}, {5741, 17063}, {5880, 32945}, {5905, 32930}, {6535, 17230}, {7191, 32946}, {7226, 29653}, {7238, 11246}, {7262, 24542}, {11269, 26132}, {14996, 29645}, {15523, 24349}, {16891, 30941}, {17017, 17778}, {17126, 29656}, {17127, 17770}, {17135, 17889}, {17140, 31017}, {17156, 23681}, {17165, 29674}, {17227, 32781}, {17232, 29687}, {17276, 32936}, {17279, 32938}, {17291, 29663}, {17297, 32926}, {17597, 32844}, {17718, 32918}, {19717, 29646}, {20292, 32941}, {24159, 27368}, {24325, 32782}, {24627, 29678}, {24725, 32942}, {24789, 32864}, {25527, 29631}, {25958, 29655}, {26102, 26580}, {26150, 29684}, {26223, 29637}, {27064, 29677}, {29676, 31029}, {29821, 31034}, {32777, 32940}, {32852, 32922}, {32857, 32929}


X(33070) = X(1)X(3454)∩X(2)X(1386)

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

X(33070) lies on these lines: {1, 3454}, {2, 1386}, {6, 3006}, {8, 5725}, {31, 29671}, {38, 32859}, {42, 4865}, {75, 32842}, {81, 3705}, {141, 17726}, {145, 3485}, {149, 27491}, {171, 29849}, {192, 5057}, {226, 3891}, {238, 29643}, {306, 24552}, {320, 4392}, {321, 26098}, {333, 29664}, {386, 5300}, {518, 29832}, {519, 25385}, {612, 5741}, {614, 18139}, {726, 24725}, {748, 29653}, {752, 4414}, {982, 32949}, {984, 32843}, {1100, 29829}, {1150, 5847}, {1203, 30172}, {1215, 32854}, {1279, 29830}, {1469, 3873}, {1836, 17147}, {1961, 25960}, {1999, 11680}, {2177, 17766}, {2308, 4438}, {2886, 3187}, {2887, 17017}, {3011, 30834}, {3120, 32921}, {3178, 3915}, {3210, 20292}, {3240, 32850}, {3434, 3896}, {3475, 19993}, {3666, 6327}, {3703, 26223}, {3706, 20017}, {3741, 32852}, {3771, 17469}, {3772, 17150}, {3791, 24892}, {3821, 31134}, {3846, 5311}, {3870, 4551}, {3875, 4442}, {3879, 26015}, {3920, 4417}, {3923, 32848}, {3944, 32928}, {3989, 4703}, {3995, 24703}, {3999, 17376}, {4062, 32941}, {4307, 17740}, {4388, 9791}, {4418, 32855}, {4429, 17012}, {4450, 17594}, {4514, 17018}, {4640, 20064}, {4645, 4850}, {4676, 32849}, {4679, 31035}, {4689, 28566}, {4851, 17721}, {4863, 20011}, {4972, 5256}, {4981, 5739}, {5015, 19767}, {5178, 20018}, {5211, 17300}, {5233, 5297}, {5718, 5846}, {5794, 20040}, {5880, 17495}, {7191, 18134}, {7290, 24542}, {7292, 17234}, {10707, 17389}, {14829, 29680}, {15523, 25496}, {16475, 29857}, {16491, 29855}, {16706, 17025}, {17011, 32773}, {17123, 29854}, {17126, 32851}, {17184, 17599}, {17276, 17491}, {17592, 32947}, {17600, 32776}, {17716, 29846}, {17717, 17763}, {17718, 20045}, {17722, 30942}, {17772, 21242}, {17889, 32924}, {19786, 25958}, {20020, 25568}, {21283, 28581}, {24325, 27476}, {24597, 30741}, {25957, 29821}, {26128, 29819}, {26228, 30828}, {26230, 30811}, {27064, 32862}, {27812, 28634}, {28595, 29663}, {29634, 30831}, {29641, 32911}, {29650, 32781}, {29654, 31237}, {29657, 32917}, {29674, 32944}, {29676, 32919}, {29688, 32916}, {29690, 32853}, {29823, 31017}, {31019, 32922}, {31053, 32926}, {31330, 32861}, {32771, 32866}, {32772, 32778}, {32847, 32931}, {32858, 32942}


X(33071) = X(1)X(3846)∩X(2)X(1386)

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

X(33071) lies on these lines: {1, 3846}, {2, 1386}, {6, 3705}, {8, 4849}, {11, 1999}, {31, 29849}, {38, 32843}, {42, 4514}, {43, 4865}, {75, 26098}, {145, 1837}, {149, 3896}, {192, 24703}, {193, 24477}, {226, 32922}, {238, 29671}, {239, 2886}, {244, 32949}, {306, 32942}, {319, 3741}, {320, 982}, {321, 32842}, {333, 29639}, {345, 4676}, {354, 5211}, {386, 5015}, {518, 29840}, {612, 5233}, {614, 18134}, {748, 29643}, {752, 17596}, {908, 32926}, {1100, 29837}, {1150, 29680}, {1155, 20101}, {1193, 7270}, {1203, 30171}, {1211, 17726}, {1215, 32866}, {1279, 29839}, {1699, 3875}, {1836, 3210}, {2887, 16706}, {2999, 4429}, {3006, 16791}, {3120, 19796}, {3175, 17777}, {3187, 11680}, {3192, 5081}, {3240, 5014}, {3293, 5100}, {3666, 4388}, {3681, 29832}, {3687, 5263}, {3703, 27064}, {3742, 17300}, {3752, 4645}, {3757, 5718}, {3840, 32846}, {3873, 31034}, {3879, 11019}, {3891, 31053}, {3920, 5741}, {3923, 32855}, {3936, 7191}, {3944, 32921}, {4003, 26840}, {4009, 26791}, {4011, 17264}, {4062, 32943}, {4201, 4719}, {4259, 25306}, {4360, 24210}, {4362, 17717}, {4383, 29641}, {4392, 32859}, {4425, 17320}, {4438, 16468}, {4649, 29655}, {4655, 17591}, {4680, 5313}, {4703, 17258}, {4850, 6327}, {4851, 20530}, {4863, 20012}, {4886, 31330}, {4894, 5312}, {4972, 17012}, {5057, 17147}, {5086, 20040}, {5252, 20037}, {5255, 17748}, {5256, 32773}, {5272, 17234}, {5278, 29664}, {5311, 25960}, {5573, 17298}, {5743, 16830}, {5794, 20036}, {5846, 7081}, {5847, 14829}, {5880, 17490}, {7292, 18139}, {7321, 24165}, {8167, 17244}, {10453, 17721}, {15523, 32944}, {16823, 17056}, {17017, 19786}, {17025, 25958}, {17034, 20544}, {17123, 17263}, {17125, 29854}, {17155, 24725}, {17289, 25496}, {17316, 26105}, {17317, 26102}, {17322, 29644}, {17469, 29846}, {17495, 20292}, {17599, 27184}, {19808, 32772}, {19851, 28628}, {26230, 30831}, {29650, 32784}, {29676, 32853}, {29681, 30834}, {29688, 32917}, {29690, 32864}, {29819, 32775}, {29823, 31037}, {29852, 31237}, {30942, 32852}, {32848, 32930}, {32854, 32931}


X(33072) = X(1)X(4202)∩X(2)X(4434)

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

X(33072) lies on these lines: {1, 4202}, {2, 4434}, {6, 20483}, {8, 2650}, {10, 1203}, {31, 29641}, {37, 32947}, {38, 4645}, {42, 30969}, {55, 29643}, {75, 32854}, {79, 24068}, {81, 29673}, {86, 29685}, {100, 29671}, {171, 3006}, {210, 32843}, {226, 32927}, {244, 29840}, {306, 32945}, {321, 32847}, {334, 18064}, {516, 32936}, {518, 32949}, {519, 5249}, {537, 17483}, {612, 25760}, {614, 25961}, {726, 20292}, {750, 3705}, {752, 3219}, {756, 4388}, {846, 4450}, {896, 20101}, {982, 29832}, {984, 4683}, {1001, 29854}, {1279, 29851}, {1376, 29849}, {1386, 29850}, {1621, 17766}, {1738, 32924}, {1836, 32925}, {1909, 21415}, {2550, 32860}, {2886, 17763}, {2887, 3920}, {3058, 17243}, {3112, 30631}, {3120, 32926}, {3178, 3871}, {3187, 32865}, {3416, 31330}, {3434, 32915}, {3666, 32948}, {3681, 32946}, {3683, 28566}, {3703, 4418}, {3717, 32938}, {3720, 4514}, {3722, 29839}, {3739, 4914}, {3744, 29632}, {3745, 29631}, {3769, 24892}, {3836, 7191}, {3846, 5297}, {3891, 17889}, {3912, 32943}, {3914, 32928}, {3923, 32862}, {3925, 5846}, {3932, 32930}, {3936, 3961}, {3938, 18134}, {3957, 17765}, {3966, 26037}, {3971, 5057}, {3989, 24723}, {3995, 21282}, {3996, 4062}, {4030, 17056}, {4038, 29835}, {4071, 5276}, {4085, 17011}, {4096, 26792}, {4359, 32866}, {4429, 17017}, {4438, 17126}, {4651, 32861}, {4655, 7226}, {4660, 28606}, {4680, 30116}, {4682, 29845}, {4847, 32919}, {4851, 4863}, {4884, 11246}, {5176, 30076}, {5263, 15523}, {5264, 30172}, {5268, 25960}, {5269, 29857}, {5311, 32773}, {5847, 25006}, {5880, 17155}, {6679, 29873}, {7262, 20064}, {7270, 10459}, {9345, 29843}, {9347, 29635}, {10327, 26098}, {10453, 31005}, {11680, 29649}, {14829, 29690}, {16706, 29819}, {17135, 32846}, {17147, 24715}, {17598, 31151}, {17715, 29830}, {17721, 30957}, {18089, 30109}, {18743, 24709}, {19684, 29659}, {19786, 29816}, {24552, 29674}, {24725, 32937}, {25496, 29679}, {25959, 26128}, {27184, 31134}, {27368, 31419}, {29634, 31237}, {29639, 32918}, {29664, 32916}, {29687, 32942}, {29848, 30811}, {31019, 32920}, {31079, 32780}, {32848, 32932}, {32858, 32941}


X(33073) = X(1)X(977)∩X(2)X(1386)

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

X(33073) lies on these lines: {1, 977}, {2, 1386}, {6, 29641}, {8, 5712}, {10, 4886}, {31, 29643}, {37, 4388}, {38, 320}, {42, 30969}, {81, 3006}, {145, 3475}, {171, 29671}, {192, 1836}, {226, 32926}, {238, 29653}, {239, 3925}, {306, 5263}, {312, 26098}, {319, 31330}, {333, 5847}, {345, 4307}, {350, 18052}, {354, 17300}, {497, 17316}, {518, 17778}, {612, 4417}, {614, 17234}, {674, 5208}, {748, 17263}, {750, 29849}, {752, 846}, {756, 32843}, {894, 3703}, {940, 3705}, {984, 32946}, {1150, 29664}, {1211, 16830}, {1215, 32847}, {1220, 5717}, {1909, 18138}, {1961, 3846}, {1962, 32947}, {1999, 2886}, {2895, 4981}, {3120, 32928}, {3178, 5255}, {3210, 5880}, {3434, 19791}, {3485, 20009}, {3662, 17599}, {3666, 4645}, {3677, 17298}, {3681, 31034}, {3706, 6542}, {3720, 17317}, {3741, 32846}, {3742, 5211}, {3744, 29839}, {3750, 17766}, {3757, 5846}, {3771, 17716}, {3821, 17600}, {3836, 29821}, {3838, 20069}, {3840, 17722}, {3873, 4259}, {3879, 4847}, {3891, 31019}, {3912, 32942}, {3914, 4360}, {3920, 3936}, {3932, 27064}, {3979, 17765}, {3980, 32855}, {3989, 4683}, {3995, 5057}, {3996, 4028}, {4038, 29655}, {4042, 17363}, {4062, 32945}, {4359, 32842}, {4387, 17242}, {4418, 32848}, {4423, 17244}, {4429, 5256}, {4447, 21321}, {4640, 20101}, {4649, 29673}, {4660, 17592}, {4676, 17776}, {4851, 10453}, {4852, 21949}, {4854, 17319}, {4884, 17365}, {4914, 26109}, {4968, 26131}, {4970, 24715}, {4972, 17011}, {5014, 17018}, {5233, 5268}, {5249, 32922}, {5266, 25650}, {5297, 5741}, {5300, 19767}, {5311, 25760}, {5564, 21020}, {5718, 7081}, {5814, 19853}, {6327, 24723}, {6679, 29862}, {7191, 18139}, {7226, 32859}, {7321, 17155}, {14829, 29639}, {15523, 17289}, {16706, 17017}, {17020, 24988}, {17147, 20292}, {17156, 17377}, {17264, 32930}, {17315, 32915}, {17320, 31134}, {17376, 21342}, {17389, 31140}, {17391, 29843}, {17469, 29632}, {17717, 29649}, {17889, 19796}, {19684, 29667}, {19717, 31079}, {19797, 24342}, {19808, 32778}, {20132, 30179}, {21026, 29850}, {21282, 27804}, {24169, 31151}, {24325, 32866}, {24552, 32858}, {24678, 29981}, {24725, 32925}, {25496, 29674}, {25959, 32774}, {26223, 32862}, {28595, 29633}, {28599, 29822}, {29634, 30811}, {29636, 31237}, {29644, 32784}, {29657, 32916}, {29665, 30834}, {29682, 32917}, {29687, 32944}, {29688, 32918}, {29690, 32919}, {29816, 32775}, {32771, 32854}


X(33074) = X(1)X(32781)∩X(2)X(4434)

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

X(33074) lies on these lines: {1, 32781}, {2, 4434}, {8, 38}, {10, 31}, {42, 3416}, {55, 15523}, {63, 484}, {75, 32948}, {81, 29659}, {100, 32778}, {141, 3938}, {171, 29667}, {226, 31134}, {238, 29679}, {306, 2177}, {312, 32947}, {321, 4660}, {594, 5282}, {672, 17275}, {726, 32950}, {748, 3883}, {752, 26223}, {756, 10327}, {846, 32862}, {896, 3617}, {899, 3966}, {902, 32777}, {940, 29685}, {1001, 29687}, {1150, 29673}, {1215, 6327}, {1279, 29677}, {1376, 5078}, {1386, 29663}, {1621, 29674}, {2239, 31330}, {2550, 21020}, {2887, 26227}, {3006, 32916}, {3011, 31237}, {3187, 4085}, {3214, 5814}, {3240, 32861}, {3550, 32779}, {3661, 32945}, {3662, 32923}, {3666, 32854}, {3703, 4414}, {3705, 32918}, {3741, 5014}, {3744, 3844}, {3745, 29647}, {3748, 17231}, {3750, 32858}, {3752, 4914}, {3757, 25957}, {3763, 29686}, {3769, 29631}, {3773, 32929}, {3790, 32936}, {3821, 3891}, {3920, 32784}, {3923, 4450}, {3936, 29670}, {3952, 4703}, {3961, 32782}, {3974, 3994}, {4026, 5311}, {4113, 4690}, {4126, 17332}, {4362, 4972}, {4388, 32931}, {4429, 32914}, {4438, 31079}, {4514, 30942}, {4643, 30615}, {4645, 32771}, {4655, 17165}, {4657, 29816}, {4672, 20064}, {4683, 32937}, {4850, 32866}, {4863, 31136}, {5015, 28242}, {5205, 25960}, {5258, 7293}, {5687, 20653}, {5695, 6535}, {5711, 19729}, {5739, 21805}, {5846, 17017}, {5905, 31161}, {6682, 29832}, {7081, 25760}, {10573, 11031}, {16587, 30647}, {16823, 25961}, {17018, 32846}, {17126, 32780}, {17184, 32920}, {17283, 29853}, {17303, 21764}, {17450, 18141}, {17594, 32848}, {17719, 25958}, {17763, 32773}, {17766, 24552}, {18139, 29651}, {20045, 26128}, {24715, 28605}, {24723, 32925}, {25496, 26251}, {26098, 31264}, {26842, 31178}, {27184, 32927}, {27186, 31151}, {28606, 32847}, {29641, 32917}, {32776, 32926}


X(33075) = X(1)X(32782)∩X(2)X(1386)

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

X(33075) lies on these lines: {1, 32782}, {2, 1386}, {4, 8}, {6, 29667}, {9, 32862}, {10, 1203}, {31, 32778}, {38, 32866}, {42, 32861}, {63, 29046}, {69, 3873}, {75, 6327}, {81, 5847}, {100, 3687}, {141, 7191}, {145, 10371}, {149, 3706}, {238, 15523}, {239, 4972}, {306, 1621}, {319, 350}, {320, 17140}, {333, 3006}, {354, 32863}, {518, 2895}, {519, 4425}, {528, 4046}, {542, 1281}, {599, 17597}, {726, 4683}, {740, 32947}, {748, 29674}, {752, 4418}, {756, 32847}, {846, 32848}, {984, 32854}, {1001, 32858}, {1150, 3705}, {1176, 26270}, {1211, 3920}, {1215, 32843}, {1330, 4968}, {1654, 4981}, {1836, 28605}, {2308, 32780}, {2887, 32914}, {3011, 30831}, {3187, 32773}, {3210, 32950}, {3219, 3703}, {3661, 24552}, {3666, 32842}, {3683, 32849}, {3685, 3969}, {3686, 4071}, {3714, 5046}, {3720, 32846}, {3741, 32844}, {3746, 21081}, {3750, 4062}, {3757, 3936}, {3763, 29666}, {3772, 25958}, {3773, 32930}, {3791, 29631}, {3821, 32924}, {3846, 17763}, {3891, 27184}, {3912, 5284}, {3932, 27065}, {3935, 4030}, {3967, 26792}, {3974, 31018}, {3989, 24697}, {4007, 9580}, {4026, 17011}, {4109, 27068}, {4307, 19822}, {4318, 26942}, {4359, 4645}, {4362, 25760}, {4383, 29679}, {4414, 32855}, {4417, 26227}, {4450, 29315}, {4643, 7226}, {4649, 29685}, {4651, 4886}, {4655, 17155}, {4660, 32860}, {4666, 17296}, {4671, 24703}, {4690, 25368}, {4697, 28498}, {4703, 32925}, {4850, 26034}, {4851, 29814}, {4865, 31330}, {4883, 17374}, {4966, 29817}, {4974, 28595}, {5255, 20653}, {5278, 29641}, {5297, 5743}, {5300, 9534}, {5526, 21082}, {5564, 17163}, {5688, 6348}, {5689, 6347}, {5737, 29664}, {5741, 7081}, {6690, 27757}, {10327, 14555}, {10886, 11679}, {14829, 26250}, {16468, 26061}, {16823, 18139}, {16825, 25957}, {17017, 32784}, {17123, 29687}, {17127, 32777}, {17147, 24723}, {17150, 19786}, {17184, 32922}, {17469, 32783}, {17722, 31241}, {17766, 21085}, {17770, 32940}, {17889, 31134}, {19742, 31079}, {20045, 31037}, {20110, 30620}, {24325, 32949}, {24349, 32859}, {24789, 25959}, {25960, 29649}, {26580, 32926}, {29655, 32919}, {29671, 32917}, {29673, 32864}, {29681, 30811}, {29821, 32781}, {29849, 32916}, {32771, 32946}, {32776, 32921}

X(33075) = anticomplement of X(3745)


X(33076) = X(1)X(141)∩X(2)X(4434)

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

X(33076) lies on these lines: {1, 141}, {2, 4434}, {6, 29659}, {7, 31178}, {8, 192}, {9, 80}, {10, 82}, {31, 29667}, {37, 32847}, {42, 32861}, {43, 3966}, {55, 32778}, {75, 4660}, {81, 29685}, {142, 31151}, {239, 4085}, {306, 3750}, {319, 519}, {321, 32947}, {333, 29673}, {355, 6210}, {518, 17344}, {537, 6646}, {551, 17317}, {726, 24723}, {748, 29679}, {752, 894}, {846, 3703}, {902, 32779}, {958, 7295}, {982, 26034}, {1001, 17267}, {1100, 28538}, {1104, 19879}, {1125, 17283}, {1211, 3961}, {1215, 4388}, {1279, 3844}, {1386, 29633}, {1423, 5252}, {1621, 15523}, {1698, 7290}, {1738, 24212}, {2321, 4693}, {2887, 3757}, {3006, 32917}, {3220, 5258}, {3241, 17373}, {3246, 17357}, {3616, 25539}, {3626, 3717}, {3632, 7174}, {3661, 4366}, {3666, 4914}, {3685, 3773}, {3705, 32916}, {3741, 4514}, {3744, 32783}, {3755, 4716}, {3763, 29660}, {3769, 29635}, {3770, 4692}, {3775, 17765}, {3792, 17792}, {3821, 32922}, {3836, 16823}, {3846, 7081}, {3871, 20653}, {3891, 32776}, {3912, 16484}, {3938, 32782}, {3996, 21085}, {4023, 5524}, {4034, 16517}, {4359, 32948}, {4362, 32773}, {4384, 26582}, {4407, 17252}, {4417, 29670}, {4418, 4450}, {4425, 32926}, {4429, 16825}, {4431, 28580}, {4432, 17280}, {4439, 17261}, {4446, 24464}, {4643, 9055}, {4645, 17153}, {4649, 5847}, {4655, 24349}, {4668, 4901}, {4677, 4971}, {4678, 27549}, {4683, 17165}, {4685, 4886}, {4697, 20101}, {4699, 24693}, {4702, 17229}, {4703, 32937}, {4709, 5564}, {4732, 6653}, {4894, 10479}, {4972, 32914}, {5014, 31330}, {5271, 32865}, {5284, 29687}, {5300, 31339}, {5315, 19867}, {5690, 6211}, {5881, 29235}, {6327, 32771}, {6682, 29840}, {7083, 9708}, {7191, 32781}, {7321, 24692}, {8616, 32777}, {12746, 24436}, {14829, 29655}, {15485, 17279}, {16478, 19784}, {16491, 29598}, {16496, 17272}, {16587, 30646}, {17018, 32852}, {17127, 26061}, {17155, 32950}, {17184, 32923}, {17234, 24331}, {17246, 28503}, {17273, 24841}, {17334, 24821}, {17484, 31161}, {17594, 32855}, {17601, 17740}, {17717, 29828}, {17719, 25760}, {17721, 29827}, {17723, 29825}, {18134, 29651}, {19812, 29842}, {19860, 26530}, {20045, 32775}, {20138, 29576}, {21282, 31025}, {26251, 32944}, {26580, 32927}, {26778, 27019}, {27184, 32920}, {28558, 31300}, {28606, 32854}, {29594, 30331}, {29669, 32946}, {29675, 30811}, {29681, 31237}, {29835, 32919}, {31019, 31134}


X(33077) = X(1)X(2)∩X(6)X(32779)

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

X(33077) lies on these lines: {1, 2}, {6, 32779}, {9, 32849}, {21, 5814}, {31, 32861}, {38, 32855}, {57, 32863}, {63, 2895}, {69, 3218}, {75, 3936}, {100, 3416}, {141, 4850}, {149, 3886}, {171, 32852}, {192, 26580}, {210, 32862}, {226, 28605}, {304, 3266}, {312, 3969}, {314, 17174}, {319, 1150}, {321, 3262}, {345, 3219}, {346, 31018}, {594, 5718}, {599, 17595}, {740, 25760}, {750, 32846}, {894, 31034}, {908, 2321}, {914, 5744}, {984, 32848}, {1043, 5016}, {1211, 4364}, {1266, 30991}, {1621, 3966}, {1738, 25959}, {1792, 27174}, {1943, 28774}, {2476, 5295}, {2886, 4046}, {2887, 32860}, {2975, 10371}, {3210, 17184}, {3306, 17296}, {3419, 4720}, {3662, 17495}, {3666, 17237}, {3681, 3703}, {3695, 3876}, {3704, 3869}, {3706, 11680}, {3714, 11681}, {3729, 17484}, {3772, 30831}, {3773, 32931}, {3790, 3952}, {3834, 24184}, {3846, 25378}, {3879, 14996}, {3896, 32773}, {3914, 25958}, {3923, 32843}, {3932, 4023}, {3944, 4365}, {3977, 4416}, {3980, 32949}, {3996, 5014}, {4007, 5219}, {4035, 5249}, {4054, 4431}, {4078, 9330}, {4144, 17281}, {4358, 5233}, {4359, 18134}, {4360, 30832}, {4361, 30811}, {4388, 32929}, {4418, 32946}, {4438, 32864}, {4454, 5905}, {4470, 5712}, {4519, 5087}, {4643, 31143}, {4655, 32845}, {4659, 31164}, {4665, 26738}, {4680, 24630}, {4683, 32934}, {4703, 32936}, {4709, 21241}, {4717, 18393}, {4766, 27474}, {4865, 32945}, {4873, 30578}, {4886, 5278}, {4970, 32776}, {5057, 5695}, {5227, 24611}, {5235, 17275}, {5241, 17243}, {5361, 5745}, {5564, 30834}, {5839, 24597}, {5847, 17126}, {6327, 32932}, {14555, 17776}, {14997, 17353}, {16610, 17231}, {16704, 17363}, {17080, 26942}, {17147, 27184}, {17229, 30818}, {17232, 24620}, {17234, 24589}, {17240, 30829}, {17242, 31035}, {17248, 27081}, {17287, 24627}, {17299, 17720}, {17300, 26627}, {17330, 27754}, {18139, 19804}, {19684, 19808}, {19789, 26132}, {20336, 27180}, {22008, 31025}, {22038, 24044}, {24715, 31134}, {25351, 25957}, {25939, 26540}, {26005, 26669}, {26128, 32924}, {32775, 32921}, {32777, 32911}, {32844, 32941}, {32859, 32939}


X(33078) = X(1)X(32781)∩X(2)X(1386)

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

X(33078) lies on these lines: {1, 32781}, {2, 1386}, {6, 29679}, {8, 443}, {10, 81}, {31, 29674}, {38, 32847}, {42, 30965}, {43, 32852}, {55, 32858}, {63, 32862}, {69, 3263}, {79, 4066}, {100, 306}, {141, 3920}, {171, 15523}, {189, 3436}, {192, 32950}, {210, 2895}, {238, 29687}, {244, 32866}, {312, 5057}, {319, 4651}, {320, 17165}, {321, 4645}, {518, 32863}, {519, 24169}, {612, 32782}, {740, 32948}, {750, 32778}, {752, 32930}, {899, 32861}, {940, 29667}, {982, 32854}, {1150, 29641}, {1211, 5297}, {1215, 32949}, {1330, 3701}, {1621, 3912}, {1836, 4671}, {1909, 16703}, {1999, 4972}, {2321, 4987}, {2475, 3714}, {2887, 17763}, {3006, 14829}, {3187, 4429}, {3218, 3703}, {3219, 3932}, {3434, 34255}, {3617, 10371}, {3621, 30614}, {3662, 3891}, {3685, 4450}, {3699, 9140}, {3710, 11684}, {3717, 4001}, {3742, 4914}, {3744, 17231}, {3752, 32842}, {3757, 18139}, {3763, 29648}, {3772, 25959}, {3773, 4418}, {3790, 32933}, {3791, 29850}, {3821, 32928}, {3836, 26724}, {3840, 32844}, {3870, 17296}, {3883, 5284}, {3896, 6542}, {3936, 7081}, {3944, 31134}, {3952, 20290}, {3957, 4030}, {3967, 17484}, {3969, 32932}, {3971, 4683}, {3974, 5905}, {3995, 24723}, {3996, 17295}, {4009, 26792}, {4026, 17019}, {4038, 29685}, {4082, 4756}, {4104, 31143}, {4358, 4388}, {4362, 25957}, {4365, 24715}, {4434, 29846}, {4514, 28599}, {4553, 22275}, {4640, 32849}, {4655, 32925}, {4660, 32915}, {4661, 30615}, {4663, 20086}, {4676, 20064}, {4767, 21060}, {4851, 17018}, {4865, 30942}, {5014, 10453}, {5086, 7270}, {5178, 5300}, {5205, 5741}, {5311, 32784}, {5432, 27757}, {5688, 6347}, {5689, 6348}, {5814, 9780}, {5846, 7191}, {5847, 32911}, {5880, 28605}, {6057, 17768}, {6541, 32936}, {7613, 19819}, {9352, 17740}, {16706, 17150}, {16741, 25280}, {16825, 25961}, {17126, 32777}, {17127, 17279}, {17135, 32850}, {17184, 32926}, {17233, 32929}, {17280, 20101}, {17302, 20069}, {17315, 27804}, {17373, 20012}, {17469, 29637}, {17596, 32848}, {17716, 24943}, {17720, 25958}, {17766, 32943}, {17770, 32938}, {17784, 29616}, {18134, 26227}, {20713, 20932}, {24477, 31091}, {25760, 29649}, {26034, 28606}, {28595, 29631}, {29643, 32916}, {29653, 32917}, {29658, 31237}, {29665, 30811}, {29671, 32918}, {29673, 32919}, {32859, 32937}, {32931, 32946}


X(33079) = X(1)X(4030)∩X(2)X(4434)

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

X(33079) lies on these lines: {1, 4030}, {2, 4434}, {8, 982}, {10, 58}, {31, 29679}, {42, 30965}, {43, 3416}, {55, 29674}, {57, 3679}, {100, 15523}, {141, 3961}, {291, 4651}, {312, 4660}, {319, 4685}, {321, 24715}, {345, 17601}, {355, 20368}, {519, 17598}, {537, 26840}, {594, 2160}, {612, 32784}, {750, 29667}, {752, 27064}, {756, 24697}, {846, 3932}, {893, 16587}, {940, 29659}, {984, 10327}, {1089, 24851}, {1215, 4645}, {1376, 5096}, {1460, 9709}, {1621, 29687}, {1698, 5269}, {1961, 4026}, {1999, 4085}, {2177, 32858}, {2887, 7081}, {2895, 21805}, {3006, 32918}, {3240, 32852}, {3550, 32777}, {3626, 18201}, {3632, 3677}, {3661, 24586}, {3662, 32920}, {3666, 32847}, {3703, 17596}, {3741, 32850}, {3744, 29637}, {3745, 29633}, {3749, 17284}, {3750, 3912}, {3752, 32866}, {3757, 3836}, {3769, 25453}, {3773, 32932}, {3790, 32934}, {3821, 32926}, {3831, 5015}, {3840, 4514}, {3844, 32783}, {3846, 5205}, {3883, 17123}, {3920, 32781}, {3952, 4683}, {3966, 16569}, {3971, 24723}, {3974, 24248}, {3979, 4966}, {4071, 26244}, {4358, 32947}, {4362, 4429}, {4388, 26791}, {4414, 32862}, {4428, 17267}, {4450, 32930}, {4553, 22325}, {4655, 32937}, {4668, 18193}, {4672, 20101}, {4703, 27538}, {4850, 32854}, {4914, 16610}, {4972, 17763}, {5014, 30942}, {5226, 27777}, {5249, 31151}, {5814, 6048}, {5846, 29821}, {6327, 32931}, {6690, 29862}, {8616, 17279}, {9347, 29647}, {11679, 32865}, {14829, 29673}, {17126, 26061}, {17184, 32927}, {17234, 29651}, {17275, 17754}, {17283, 29672}, {17483, 31161}, {17725, 25527}, {17766, 32942}, {17780, 31037}, {18134, 29670}, {24169, 32922}, {24217, 30567}, {25957, 26227}, {26251, 32772}, {29641, 32916}, {29649, 32773}, {29665, 31237}, {31053, 31134}, {32925, 32950}


X(33080) = X(1)X(32863)∩X(2)X(2308)

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

X(33080) lies on these lines: {1, 32863}, {2, 2308}, {6, 29663}, {8, 17155}, {9, 29687}, {10, 4001}, {31, 141}, {38, 3416}, {42, 69}, {43, 2895}, {46, 20653}, {55, 599}, {63, 15523}, {81, 29647}, {171, 32782}, {210, 17344}, {238, 29677}, {244, 3966}, {306, 4414}, {312, 4683}, {319, 32860}, {320, 32771}, {321, 4655}, {333, 25957}, {594, 11246}, {612, 17272}, {740, 32950}, {750, 1211}, {752, 24552}, {756, 4643}, {846, 32858}, {896, 32777}, {899, 5739}, {902, 3620}, {968, 17296}, {1150, 2887}, {1215, 32859}, {1654, 26037}, {1698, 26131}, {1757, 29679}, {1962, 4851}, {1999, 32776}, {2177, 3631}, {2206, 24632}, {2223, 7854}, {2886, 31134}, {3120, 11679}, {3187, 3821}, {3218, 32778}, {3219, 29674}, {3434, 31136}, {3619, 21747}, {3661, 4418}, {3662, 32914}, {3666, 32852}, {3683, 17231}, {3729, 6535}, {3741, 6327}, {3745, 17237}, {3757, 17288}, {3769, 32775}, {3771, 31017}, {3773, 32933}, {3791, 32774}, {3836, 5278}, {3844, 4641}, {3936, 29678}, {3969, 32934}, {4023, 9350}, {4062, 17594}, {4357, 5311}, {4358, 4703}, {4362, 17184}, {4365, 24248}, {4388, 30942}, {4389, 32928}, {4392, 32866}, {4416, 17007}, {4417, 32918}, {4429, 32864}, {4450, 32941}, {4642, 10371}, {4645, 31330}, {4650, 32779}, {4660, 17135}, {4734, 14459}, {4741, 32937}, {4850, 32861}, {4914, 21342}, {4970, 20017}, {4972, 32853}, {5287, 6536}, {5361, 25959}, {5372, 25958}, {5743, 17124}, {5814, 24443}, {5847, 17017}, {5880, 21020}, {6057, 17334}, {6646, 32925}, {6685, 31034}, {7226, 32847}, {8013, 17270}, {8040, 16831}, {9316, 26942}, {10453, 32947}, {14829, 25760}, {16475, 29684}, {16704, 25453}, {17126, 32783}, {17127, 29637}, {17232, 29851}, {17233, 32936}, {17273, 32926}, {17277, 25961}, {17287, 32932}, {17291, 29852}, {17343, 26135}, {17347, 32938}, {17591, 32842}, {17763, 27184}, {17770, 26223}, {18134, 29661}, {18141, 30950}, {20086, 28650}, {24597, 29867}, {24627, 29849}, {24723, 32915}, {24890, 24941}, {24991, 26625}, {26098, 31241}, {26580, 29649}, {28605, 32857}, {28606, 32846}, {29667, 32913}, {32773, 32919}


X(33081) = X(1)X(32782)∩X(2)X(3775)

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

X(33081) lies on these lines: {1, 32782}, {2, 3775}, {6, 24943}, {8, 25957}, {10, 18139}, {31, 69}, {38, 306}, {42, 141}, {55, 599}, {81, 32783}, {171, 32863}, {210, 17231}, {238, 2895}, {244, 3687}, {319, 32914}, {320, 4418}, {321, 32856}, {333, 29632}, {343, 25941}, {518, 15523}, {519, 4972}, {524, 2308}, {612, 17296}, {726, 3969}, {740, 17184}, {748, 5739}, {752, 20290}, {756, 3912}, {896, 4001}, {902, 3631}, {942, 20653}, {968, 17272}, {984, 32858}, {1086, 4046}, {1125, 4938}, {1150, 3771}, {1211, 3720}, {1386, 29686}, {1458, 26942}, {1962, 4357}, {1999, 32775}, {2177, 3620}, {2223, 7794}, {2886, 31136}, {2887, 17135}, {3120, 3706}, {3187, 26128}, {3242, 32854}, {3416, 3938}, {3434, 31134}, {3578, 24542}, {3630, 21747}, {3661, 32771}, {3662, 32860}, {3666, 4062}, {3670, 21081}, {3681, 29674}, {3683, 17344}, {3685, 4683}, {3715, 17267}, {3739, 8013}, {3741, 3936}, {3745, 17374}, {3751, 26061}, {3757, 17287}, {3759, 29852}, {3763, 29663}, {3769, 29848}, {3773, 17165}, {3782, 4365}, {3783, 30965}, {3791, 26230}, {3821, 3896}, {3823, 4113}, {3836, 4651}, {3840, 5741}, {3846, 29824}, {3873, 32778}, {3920, 32846}, {3923, 32859}, {3924, 10371}, {3996, 32948}, {4022, 20966}, {4035, 29639}, {4061, 21255}, {4085, 20011}, {4359, 21085}, {4383, 29677}, {4388, 32943}, {4392, 32855}, {4417, 30942}, {4457, 25351}, {4645, 32945}, {4655, 32929}, {4708, 8040}, {4722, 5294}, {4766, 31027}, {4851, 5311}, {4864, 4914}, {4981, 29653}, {5233, 30957}, {5249, 21020}, {5263, 32949}, {5278, 29642}, {5284, 31143}, {5333, 19856}, {5361, 29866}, {5718, 31241}, {5737, 29661}, {5743, 30950}, {5814, 28082}, {5847, 17469}, {6327, 32941}, {6535, 17229}, {6536, 15569}, {6542, 32928}, {6646, 32936}, {6679, 16704}, {7191, 32861}, {10449, 21935}, {10453, 25760}, {14555, 17125}, {14829, 29846}, {15526, 23207}, {16991, 17363}, {17018, 32784}, {17056, 30970}, {17124, 18141}, {17150, 17772}, {17156, 25527}, {17230, 32937}, {17232, 25961}, {17233, 32925}, {17234, 26037}, {17277, 29851}, {17280, 32938}, {17288, 32932}, {17295, 32926}, {17360, 29638}, {17598, 32842}, {17765, 28599}, {17778, 32772}, {18134, 31330}, {20017, 32921}, {21026, 25006}, {24550, 26579}, {24552, 32946}, {24892, 30811}, {25496, 31034}, {25959, 32865}, {26176, 32927}, {26840, 32845}, {27184, 32915}, {29594, 31161}, {29637, 32911}, {29839, 32917}, {29845, 30832}, {32777, 32912}, {32779, 32913}, {32843, 32942}


X(33082) = X(1)X(69)∩X(2)X(2308)

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

X(33082) lies on these lines: {1, 69}, {2, 2308}, {3, 29287}, {6, 29633}, {8, 726}, {9, 29674}, {10, 894}, {31, 32782}, {37, 24697}, {38, 32866}, {42, 2895}, {43, 5739}, {44, 3844}, {63, 32778}, {71, 191}, {72, 17792}, {75, 4655}, {100, 31143}, {141, 238}, {149, 31136}, {171, 1211}, {190, 3773}, {193, 28650}, {239, 3821}, {291, 24690}, {306, 846}, {307, 5018}, {312, 4703}, {319, 740}, {320, 24325}, {321, 4683}, {333, 2887}, {355, 29369}, {518, 17344}, {519, 17254}, {524, 4026}, {527, 1478}, {594, 17768}, {599, 1001}, {668, 4710}, {732, 20969}, {742, 984}, {752, 3775}, {896, 32779}, {966, 1698}, {982, 3966}, {986, 5814}, {1125, 17300}, {1150, 25760}, {1281, 30179}, {1352, 6210}, {1386, 17237}, {1423, 12588}, {1699, 12555}, {1738, 3686}, {1756, 21061}, {1999, 4425}, {2228, 4283}, {2239, 4279}, {2345, 24695}, {2796, 6653}, {3187, 32776}, {3219, 15523}, {3578, 4972}, {3589, 16477}, {3616, 17375}, {3617, 31300}, {3620, 15485}, {3624, 4648}, {3626, 4899}, {3631, 4966}, {3661, 3923}, {3662, 16825}, {3666, 32861}, {3670, 24478}, {3685, 17287}, {3687, 17596}, {3696, 4690}, {3720, 32863}, {3741, 4388}, {3751, 29659}, {3779, 5904}, {3781, 5692}, {3786, 3888}, {3790, 17333}, {3791, 19786}, {3826, 17330}, {3836, 17277}, {3840, 26139}, {3842, 17256}, {3846, 14829}, {3876, 25279}, {3932, 17332}, {3936, 29640}, {3944, 11679}, {3969, 32936}, {3993, 6542}, {4001, 32913}, {4042, 32865}, {4060, 28557}, {4307, 5232}, {4360, 17772}, {4362, 27184}, {4368, 31027}, {4389, 32921}, {4417, 32916}, {4429, 17346}, {4431, 28526}, {4445, 5695}, {4450, 32945}, {4478, 28530}, {4641, 32780}, {4651, 32948}, {4672, 17289}, {4676, 17228}, {4677, 4929}, {4697, 19808}, {4716, 17362}, {4741, 24349}, {4759, 29587}, {4938, 21806}, {4974, 16706}, {5224, 19856}, {5247, 15985}, {5271, 17889}, {5278, 25957}, {5295, 24851}, {5361, 24892}, {5372, 29662}, {5741, 32918}, {5743, 17122}, {5791, 25613}, {5849, 18162}, {5880, 17275}, {5988, 7081}, {6327, 31330}, {6536, 17019}, {6541, 17261}, {7184, 18792}, {7226, 32854}, {7262, 32777}, {7290, 29660}, {9355, 12618}, {10198, 27267}, {10449, 21299}, {12514, 22370}, {13174, 21085}, {14555, 16569}, {15254, 17231}, {15569, 17374}, {16475, 17306}, {16704, 29631}, {16823, 17288}, {16826, 25354}, {16828, 26045}, {16830, 17252}, {17031, 31004}, {17127, 24943}, {17135, 32947}, {17152, 20561}, {17184, 32914}, {17239, 28570}, {17273, 32922}, {17283, 31289}, {17292, 24295}, {17337, 31252}, {17347, 32935}, {17491, 31025}, {17763, 26580}, {18141, 25502}, {19742, 29850}, {19950, 19987}, {20292, 21020}, {20345, 21443}, {20533, 29594}, {23570, 25473}, {23689, 26563}, {24165, 26840}, {24597, 29856}, {25903, 26530}, {27065, 29687}, {27713, 27958}, {28606, 32852}, {29632, 31017}, {29667, 32912}, {29829, 31303}, {29846, 31037}, {32771, 32859}, {32773, 32853}, {32781, 32911}, {32860, 32950}

X(33082) = anticomplement of X(33682)


X(33083) = X(1)X(32863)∩X(2)X(31)

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

X(33083) lies on these lines: {1, 32863}, {2, 31}, {8, 4424}, {9, 29679}, {10, 191}, {42, 2895}, {55, 32782}, {63, 29667}, {69, 17018}, {75, 32950}, {81, 4026}, {100, 1211}, {141, 1621}, {149, 3741}, {319, 3896}, {321, 24723}, {333, 4972}, {451, 14975}, {756, 24697}, {846, 15523}, {896, 32780}, {902, 32783}, {968, 32858}, {1150, 32773}, {1215, 4683}, {1330, 26115}, {1654, 4651}, {1918, 27270}, {1961, 6536}, {1962, 32846}, {2308, 29633}, {3240, 5739}, {3416, 28606}, {3474, 19822}, {3661, 32929}, {3666, 32842}, {3681, 4643}, {3683, 3844}, {3744, 17237}, {3757, 17184}, {3773, 32936}, {3775, 20095}, {3821, 32914}, {3870, 17272}, {3883, 7191}, {3891, 4389}, {3920, 4357}, {3925, 5235}, {3952, 5992}, {3966, 4850}, {3989, 32847}, {3995, 9791}, {3996, 17271}, {4085, 32864}, {4362, 32776}, {4414, 32778}, {4425, 17763}, {4429, 5278}, {4450, 5263}, {4640, 32779}, {4649, 20086}, {4655, 17483}, {4660, 24259}, {4703, 26792}, {4981, 32850}, {5232, 17784}, {5241, 9342}, {5372, 11269}, {5745, 29872}, {5847, 17011}, {6542, 27804}, {6646, 17165}, {6682, 32844}, {6685, 32843}, {6690, 30831}, {7081, 26580}, {7262, 26061}, {7290, 29666}, {8013, 13174}, {8616, 24943}, {9709, 26867}, {10327, 17007}, {10328, 20994}, {15485, 29677}, {16468, 29663}, {17140, 26840}, {17150, 17302}, {17306, 29648}, {17343, 20012}, {17592, 32852}, {17751, 26117}, {17778, 20290}, {20292, 31993}, {20553, 30966}, {21020, 24715}, {24248, 28605}, {24325, 26842}, {24597, 29868}, {25527, 29681}, {26227, 27184}, {26237, 31004}, {26251, 27064}, {29659, 32912}, {29685, 32913}, {29828, 31053}, {29839, 31017}

X(33083) = anticomplement of X(32772)


X(33084) = X(1)X(1211)∩X(2)X(3775)

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

X(33084) lies on these lines: {1, 1211}, {2, 3775}, {6, 32783}, {8, 2887}, {10, 18134}, {31, 2895}, {38, 32855}, {42, 32782}, {43, 141}, {69, 171}, {75, 21085}, {209, 5904}, {210, 29674}, {238, 5739}, {239, 26128}, {306, 984}, {319, 4362}, {320, 3980}, {333, 3771}, {495, 3679}, {518, 32778}, {519, 32773}, {599, 1376}, {612, 32846}, {740, 27184}, {750, 32863}, {756, 32858}, {846, 4643}, {968, 24697}, {982, 3687}, {1150, 29846}, {1215, 3661}, {1621, 31143}, {1654, 29839}, {1738, 4061}, {1757, 32777}, {1961, 4851}, {3187, 32775}, {3240, 32781}, {3242, 32866}, {3314, 7081}, {3416, 3961}, {3681, 15523}, {3685, 4703}, {3696, 17889}, {3706, 3944}, {3740, 17231}, {3741, 4417}, {3751, 32780}, {3759, 29654}, {3769, 17360}, {3773, 32937}, {3782, 4046}, {3791, 17363}, {3816, 31137}, {3840, 5233}, {3844, 4849}, {3846, 10453}, {3868, 20653}, {3883, 17715}, {3896, 32776}, {3912, 4104}, {3920, 32852}, {3936, 31330}, {3967, 17229}, {3969, 32925}, {3971, 17233}, {3996, 4660}, {4001, 4650}, {4007, 21956}, {4023, 16569}, {4028, 4357}, {4042, 30811}, {4062, 28606}, {4085, 20012}, {4383, 29637}, {4388, 32941}, {4389, 4970}, {4416, 7262}, {4418, 32859}, {4429, 4685}, {4445, 20541}, {4640, 17344}, {4651, 25957}, {4655, 32932}, {4662, 25137}, {4682, 17374}, {4683, 32929}, {4690, 29675}, {4697, 17364}, {4716, 19785}, {4734, 17236}, {4886, 16825}, {4966, 5743}, {4981, 29643}, {5235, 29661}, {5241, 25502}, {5263, 32946}, {5268, 17296}, {5278, 29632}, {5737, 29640}, {5741, 30942}, {5847, 17716}, {6327, 32945}, {6646, 32934}, {7226, 32848}, {10180, 17248}, {11679, 17719}, {11680, 31136}, {12609, 31327}, {14555, 17123}, {17061, 17362}, {17135, 25760}, {17184, 32860}, {17227, 24169}, {17230, 27538}, {17232, 26038}, {17272, 17594}, {17277, 29642}, {17294, 26590}, {18139, 26037}, {19701, 19856}, {20017, 32928}, {21020, 31019}, {21060, 29594}, {21805, 29679}, {24552, 32843}, {24892, 30831}, {24943, 32911}, {25960, 29824}, {26580, 32915}, {28605, 32856}, {29635, 30832}, {31034, 32772}, {32779, 32912}


X(33085) = X(1)X(26034)∩X(2)X(2308)

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

X(33085) lies on these lines: {1, 26034}, {2, 2308}, {8, 24165}, {10, 32913}, {31, 29637}, {38, 32847}, {42, 32863}, {43, 69}, {57, 12588}, {63, 29674}, {81, 29633}, {141, 171}, {239, 24169}, {306, 17596}, {312, 4655}, {320, 1215}, {321, 32857}, {333, 3836}, {497, 31137}, {599, 1376}, {726, 26840}, {750, 32782}, {752, 32942}, {846, 3912}, {899, 2895}, {940, 32784}, {982, 3416}, {1054, 3687}, {1150, 25957}, {1211, 17122}, {1330, 3831}, {1352, 20368}, {1468, 19879}, {1707, 17284}, {1757, 4001}, {1961, 4357}, {1999, 3821}, {2239, 30965}, {2887, 14829}, {3218, 15523}, {3219, 29687}, {3578, 24988}, {3634, 26044}, {3661, 3980}, {3662, 4362}, {3666, 32846}, {3706, 24715}, {3740, 17344}, {3741, 4645}, {3750, 4966}, {3752, 32861}, {3769, 17227}, {3773, 32939}, {3791, 16706}, {3792, 22275}, {3840, 4388}, {3844, 32780}, {3883, 29820}, {3925, 31151}, {3936, 32918}, {3966, 17063}, {3967, 17345}, {3969, 32845}, {3971, 6646}, {3979, 4684}, {3999, 4914}, {4026, 4038}, {4358, 4683}, {4392, 32854}, {4414, 32858}, {4429, 32853}, {4450, 32943}, {4640, 17231}, {4650, 32777}, {4660, 10453}, {4682, 17237}, {4697, 17289}, {4703, 18743}, {4734, 17373}, {4741, 27538}, {4850, 32852}, {4851, 17592}, {4970, 6542}, {4972, 32919}, {5268, 17272}, {5278, 25961}, {5372, 24892}, {5429, 19869}, {5712, 29825}, {5739, 16569}, {5745, 29862}, {5814, 24174}, {5846, 17598}, {5847, 29821}, {6327, 30942}, {6536, 17021}, {6685, 17778}, {7081, 17288}, {7262, 17279}, {9342, 31143}, {9364, 26942}, {10180, 17317}, {10371, 24440}, {11679, 17889}, {11680, 31134}, {14996, 29647}, {16704, 29850}, {17126, 24943}, {17127, 29677}, {17135, 32948}, {17184, 17763}, {17232, 29642}, {17233, 32934}, {17287, 21085}, {17291, 29654}, {17296, 17594}, {17343, 26038}, {17595, 32855}, {17770, 27064}, {18134, 29640}, {18139, 32917}, {18141, 26102}, {24248, 34255}, {24259, 31027}, {24627, 29671}, {25527, 29658}, {25958, 29662}, {26098, 29827}, {27184, 29649}, {29679, 32912}, {29824, 32947}, {29846, 31017}, {32859, 32931}, {32915, 32950}


X(33086) = X(2)X(31)∩X(8)X(3670)

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

X(33086) lies on these lines: {2, 31}, {8, 3670}, {10, 3218}, {42, 32863}, {43, 2895}, {57, 29667}, {63, 29679}, {69, 3240}, {100, 141}, {109, 28780}, {149, 4660}, {312, 32950}, {846, 29687}, {894, 26251}, {901, 24250}, {902, 29637}, {1150, 4429}, {1155, 3844}, {1215, 17483}, {1330, 26030}, {1376, 32782}, {1654, 21220}, {1698, 26064}, {2094, 5772}, {3006, 24627}, {3416, 4850}, {3454, 27529}, {3550, 24943}, {3662, 26227}, {3699, 17273}, {3741, 32948}, {3769, 32774}, {3773, 32845}, {3821, 17763}, {3826, 5235}, {3831, 5046}, {3840, 32947}, {3883, 7292}, {3952, 6646}, {4023, 31143}, {4085, 32919}, {4201, 17751}, {4357, 5297}, {4358, 24723}, {4414, 29674}, {4418, 20369}, {4427, 17280}, {4434, 32775}, {4450, 32942}, {4650, 26061}, {4655, 17484}, {4657, 9347}, {4671, 24248}, {4683, 26792}, {4689, 17231}, {4734, 20017}, {4756, 17334}, {4781, 29587}, {4972, 14829}, {5057, 30818}, {5205, 26580}, {5269, 29648}, {5432, 30831}, {5743, 9342}, {5745, 29873}, {5847, 17012}, {6685, 32949}, {7081, 17184}, {7226, 10327}, {8616, 29677}, {9330, 17257}, {9708, 26866}, {9780, 21291}, {9791, 31035}, {15523, 17596}, {17165, 26840}, {17232, 29830}, {17277, 24988}, {17283, 24542}, {17291, 26230}, {17300, 29822}, {17591, 32854}, {17593, 32848}, {17594, 32858}, {18141, 29814}, {20095, 32941}, {24169, 32914}, {24344, 29611}, {25527, 29665}, {26150, 29831}, {26842, 32771}, {27811, 29569}, {28599, 29840}, {29649, 32776}, {29828, 31019}

X(33086) = anticomplement of X(32944)


X(33087) = X(1)X(141)∩X(2)X(3775)

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

X(33087) lies on these lines: {1, 141}, {2, 3775}, {6, 29637}, {8, 3836}, {10, 4684}, {11, 31137}, {31, 32863}, {38, 32858}, {69, 238}, {81, 24943}, {145, 4085}, {149, 31134}, {193, 16477}, {306, 982}, {312, 21093}, {319, 16825}, {320, 3923}, {333, 29642}, {354, 32778}, {518, 17231}, {519, 4429}, {524, 16468}, {537, 3790}, {594, 25557}, {599, 1001}, {614, 32861}, {726, 17233}, {740, 3662}, {748, 2895}, {940, 32783}, {984, 3912}, {1100, 29646}, {1125, 3879}, {1150, 29632}, {1211, 26102}, {1213, 1449}, {1266, 4133}, {1278, 4527}, {1386, 17374}, {1698, 17245}, {1738, 21255}, {1757, 17279}, {1999, 26128}, {2108, 24691}, {2321, 24231}, {2550, 31151}, {2887, 10453}, {3242, 32847}, {3243, 3679}, {3589, 28650}, {3616, 17238}, {3620, 16484}, {3631, 15485}, {3661, 24325}, {3681, 29687}, {3685, 4655}, {3687, 17063}, {3696, 3834}, {3706, 17889}, {3720, 32782}, {3736, 30965}, {3741, 18134}, {3750, 26034}, {3751, 17284}, {3758, 24295}, {3763, 29633}, {3769, 29656}, {3771, 14829}, {3773, 17230}, {3783, 30945}, {3792, 10477}, {3821, 17227}, {3840, 4417}, {3842, 17244}, {3844, 29659}, {3873, 15523}, {3886, 24715}, {3936, 17717}, {3953, 4446}, {3966, 29820}, {3969, 17155}, {3993, 4389}, {4000, 4716}, {4001, 7262}, {4035, 24239}, {4062, 4850}, {4310, 29616}, {4392, 32848}, {4393, 26150}, {4398, 28522}, {4407, 29572}, {4439, 31302}, {4645, 32941}, {4651, 25961}, {4662, 25108}, {4663, 17357}, {4671, 32856}, {4672, 17364}, {4675, 24342}, {4676, 17361}, {4693, 24248}, {4753, 29629}, {4871, 5233}, {4929, 16496}, {4974, 17363}, {4981, 29854}, {5220, 17267}, {5223, 16593}, {5263, 17297}, {5278, 29851}, {5361, 29870}, {5372, 29866}, {5542, 29594}, {5625, 17397}, {5695, 7232}, {5718, 29827}, {5739, 17123}, {5741, 30957}, {5743, 25502}, {5852, 17340}, {6327, 32943}, {6541, 17240}, {6542, 32921}, {7191, 32852}, {8298, 24586}, {15254, 17344}, {15569, 17237}, {15668, 19856}, {16020, 32099}, {16823, 17287}, {16830, 17312}, {17018, 32781}, {17023, 25539}, {17122, 18141}, {17135, 25957}, {17145, 31079}, {17184, 32915}, {17250, 25354}, {17272, 24697}, {17280, 32935}, {17294, 26582}, {17295, 32922}, {17349, 31289}, {17350, 17771}, {17373, 17772}, {17597, 32866}, {17725, 17763}, {17740, 18201}, {17778, 25496}, {17793, 31028}, {18139, 31330}, {19804, 21085}, {20017, 32924}, {21020, 27186}, {21081, 24046}, {21296, 24695}, {24217, 25760}, {24552, 32949}, {25960, 31037}, {26094, 26772}, {26840, 32934}, {27680, 29960}, {29662, 30831}, {29677, 32911}, {29830, 32917}, {29839, 32916}, {31034, 32944}, {32777, 32913}, {32859, 32930}, {32942, 32946}


X(33088) = X(1)X(2)∩X(6)X(3703)

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

X(33088) lies on these lines: {1, 2}, {6, 3703}, {7, 17155}, {31, 345}, {37, 3966}, {38, 69}, {55, 5846}, {63, 5847}, {100, 5329}, {141, 17599}, {171, 17740}, {192, 4388}, {193, 32912}, {194, 17485}, {238, 17776}, {244, 18141}, {321, 26098}, {329, 32843}, {344, 748}, {346, 32930}, {354, 4851}, {497, 3930}, {518, 17441}, {524, 4884}, {536, 1836}, {726, 5905}, {740, 3434}, {752, 32934}, {756, 14555}, {966, 21840}, {968, 3883}, {982, 32846}, {984, 5739}, {1043, 14012}, {1386, 32777}, {1397, 17977}, {1479, 2901}, {1707, 3977}, {1848, 7102}, {1992, 4722}, {2269, 5227}, {2280, 5839}, {2308, 26065}, {2345, 32772}, {2550, 32860}, {2887, 19785}, {2895, 7226}, {3052, 3712}, {3120, 30699}, {3169, 3509}, {3175, 24703}, {3210, 4645}, {3262, 17871}, {3305, 4078}, {3416, 3666}, {3474, 32845}, {3475, 32923}, {3618, 26061}, {3672, 32776}, {3677, 17296}, {3695, 16466}, {3704, 5710}, {3706, 17299}, {3769, 32851}, {3773, 25496}, {3790, 27064}, {3791, 4438}, {3875, 3914}, {3891, 3936}, {3896, 5014}, {3925, 4361}, {3932, 4383}, {3943, 4387}, {3969, 24552}, {3971, 31018}, {3974, 32931}, {3989, 17257}, {4000, 25957}, {4011, 6541}, {4026, 20182}, {4042, 17362}, {4191, 4447}, {4307, 4418}, {4329, 20537}, {4360, 32773}, {4392, 32863}, {4417, 32926}, {4419, 4683}, {4423, 17243}, {4427, 20064}, {4640, 28538}, {4644, 32940}, {4660, 4970}, {4716, 32865}, {4849, 30615}, {4854, 17318}, {4863, 28581}, {4903, 26791}, {4966, 17597}, {4971, 31140}, {5294, 16475}, {5698, 32936}, {5712, 32771}, {5737, 16445}, {6327, 17147}, {9025, 26892}, {10431, 28850}, {16478, 17526}, {17061, 30811}, {17127, 32849}, {17165, 31034}, {17233, 32942}, {17374, 21342}, {17600, 32784}, {17766, 20075}, {17769, 32920}, {17770, 20078}, {17772, 32853}, {17778, 24349}, {17874, 18697}, {17889, 19789}, {18134, 32922}, {19825, 24342}, {20590, 21216}, {24477, 32919}, {24695, 32933}, {25568, 32927}, {25760, 32928}, {32862, 32911}

X(33088) = anticomplement of X(4362)


X(33089) = X(1)X(32779)∩X(2)X(1390)

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

X(33089) lies on these lines: {1, 32779}, {2, 1390}, {3, 8}, {6, 32842}, {10, 4850}, {11, 4671}, {31, 32866}, {38, 32778}, {42, 32855}, {63, 29046}, {75, 3006}, {141, 4392}, {145, 3704}, {149, 5695}, {171, 32854}, {244, 29674}, {262, 321}, {306, 3873}, {345, 1621}, {354, 32858}, {594, 17756}, {726, 25760}, {750, 32847}, {982, 15523}, {1001, 32849}, {1086, 25959}, {1089, 4193}, {1211, 4884}, {1215, 29849}, {1278, 4442}, {2321, 8568}, {2476, 30171}, {2550, 31091}, {2886, 28605}, {2887, 17155}, {3210, 4972}, {3218, 3416}, {3219, 3966}, {3589, 17025}, {3616, 3695}, {3666, 29667}, {3681, 3687}, {3729, 5057}, {3752, 29679}, {3771, 32923}, {3772, 29872}, {3773, 30942}, {3782, 25958}, {3790, 4358}, {3816, 6057}, {3844, 4003}, {3846, 32925}, {3883, 3977}, {3912, 24629}, {3923, 32844}, {3936, 24349}, {3952, 5233}, {3967, 27131}, {3969, 10453}, {3971, 25960}, {3999, 17231}, {4054, 10129}, {4066, 7741}, {4197, 30172}, {4359, 29641}, {4360, 29829}, {4385, 11681}, {4388, 32933}, {4417, 17165}, {4418, 4865}, {4429, 17495}, {4438, 32914}, {4514, 32929}, {4553, 7998}, {4640, 4914}, {4660, 32845}, {4680, 17579}, {4756, 31018}, {4819, 20048}, {5014, 32932}, {5211, 17280}, {5241, 9330}, {5263, 29832}, {5284, 17776}, {5741, 32937}, {5846, 17126}, {6327, 32939}, {7191, 32777}, {7292, 17279}, {16687, 17135}, {17017, 32780}, {17063, 29687}, {17140, 18134}, {17147, 32773}, {17154, 31017}, {17233, 29824}, {17281, 17721}, {17369, 17726}, {17591, 32781}, {17592, 29685}, {17598, 24943}, {17600, 29647}, {17718, 27757}, {20068, 31037}, {24165, 25957}, {24325, 29643}, {24552, 29840}, {24620, 24988}, {24789, 29873}, {25453, 32924}, {26061, 29821}, {26227, 32851}, {28808, 31272}, {29631, 32921}, {29635, 32928}, {29655, 32915}, {29664, 31993}, {29671, 32771}, {29673, 32860}, {29844, 32943}, {29846, 32920}, {31134, 32857}, {32843, 32935}, {32852, 32913}, {32861, 32912}, {32934, 32947}, {32940, 32946}

X(33089) = anticomplement of X(17602)


X(33090) = X(1)X(2)∩X(22)X(956)

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

X(33090) lies on these lines: {1, 2}, {22, 956}, {69, 4430}, {75, 1369}, {81, 5846}, {100, 4030}, {149, 321}, {251, 5291}, {319, 26234}, {497, 4671}, {518, 2895}, {537, 4683}, {726, 32947}, {752, 32940}, {952, 4220}, {1001, 32862}, {1150, 5347}, {1180, 16975}, {1211, 9053}, {1215, 32844}, {1219, 20076}, {1370, 5082}, {1621, 3703}, {1897, 24989}, {2177, 32855}, {2475, 4968}, {2887, 32923}, {2975, 6636}, {3219, 3883}, {3242, 32782}, {3263, 5564}, {3305, 4901}, {3416, 3873}, {3421, 6997}, {3434, 7391}, {3436, 7394}, {3681, 3966}, {3696, 20344}, {3717, 27065}, {3744, 32779}, {3750, 32848}, {3773, 32943}, {3846, 32927}, {3891, 32773}, {3932, 5284}, {3967, 30578}, {4042, 26241}, {4066, 4857}, {4085, 32924}, {4359, 32850}, {4385, 5046}, {4388, 17165}, {4392, 26034}, {4418, 17766}, {4450, 32939}, {4645, 17140}, {4647, 5189}, {4660, 17155}, {4661, 5739}, {4692, 5080}, {4854, 28503}, {4865, 32771}, {4972, 32922}, {5016, 20060}, {5133, 24390}, {5258, 5310}, {5276, 17362}, {5288, 5322}, {5372, 24477}, {5687, 7485}, {5690, 19649}, {5847, 20086}, {6043, 16704}, {6327, 17483}, {6646, 20068}, {8024, 17143}, {8267, 21226}, {9041, 31143}, {12245, 26118}, {12645, 19544}, {17007, 26274}, {17154, 26840}, {17275, 26242}, {17469, 32780}, {17598, 32781}, {17722, 31264}, {17724, 30831}, {17765, 32945}, {17769, 32928}, {19565, 21217}, {20095, 32932}, {23853, 27629}, {24165, 32948}, {25760, 32920}, {26065, 30653}, {26792, 32937}

X(33090) = anticomplement of X(3920)


X(33091) = X(1)X(2)∩X(22)X(5687)

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

X(33091) lies on these lines: {1, 2}, {22, 5687}, {23, 3704}, {55, 32849}, {63, 4901}, {69, 4661}, {82, 17280}, {100, 3703}, {149, 312}, {190, 4450}, {192, 17007}, {319, 3263}, {321, 32850}, {341, 5016}, {346, 20075}, {518, 32863}, {528, 6057}, {594, 5276}, {668, 8024}, {726, 32948}, {752, 32938}, {952, 19649}, {956, 7485}, {1369, 20934}, {1370, 3421}, {1621, 3932}, {1627, 5291}, {1654, 31087}, {1890, 7408}, {2321, 16547}, {2475, 4385}, {2550, 28605}, {2836, 2895}, {2887, 32927}, {2975, 15246}, {3219, 3717}, {3434, 3974}, {3436, 7391}, {3583, 4125}, {3695, 3871}, {3699, 5741}, {3701, 5015}, {3702, 5100}, {3714, 5178}, {3740, 4914}, {3751, 20086}, {3773, 32945}, {3790, 20095}, {3823, 26724}, {3836, 32923}, {3883, 27065}, {3886, 20097}, {3891, 4429}, {3952, 4388}, {3967, 5057}, {3969, 3996}, {3971, 32947}, {4001, 4899}, {4085, 32928}, {4090, 32843}, {4220, 5690}, {4228, 4720}, {4358, 4514}, {4417, 31084}, {4439, 32936}, {4645, 17165}, {4660, 32925}, {4680, 5080}, {4696, 7270}, {4865, 32931}, {4972, 32926}, {5082, 6997}, {5133, 17757}, {5380, 8877}, {5423, 31018}, {5564, 26234}, {5846, 32911}, {6327, 17484}, {7033, 30632}, {7226, 26034}, {7283, 20066}, {7500, 9536}, {7779, 31111}, {8267, 17759}, {9464, 25278}, {10005, 14552}, {12607, 31100}, {12645, 16434}, {14829, 31073}, {17299, 26242}, {17300, 31077}, {17350, 20064}, {17372, 30748}, {17716, 26061}, {17725, 31237}, {17765, 32943}, {17766, 32930}, {17769, 32924}, {18526, 21487}, {20068, 26840}, {21805, 32861}, {24349, 26842}, {24703, 30578}, {25957, 32920}, {26065, 30652}, {28595, 32775}

X(33091) = anticomplement of X(7191)


X(33092) = X(1)X(3695)∩X(2)X(3773)

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

X(33092) lies on these lines: {1, 3695}, {2, 3773}, {8, 3750}, {9, 32861}, {10, 17592}, {31, 32849}, {37, 32778}, {38, 32858}, {42, 32862}, {43, 3932}, {55, 32847}, {63, 32846}, {75, 29653}, {171, 345}, {190, 32946}, {192, 2887}, {238, 17776}, {306, 984}, {312, 6541}, {321, 29643}, {344, 17123}, {346, 26098}, {519, 17715}, {536, 17889}, {726, 18134}, {740, 29641}, {748, 32842}, {846, 3416}, {982, 3912}, {1001, 32866}, {1215, 3790}, {1621, 32854}, {1962, 29667}, {1999, 4438}, {2276, 16587}, {2886, 3943}, {2901, 30172}, {3006, 32915}, {3175, 3944}, {3178, 4385}, {3210, 3836}, {3219, 32852}, {3434, 4693}, {3550, 3712}, {3632, 10389}, {3666, 29674}, {3679, 4046}, {3681, 4062}, {3685, 4865}, {3687, 4078}, {3705, 17242}, {3717, 4028}, {3741, 17233}, {3771, 17725}, {3772, 29862}, {3838, 22034}, {3891, 29632}, {3936, 32925}, {3950, 24210}, {3969, 31330}, {3971, 4417}, {3977, 4650}, {3989, 32782}, {3993, 32773}, {3994, 31053}, {3995, 25760}, {4011, 17264}, {4037, 24064}, {4038, 17316}, {4119, 17314}, {4358, 29849}, {4359, 29854}, {4360, 25453}, {4425, 4664}, {4429, 4970}, {4439, 32937}, {4645, 32934}, {4703, 17261}, {4850, 29687}, {4851, 32913}, {4884, 4966}, {5311, 32779}, {5718, 6057}, {5846, 8616}, {5847, 7262}, {6327, 32936}, {6535, 29682}, {6542, 32853}, {15523, 28606}, {17011, 26061}, {17061, 29858}, {17122, 17740}, {17147, 25957}, {17155, 18139}, {17234, 24165}, {17243, 26102}, {17279, 29821}, {17280, 25496}, {17289, 29644}, {17495, 25961}, {17599, 29637}, {17778, 32935}, {18141, 18201}, {20017, 32864}, {20182, 29633}, {21949, 28484}, {25960, 31035}, {27804, 31079}, {29642, 32922}, {29649, 32851}, {29830, 32923}, {29832, 32943}, {29839, 32920}, {31034, 32938}, {32933, 32949}


X(33093) = X(1)X(2)∩X(6)X(32862)

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

X(33093) lies on these lines: {1, 2}, {6, 32862}, {31, 32849}, {38, 32846}, {69, 7226}, {81, 3703}, {100, 5347}, {149, 4865}, {171, 32848}, {192, 744}, {319, 4981}, {345, 17126}, {536, 20292}, {726, 17483}, {750, 32855}, {752, 32936}, {756, 32861}, {984, 2895}, {1621, 5846}, {2887, 32928}, {3175, 5057}, {3219, 5847}, {3416, 28606}, {3434, 17314}, {3683, 28538}, {3745, 32779}, {3773, 32772}, {3790, 26223}, {3836, 32924}, {3873, 4851}, {3891, 18134}, {3896, 32850}, {3932, 32911}, {3936, 32926}, {3969, 5263}, {3971, 26792}, {3993, 32947}, {3995, 4388}, {4078, 27065}, {4210, 4447}, {4360, 4972}, {4427, 20101}, {4439, 32938}, {4514, 17315}, {4645, 17147}, {4671, 26098}, {4914, 15569}, {4970, 32948}, {5284, 17243}, {5525, 16555}, {6541, 32930}, {6646, 20290}, {9330, 14555}, {17127, 17776}, {17140, 17300}, {17155, 26842}, {17165, 17778}, {17233, 24552}, {17311, 17597}, {17484, 32925}, {17600, 32781}, {17602, 30831}, {17769, 32923}, {17772, 32864}, {18059, 20932}, {18139, 32922}, {19785, 25959}, {20086, 32912}, {21282, 21829}, {25957, 32921}, {27804, 28599}, {31034, 32937}

X(33093) = anticomplement of X(32914)


X(33094) = X(1)X(11015)∩X(2)X(4432)

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

X(33094) lies on these lines: {1, 11015}, {2, 4432}, {4, 2181}, {8, 4683}, {31, 516}, {38, 3434}, {40, 21935}, {42, 1836}, {43, 5057}, {55, 3120}, {75, 32947}, {100, 3944}, {149, 982}, {226, 2177}, {244, 497}, {306, 28580}, {312, 32948}, {321, 4660}, {329, 21805}, {519, 32859}, {528, 3782}, {536, 4799}, {614, 9580}, {726, 5014}, {740, 6327}, {748, 1738}, {750, 24210}, {752, 3187}, {756, 2550}, {899, 24703}, {902, 3772}, {1086, 3058}, {1109, 17860}, {1125, 19336}, {1155, 29662}, {1193, 12699}, {1201, 12701}, {1468, 1770}, {1479, 24443}, {1621, 17889}, {1647, 11238}, {2170, 2549}, {2650, 4295}, {2796, 29673}, {2886, 4414}, {2887, 17764}, {3006, 32934}, {3125, 9664}, {3210, 32844}, {3219, 32865}, {3416, 4365}, {3452, 9350}, {3474, 11269}, {3662, 32943}, {3683, 21949}, {3685, 25957}, {3703, 28530}, {3705, 32845}, {3720, 5880}, {3722, 20075}, {3741, 32950}, {3750, 31019}, {3791, 20064}, {3821, 24552}, {3838, 4689}, {3870, 32856}, {3873, 32857}, {3891, 17766}, {3896, 32946}, {3915, 23537}, {3923, 4972}, {3924, 6284}, {3994, 10327}, {4085, 26223}, {4256, 18393}, {4257, 15228}, {4309, 24159}, {4362, 4442}, {4363, 29685}, {4387, 29687}, {4388, 32860}, {4418, 32773}, {4427, 4438}, {4428, 29689}, {4429, 32930}, {4514, 17155}, {4640, 24892}, {4641, 28534}, {4645, 32915}, {4651, 4703}, {4655, 17135}, {4676, 29850}, {4686, 4914}, {4693, 32858}, {4697, 29829}, {4722, 24695}, {4854, 5311}, {4857, 24046}, {4863, 17276}, {4865, 17147}, {5046, 24440}, {5230, 6361}, {5263, 32776}, {5282, 21956}, {5695, 15523}, {5712, 21806}, {7986, 18499}, {9598, 17451}, {9669, 28096}, {9670, 17054}, {10483, 15955}, {10624, 23536}, {11235, 17595}, {11677, 17872}, {11680, 17596}, {12053, 32577}, {12575, 23675}, {13405, 17782}, {15171, 28082}, {15485, 26724}, {16484, 27186}, {17184, 32941}, {17301, 29819}, {17469, 19785}, {17491, 20011}, {17593, 29680}, {17768, 32912}, {17776, 21026}, {19732, 21027}, {24217, 27003}, {24723, 31330}, {25760, 32932}, {26064, 31327}, {27184, 32945}, {29641, 32936}, {29690, 31140}, {32850, 32925}


X(33095) = X(1)X(30)∩X(2)X(4432)

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

X(33095) lies on these lines: {1, 30}, {2, 4432}, {4, 18677}, {8, 4703}, {9, 21956}, {11, 17596}, {38, 149}, {42, 5057}, {43, 24703}, {55, 3944}, {57, 24217}, {171, 516}, {181, 29309}, {190, 29673}, {192, 4865}, {226, 3750}, {238, 3914}, {306, 4693}, {312, 4660}, {321, 32947}, {354, 32857}, {390, 17715}, {497, 982}, {528, 3961}, {536, 32866}, {726, 4514}, {740, 4388}, {752, 1999}, {846, 2886}, {984, 3434}, {986, 1479}, {988, 9614}, {1001, 17889}, {1054, 3816}, {1086, 29820}, {1621, 3120}, {1699, 17594}, {1738, 17123}, {2177, 31053}, {2478, 24440}, {2796, 29655}, {2887, 3685}, {3006, 32936}, {3052, 29658}, {3061, 9598}, {3175, 32847}, {3550, 17720}, {3583, 4424}, {3586, 5928}, {3663, 4872}, {3666, 17722}, {3670, 4857}, {3679, 4126}, {3687, 28580}, {3705, 32934}, {3720, 20292}, {3735, 9664}, {3741, 24723}, {3749, 17725}, {3772, 8616}, {3821, 32942}, {3838, 29640}, {3846, 17764}, {3865, 13077}, {3896, 32843}, {3923, 32773}, {3931, 22793}, {3957, 32856}, {3971, 32850}, {3995, 21282}, {4011, 4429}, {4085, 27064}, {4192, 5143}, {4256, 11813}, {4358, 32948}, {4387, 29674}, {4389, 29652}, {4414, 11680}, {4419, 24694}, {4425, 5263}, {4428, 29675}, {4442, 32914}, {4450, 17763}, {4512, 17064}, {4642, 5046}, {4650, 11269}, {4655, 10453}, {4676, 25453}, {4679, 16569}, {4683, 17135}, {4689, 17605}, {4697, 29837}, {4709, 4886}, {4892, 29839}, {4902, 30350}, {4972, 32930}, {5014, 32925}, {5248, 24161}, {5249, 16484}, {5530, 18483}, {5695, 32778}, {5698, 7262}, {5880, 26102}, {6327, 32846}, {7186, 15310}, {9812, 17592}, {10129, 29678}, {10624, 13161}, {11019, 18201}, {11235, 29676}, {11238, 17595}, {15254, 21949}, {15485, 24789}, {17018, 24725}, {17147, 32844}, {17184, 32943}, {17280, 28595}, {17450, 26842}, {17591, 17721}, {17593, 24239}, {17738, 26590}, {17766, 32926}, {17768, 32913}, {20101, 28494}, {21090, 21939}, {21805, 26792}, {24552, 32776}, {24697, 31330}, {25760, 32929}, {26580, 32945}, {27184, 32941}, {29835, 32940}, {30942, 32950}, {31134, 32858}


X(33096) = X(1)X(529)∩X(2)X(896)

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

X(33096) lies on these lines: {1, 529}, {2, 896}, {5, 1046}, {6, 3944}, {7, 17063}, {11, 32913}, {31, 17719}, {38, 17484}, {42, 5057}, {43, 1836}, {44, 3838}, {63, 17717}, {79, 3216}, {171, 908}, {190, 29671}, {226, 238}, {244, 17483}, {312, 32846}, {320, 3840}, {321, 32843}, {329, 984}, {333, 25385}, {386, 24851}, {527, 24239}, {537, 29840}, {553, 5121}, {614, 31164}, {748, 31019}, {750, 27131}, {752, 7081}, {756, 26792}, {846, 5718}, {894, 3846}, {899, 20292}, {982, 5905}, {1054, 11246}, {1215, 4388}, {1699, 3751}, {1707, 5219}, {1724, 24161}, {1739, 11552}, {1743, 17064}, {1757, 2886}, {2650, 5046}, {2887, 27064}, {3006, 32938}, {3058, 3979}, {3120, 32911}, {3452, 17122}, {3683, 29640}, {3705, 32935}, {3729, 32855}, {3752, 32857}, {3758, 29635}, {3771, 4676}, {3772, 16468}, {3782, 29821}, {3816, 17365}, {3923, 4417}, {3936, 32930}, {3967, 32847}, {3980, 5233}, {4011, 18134}, {4028, 4693}, {4080, 17150}, {4090, 32850}, {4138, 17353}, {4224, 24436}, {4295, 24440}, {4358, 32949}, {4383, 17889}, {4389, 29650}, {4418, 5741}, {4432, 29839}, {4434, 20101}, {4438, 17350}, {4641, 17605}, {4644, 24702}, {4649, 24210}, {4654, 5272}, {4671, 32852}, {4675, 25502}, {4679, 26102}, {4865, 32937}, {4884, 24821}, {5247, 12047}, {5249, 17123}, {5255, 21077}, {5268, 31142}, {5529, 11112}, {5540, 14109}, {5743, 24342}, {5880, 16569}, {6327, 32931}, {6646, 6682}, {6685, 24723}, {6686, 24692}, {7191, 32856}, {8616, 17718}, {8727, 9355}, {10129, 24892}, {10404, 21214}, {11680, 32912}, {14450, 24443}, {14829, 17770}, {16592, 30646}, {17125, 27186}, {17165, 32844}, {17184, 32944}, {17276, 17591}, {17596, 17768}, {17777, 17778}, {17781, 29639}, {21093, 32926}, {24003, 26791}, {24514, 30953}, {24693, 26038}, {25496, 27184}, {25760, 26223}, {25958, 26061}, {25961, 26688}, {26580, 32772}, {26738, 29661}, {29679, 31134}, {29849, 32933}, {30942, 32859}, {31034, 32915}

X(33096) = {X(2),X(24725)}-harmonic conjugate of X(33097)


X(33097) = X(1)X(30)∩X(2)X(896)

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

X(33097) lies on these lines: {1, 30}, {2, 896}, {6, 17889}, {7, 256}, {31, 29681}, {38, 17483}, {42, 20292}, {43, 5880}, {56, 30362}, {57, 1756}, {58, 11263}, {75, 32861}, {81, 3120}, {86, 4425}, {98, 109}, {142, 17123}, {190, 29653}, {238, 5249}, {244, 26842}, {257, 6625}, {320, 3741}, {321, 32846}, {333, 17770}, {442, 1046}, {513, 18165}, {514, 23763}, {516, 3750}, {528, 3979}, {553, 18201}, {612, 31164}, {740, 17778}, {748, 27186}, {750, 31053}, {752, 3757}, {756, 17484}, {846, 17056}, {893, 16592}, {894, 2887}, {908, 17122}, {940, 3944}, {984, 5905}, {1086, 29821}, {1109, 30690}, {1211, 24342}, {1215, 4645}, {1654, 27798}, {1699, 4888}, {1707, 25525}, {1743, 26730}, {1757, 3925}, {1961, 4415}, {2292, 14450}, {2475, 2650}, {2886, 17365}, {2895, 21020}, {3006, 32940}, {3052, 29675}, {3474, 17601}, {3475, 17715}, {3550, 17718}, {3648, 24936}, {3662, 25496}, {3663, 17600}, {3664, 4038}, {3666, 32857}, {3705, 7840}, {3720, 5057}, {3751, 32865}, {3758, 25453}, {3836, 27064}, {3914, 4649}, {3919, 26727}, {3920, 32856}, {3923, 18134}, {3936, 4418}, {3980, 4417}, {3982, 17598}, {4011, 17234}, {4228, 24436}, {4292, 7415}, {4307, 17716}, {4312, 17594}, {4359, 32843}, {4363, 32778}, {4388, 24325}, {4389, 29644}, {4424, 11552}, {4640, 29640}, {4644, 24694}, {4663, 21949}, {4670, 24704}, {4675, 24703}, {4676, 29642}, {4679, 25502}, {4865, 24349}, {4896, 11019}, {4987, 26244}, {5018, 6354}, {5247, 12609}, {5255, 13407}, {5268, 28609}, {5269, 17725}, {5272, 6173}, {5327, 25361}, {5333, 6536}, {5432, 17775}, {5712, 17592}, {5718, 11246}, {5928, 9612}, {6327, 32771}, {6682, 26840}, {6685, 24692}, {6701, 24880}, {7018, 8033}, {7321, 24165}, {8013, 31143}, {8226, 9355}, {9791, 10180}, {10129, 29662}, {10980, 21267}, {11684, 21674}, {14829, 25385}, {16468, 24789}, {16475, 23681}, {16477, 26723}, {16478, 24159}, {17124, 27131}, {17140, 32844}, {17184, 32772}, {17364, 32853}, {17591, 17723}, {17593, 30424}, {18139, 32930}, {19684, 32776}, {20290, 31025}, {24850, 25650}, {25354, 25507}, {25557, 29820}, {25957, 26223}, {25959, 26061}, {25960, 26627}, {26738, 29678}, {28605, 32852}, {29641, 32935}, {29643, 32933}, {29667, 31134}, {29671, 32939}, {31034, 32860}, {31330, 32859}

X(33097) = {X(2),X(24725)}-harmonic conjugate of X(33096)


X(33098) = X(1)X(5180)∩X(2)X(32857)

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

X(33098) lies on these lines: {1, 5180}, {2, 32857}, {7, 3720}, {31, 3782}, {38, 1836}, {42, 5905}, {43, 17484}, {55, 32856}, {63, 3120}, {69, 4365}, {75, 4683}, {190, 25957}, {192, 32949}, {201, 7702}, {226, 4414}, {244, 24703}, {306, 28526}, {320, 32915}, {321, 4655}, {329, 899}, {497, 17449}, {516, 3938}, {527, 3914}, {536, 32852}, {537, 5014}, {545, 3703}, {612, 4312}, {614, 4862}, {726, 6327}, {740, 32859}, {748, 1086}, {750, 4415}, {752, 3891}, {756, 5880}, {846, 29661}, {894, 29647}, {896, 3772}, {968, 4654}, {976, 1770}, {982, 5057}, {984, 20292}, {1054, 27131}, {1201, 11415}, {1215, 32950}, {1647, 18193}, {1738, 17781}, {2308, 19785}, {2796, 32929}, {2887, 17767}, {3187, 17770}, {3210, 32843}, {3218, 3944}, {3219, 17889}, {3649, 10448}, {3662, 29677}, {3663, 17017}, {3666, 24725}, {3681, 24715}, {3706, 17345}, {3729, 15523}, {3744, 28534}, {3771, 4427}, {3791, 28558}, {3821, 26223}, {3868, 24851}, {3917, 4014}, {3923, 17184}, {3925, 17334}, {3936, 32934}, {3971, 24692}, {3977, 4138}, {3980, 26580}, {3989, 4419}, {4137, 8680}, {4295, 10459}, {4303, 10052}, {4307, 29816}, {4310, 29818}, {4359, 4703}, {4387, 7232}, {4388, 4440}, {4389, 32772}, {4398, 32924}, {4417, 32845}, {4418, 27184}, {4429, 32938}, {4442, 32853}, {4450, 32920}, {4512, 29689}, {4643, 21020}, {4645, 32925}, {4656, 30424}, {4660, 17165}, {4672, 32774}, {4854, 17365}, {4902, 10582}, {4970, 31034}, {4972, 32935}, {6536, 10436}, {6646, 31330}, {9965, 11269}, {11552, 30116}, {16569, 26792}, {17139, 17187}, {17147, 17491}, {17154, 29844}, {17261, 29854}, {17304, 29684}, {17347, 32864}, {17350, 29850}, {17351, 26061}, {17441, 17635}, {17594, 31164}, {17596, 31053}, {17753, 21352}, {17777, 30957}, {18134, 32936}, {20017, 28522}, {20064, 28508}, {20068, 21282}, {24349, 32947}, {24723, 32771}, {25760, 32939}, {25938, 26611}, {26065, 29867}, {26102, 26842}, {26132, 29865}, {26840, 30942}, {32773, 32940}, {32937, 32948}


X(33099) = X(1)X(5905)∩X(2)X(32857)

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

X(33099) lies on these lines: {1, 5905}, {2, 32857}, {7, 25421}, {9, 17889}, {35, 21319}, {38, 5057}, {42, 17484}, {43, 329}, {63, 3944}, {72, 24851}, {75, 4703}, {171, 4415}, {190, 2887}, {192, 32946}, {210, 24715}, {226, 846}, {238, 3782}, {312, 4655}, {321, 4683}, {513, 7186}, {516, 3961}, {527, 24210}, {536, 32861}, {537, 4514}, {726, 4388}, {752, 32926}, {756, 20292}, {894, 4425}, {899, 26792}, {908, 17596}, {968, 31164}, {982, 17276}, {984, 1836}, {1054, 3452}, {1086, 17123}, {1215, 24723}, {1621, 32856}, {1699, 29676}, {1707, 29658}, {1757, 3914}, {1770, 5293}, {1961, 4656}, {1999, 17770}, {2796, 32932}, {2886, 17334}, {2895, 4365}, {3052, 17725}, {3120, 3219}, {3175, 32846}, {3583, 20242}, {3647, 24160}, {3662, 4011}, {3663, 29821}, {3687, 28526}, {3720, 17483}, {3729, 32778}, {3741, 6646}, {3772, 7262}, {3794, 4499}, {3816, 18201}, {3819, 4014}, {3821, 27064}, {3840, 17777}, {3846, 17767}, {3923, 27184}, {3929, 17064}, {3936, 32936}, {3952, 32948}, {3971, 4645}, {3993, 17778}, {3995, 17491}, {3996, 17764}, {4038, 17365}, {4138, 29862}, {4312, 5268}, {4389, 25496}, {4414, 31053}, {4417, 32934}, {4418, 26580}, {4419, 26098}, {4427, 29846}, {4440, 24165}, {4442, 32864}, {4450, 32927}, {4480, 29861}, {4512, 29675}, {4640, 17719}, {4649, 4854}, {4650, 17720}, {4660, 32937}, {4672, 19786}, {4676, 26128}, {4679, 17063}, {4862, 5272}, {4972, 32938}, {4974, 19796}, {5220, 32865}, {5524, 21060}, {5698, 8616}, {5741, 32845}, {5992, 7081}, {6327, 32847}, {6686, 26791}, {7240, 17183}, {9580, 16496}, {11246, 17122}, {11269, 20078}, {11684, 21935}, {11814, 27002}, {15481, 21949}, {16468, 19785}, {16569, 31018}, {16826, 23812}, {17139, 18169}, {17147, 32843}, {17165, 32947}, {17184, 29637}, {17246, 17600}, {17247, 29644}, {17256, 27798}, {17261, 29653}, {17347, 32853}, {17350, 25453}, {17351, 32780}, {17594, 28609}, {20101, 28508}, {21616, 30078}, {24161, 31445}, {24231, 29820}, {24697, 31993}, {24725, 28606}, {25501, 26806}, {25734, 29857}, {25760, 32933}, {26065, 29856}, {26132, 29858}, {26223, 29633}, {26842, 30950}, {29837, 31300}, {31134, 32862}, {32773, 32935}, {32859, 32915}, {32931, 32950}


X(33100) = X(1)X(5180)∩X(2)X(846)

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

X(33100) lies on these lines: {1, 5180}, {2, 846}, {4, 5492}, {7, 29814}, {8, 24068}, {37, 20292}, {38, 149}, {42, 17484}, {43, 26792}, {55, 13589}, {58, 3648}, {79, 3743}, {81, 4854}, {100, 4415}, {190, 4972}, {191, 24883}, {192, 744}, {312, 32950}, {321, 24723}, {329, 3240}, {333, 4442}, {345, 25958}, {497, 4392}, {500, 16116}, {516, 3920}, {726, 32947}, {740, 2895}, {752, 32928}, {756, 24715}, {851, 13097}, {968, 31019}, {976, 20066}, {982, 24429}, {986, 5046}, {1046, 31888}, {1086, 5284}, {1211, 28530}, {1284, 4184}, {1621, 3782}, {1654, 17163}, {1699, 29680}, {1738, 27065}, {1834, 11684}, {1836, 28606}, {2292, 2475}, {2887, 32849}, {3218, 24210}, {3219, 3914}, {3434, 4419}, {3616, 17539}, {3663, 7191}, {3666, 5057}, {3685, 17184}, {3712, 30831}, {3720, 26842}, {3729, 29667}, {3745, 28534}, {3750, 32856}, {3755, 17781}, {3846, 32845}, {3873, 17276}, {3961, 20095}, {3971, 32948}, {3977, 29872}, {3993, 32949}, {3995, 4645}, {4046, 31143}, {4085, 32938}, {4201, 25253}, {4312, 5287}, {4388, 17147}, {4389, 24552}, {4424, 5080}, {4440, 17140}, {4450, 32926}, {4512, 29681}, {4647, 26064}, {4655, 32863}, {4656, 5297}, {4660, 32925}, {4666, 4862}, {4671, 26034}, {4676, 32774}, {4697, 28546}, {4703, 32860}, {4850, 24703}, {4914, 28555}, {4970, 32843}, {4981, 17258}, {5695, 32782}, {5698, 17127}, {5905, 17018}, {6542, 20290}, {6646, 17135}, {8041, 24289}, {8143, 16159}, {9335, 26105}, {11263, 24936}, {15254, 26724}, {15674, 24161}, {17070, 31204}, {17164, 26117}, {17262, 32862}, {17304, 29666}, {17491, 17778}, {17592, 24725}, {17594, 31053}, {17764, 32945}, {17767, 32940}, {17770, 20086}, {17776, 25959}, {17874, 30690}, {20295, 30547}, {21020, 24697}, {24046, 26127}, {24231, 29817}, {24311, 27688}, {25760, 32934}, {26044, 27812}, {26065, 29868}, {26109, 27811}, {26132, 29866}, {26580, 32932}, {26840, 29824}, {27184, 32929}, {32773, 32933}

X(33100) = anticomplement of X(4418)


X(33101) = X(1)X(529)∩X(2)X(18201)

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

X(33101) lies on these lines: {1, 529}, {2, 18201}, {7, 17122}, {31, 17484}, {38, 17717}, {43, 3782}, {63, 17719}, {171, 5905}, {190, 3771}, {200, 24715}, {210, 17889}, {226, 984}, {238, 329}, {244, 27131}, {291, 30961}, {312, 21093}, {320, 29649}, {518, 3944}, {527, 4650}, {537, 3705}, {612, 31164}, {726, 4417}, {748, 26792}, {750, 17483}, {756, 31019}, {846, 17718}, {896, 29665}, {908, 982}, {986, 21077}, {1086, 16569}, {1215, 27184}, {1376, 32857}, {1699, 16496}, {1738, 21060}, {1757, 3772}, {1836, 3961}, {2887, 32937}, {3011, 7262}, {3120, 3681}, {3452, 17063}, {3475, 16484}, {3550, 17768}, {3683, 29675}, {3717, 4138}, {3757, 4703}, {3758, 29645}, {3769, 17770}, {3811, 24851}, {3836, 27538}, {3846, 24349}, {3873, 24217}, {3891, 32843}, {3899, 24222}, {3920, 24725}, {3936, 32925}, {3938, 5057}, {3952, 25957}, {3967, 29674}, {3971, 18134}, {3976, 21616}, {3994, 32858}, {4080, 17135}, {4090, 4429}, {4135, 17233}, {4192, 21320}, {4388, 32920}, {4389, 6685}, {4641, 29658}, {4654, 5268}, {4655, 7081}, {4672, 29634}, {4676, 29656}, {4679, 29820}, {4683, 26227}, {4716, 30699}, {4887, 20103}, {4892, 29641}, {4903, 17232}, {5087, 21342}, {5223, 17064}, {5233, 24165}, {5272, 31142}, {5741, 17155}, {6327, 32927}, {6646, 32916}, {6679, 17350}, {6690, 17334}, {8616, 17724}, {10129, 29690}, {16468, 17061}, {17123, 31018}, {17124, 26842}, {17140, 25960}, {17165, 25760}, {17184, 32931}, {17276, 17596}, {17533, 31520}, {17605, 29676}, {17720, 32913}, {17763, 32859}, {17794, 30953}, {18193, 30827}, {21075, 24440}, {24248, 25568}, {24723, 29670}, {24841, 29844}, {25502, 25557}, {26128, 27064}, {26223, 32775}, {26580, 32771}, {26738, 29682}, {29667, 31161}, {29846, 32933}, {30566, 30957}, {31034, 32928}, {32926, 32946}


X(33102) = X(1)X(20066)∩X(2)X(846)

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

X(33102) lies on these lines: {1, 20066}, {2, 846}, {7, 8049}, {8, 20068}, {38, 24715}, {42, 17483}, {43, 17484}, {75, 32950}, {81, 5196}, {88, 3816}, {100, 3782}, {149, 982}, {165, 29665}, {320, 3896}, {345, 25959}, {386, 14450}, {516, 7191}, {726, 32948}, {740, 32863}, {752, 32924}, {899, 26792}, {968, 27186}, {986, 2475}, {995, 5180}, {1086, 1621}, {1284, 4210}, {1724, 3648}, {1738, 3219}, {1770, 5262}, {1836, 4850}, {2550, 7226}, {2887, 32845}, {2895, 4655}, {3058, 3315}, {3210, 6327}, {3218, 3914}, {3240, 5905}, {3434, 4392}, {3474, 17126}, {3662, 32929}, {3663, 3920}, {3666, 20292}, {3681, 17276}, {3683, 26724}, {3729, 29679}, {3752, 5057}, {3836, 32936}, {3870, 4862}, {3891, 4398}, {3924, 15680}, {3938, 20095}, {3957, 24231}, {3977, 29873}, {4000, 17127}, {4085, 32940}, {4138, 27757}, {4201, 17164}, {4292, 17016}, {4310, 20075}, {4312, 5256}, {4331, 21454}, {4346, 17784}, {4359, 24723}, {4388, 17495}, {4429, 32933}, {4440, 17165}, {4442, 14829}, {4450, 32922}, {4642, 20060}, {4645, 17147}, {4651, 6646}, {4660, 17155}, {4734, 31034}, {4857, 24167}, {4970, 24692}, {4972, 32939}, {5012, 5091}, {5046, 24443}, {5492, 6900}, {5880, 28606}, {6057, 28556}, {7292, 24177}, {8272, 17150}, {9330, 26040}, {9352, 17720}, {9778, 26228}, {11269, 23958}, {11680, 17595}, {17074, 24465}, {17135, 26840}, {17184, 32932}, {17300, 27804}, {17304, 29648}, {17485, 21224}, {17594, 31019}, {17680, 25248}, {17740, 25958}, {17764, 32943}, {17767, 32938}, {17768, 32911}, {20859, 24289}, {21282, 29840}, {23681, 29681}, {24165, 32947}, {24210, 27003}, {25957, 32849}, {26034, 28605}, {26064, 28612}, {31134, 32855}

X(33102) = anticomplement of X(32930)


X(33103) = X(1)X(30)∩X(2)X(18201)

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

X(33103) lies on these lines: {1, 30}, {2, 18201}, {5, 31520}, {7, 171}, {31, 17483}, {38, 29664}, {43, 1086}, {55, 32857}, {57, 17719}, {75, 21085}, {165, 4902}, {190, 29642}, {226, 262}, {238, 5905}, {244, 31053}, {291, 30985}, {320, 4362}, {329, 17123}, {354, 3944}, {516, 17715}, {518, 17889}, {527, 7262}, {537, 29641}, {614, 31164}, {726, 18134}, {748, 17484}, {750, 26842}, {756, 27186}, {846, 17276}, {894, 26128}, {896, 29681}, {908, 17063}, {984, 5249}, {986, 13407}, {1215, 3662}, {1266, 4028}, {1757, 24789}, {1961, 4675}, {2887, 24349}, {3011, 4650}, {3120, 3873}, {3475, 3750}, {3550, 11246}, {3663, 17592}, {3677, 17722}, {3705, 4892}, {3749, 4312}, {3751, 23681}, {3757, 4655}, {3758, 29654}, {3771, 32939}, {3772, 32913}, {3791, 17364}, {3817, 24216}, {3834, 3967}, {3836, 32937}, {3838, 21342}, {3870, 24715}, {3891, 32949}, {3915, 14450}, {3924, 26729}, {3936, 17155}, {3938, 20292}, {3952, 25961}, {3961, 5880}, {3971, 17234}, {3976, 12047}, {3980, 7321}, {3982, 17716}, {3999, 17605}, {4104, 24199}, {4310, 17598}, {4334, 6354}, {4363, 32783}, {4398, 4970}, {4415, 25557}, {4417, 24165}, {4440, 29839}, {4640, 29675}, {4645, 20056}, {4649, 19785}, {4676, 29672}, {4694, 18393}, {4697, 29634}, {4703, 16823}, {4716, 19789}, {4862, 17594}, {4887, 13405}, {4942, 17267}, {5219, 18193}, {5247, 24159}, {5268, 6173}, {5272, 28609}, {5542, 24210}, {5712, 17600}, {5718, 17591}, {6327, 32923}, {7191, 24725}, {8616, 17768}, {10180, 17247}, {10327, 31151}, {11680, 17449}, {16056, 21320}, {16592, 20284}, {17061, 17365}, {17125, 26792}, {17140, 25760}, {17165, 25957}, {17184, 32771}, {17596, 17718}, {17778, 32921}, {18139, 32925}, {18743, 21093}, {18788, 24796}, {21077, 24174}, {21267, 30308}, {21936, 24046}, {24325, 27184}, {24703, 29820}, {24723, 29651}, {25527, 32780}, {26738, 29688}, {26840, 32916}, {29632, 32933}, {29679, 31161}, {29830, 32936}, {31034, 32924}, {32859, 32914}, {32922, 32946}


X(33104) = X(1)X(149)∩X(2)X(902)

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

X(33104) lies on these lines: {1, 149}, {2, 902}, {4, 10459}, {6, 31140}, {7, 17449}, {8, 32843}, {11, 750}, {31, 2886}, {38, 1836}, {42, 3434}, {55, 29678}, {63, 29690}, {69, 31136}, {75, 32844}, {100, 17717}, {141, 31134}, {171, 11680}, {226, 3938}, {244, 5880}, {321, 4865}, {350, 18054}, {377, 1201}, {381, 1480}, {442, 3915}, {443, 28352}, {497, 2293}, {516, 4414}, {518, 24725}, {519, 4054}, {528, 2177}, {535, 16499}, {601, 26470}, {603, 10957}, {612, 1699}, {614, 4859}, {726, 29832}, {748, 3925}, {752, 1150}, {756, 24703}, {846, 29664}, {899, 2550}, {940, 11235}, {968, 9580}, {976, 12047}, {982, 20292}, {984, 5057}, {1215, 5014}, {1468, 24390}, {1621, 29661}, {1647, 3306}, {1654, 4388}, {2292, 12699}, {2476, 5255}, {2887, 24552}, {3006, 3923}, {3010, 21352}, {3052, 31245}, {3058, 17056}, {3218, 29676}, {3242, 32856}, {3583, 30116}, {3685, 29643}, {3691, 31416}, {3705, 4418}, {3706, 17372}, {3722, 17718}, {3724, 31394}, {3741, 6327}, {3744, 3838}, {3749, 31266}, {3772, 17469}, {3816, 17124}, {3826, 17125}, {3886, 4062}, {3914, 3946}, {3920, 3944}, {3936, 32941}, {3961, 31053}, {3966, 21020}, {3989, 9812}, {4307, 11269}, {4384, 21027}, {4392, 32857}, {4417, 32945}, {4429, 32944}, {4442, 32921}, {4450, 32916}, {4514, 32771}, {4645, 30942}, {4671, 32847}, {4675, 17450}, {4683, 17329}, {4703, 4981}, {4766, 20172}, {4799, 25368}, {4847, 32912}, {4850, 17722}, {4888, 31146}, {4972, 25496}, {5230, 31418}, {5250, 21674}, {5263, 25760}, {5264, 25639}, {5269, 29683}, {5311, 24210}, {5695, 32848}, {5710, 21935}, {6284, 10448}, {6682, 32950}, {7191, 17889}, {10129, 17719}, {10453, 17375}, {10707, 24217}, {12436, 28018}, {12609, 28082}, {15523, 17286}, {16483, 17528}, {16496, 31164}, {17050, 26099}, {17135, 32946}, {17140, 29844}, {17146, 20042}, {17155, 29840}, {17184, 29652}, {17279, 21026}, {17283, 25957}, {17315, 32915}, {17324, 32776}, {17339, 29641}, {17381, 29647}, {17594, 29688}, {17596, 29680}, {17766, 25385}, {18134, 32943}, {18393, 30115}, {19785, 29819}, {21747, 24597}, {24589, 24693}, {24709, 30829}, {25525, 29689}, {25527, 29686}, {25958, 32783}, {25959, 29637}, {26034, 31241}, {26223, 29673}, {27186, 29820}, {28605, 32866}, {29671, 32929}, {29849, 32932}, {32850, 32931}, {32865, 32911}


X(33105) = X(1)X(2476)∩X(2)X(31)

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

X(33105) lies on these lines: {1, 2476}, {2, 31}, {4, 10448}, {5, 1064}, {6, 24892}, {10, 5741}, {11, 3136}, {12, 1457}, {37, 17605}, {38, 226}, {42, 2886}, {55, 29678}, {63, 24725}, {73, 26481}, {75, 29849}, {86, 29845}, {141, 31241}, {149, 3750}, {244, 5249}, {312, 29643}, {321, 25385}, {333, 32843}, {442, 1193}, {518, 29690}, {601, 6862}, {612, 5219}, {614, 25525}, {756, 908}, {846, 5057}, {851, 21321}, {896, 5745}, {899, 3925}, {902, 6690}, {940, 29662}, {960, 21674}, {968, 1699}, {976, 11374}, {978, 4197}, {982, 29680}, {984, 29664}, {1001, 29661}, {1042, 15844}, {1125, 5051}, {1150, 32946}, {1201, 25466}, {1203, 24880}, {1211, 30970}, {1215, 3006}, {1279, 29689}, {1468, 26363}, {1475, 31466}, {1621, 29640}, {1647, 3742}, {1836, 4414}, {1962, 24210}, {2177, 3434}, {2181, 30687}, {2292, 12047}, {2650, 6734}, {3011, 17469}, {3072, 6853}, {3073, 6852}, {3120, 3666}, {3178, 3702}, {3214, 31419}, {3216, 3841}, {3240, 32865}, {3454, 19863}, {3583, 4653}, {3589, 29867}, {3670, 11263}, {3687, 21020}, {3705, 31120}, {3706, 4062}, {3722, 13405}, {3741, 3936}, {3745, 29683}, {3757, 32844}, {3771, 24552}, {3772, 17017}, {3775, 31037}, {3816, 30950}, {3840, 18139}, {3873, 26738}, {3915, 10198}, {3920, 17719}, {3924, 28628}, {3938, 17718}, {3944, 10129}, {3989, 4415}, {4300, 6831}, {4358, 29653}, {4390, 31409}, {4417, 31330}, {4418, 32851}, {4438, 26223}, {4442, 4970}, {4642, 5530}, {4648, 10589}, {4660, 31281}, {4675, 17728}, {4847, 4924}, {4850, 17889}, {4865, 26227}, {4892, 6682}, {4972, 6685}, {5014, 29670}, {5230, 6856}, {5233, 26037}, {5256, 17064}, {5262, 24161}, {5263, 29846}, {5268, 30852}, {5311, 17720}, {5439, 28096}, {5712, 11269}, {6051, 9955}, {6686, 24988}, {6708, 21717}, {7191, 17722}, {7951, 30116}, {7988, 17022}, {8728, 27627}, {10458, 14009}, {11019, 17450}, {11679, 32852}, {12609, 24443}, {14829, 32949}, {16374, 28268}, {16470, 24937}, {16592, 23632}, {17061, 17726}, {17063, 27186}, {17135, 21242}, {17234, 30957}, {17529, 28257}, {17596, 20292}, {17602, 29816}, {17716, 29665}, {17725, 29815}, {17778, 32919}, {17782, 20075}, {17874, 24026}, {18134, 30942}, {18165, 20961}, {18201, 26842}, {18210, 21325}, {18743, 29854}, {19684, 29635}, {19721, 21912}, {19856, 31247}, {20963, 31488}, {21326, 21807}, {21805, 25006}, {21820, 24071}, {24217, 29814}, {24943, 30811}, {25500, 26099}, {25527, 29826}, {25529, 29834}, {26061, 29857}, {26251, 28595}, {26725, 30117}, {28605, 32855}, {29632, 32942}, {29641, 32931}, {29650, 32774}, {29687, 30818}, {29832, 32920}, {29839, 32943}, {29840, 32923}, {29872, 32780}, {30831, 32783}, {31034, 32853}


X(33106) = X(1)X(4)∩X(2)X(902)

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

X(33106) lies on these lines: {1, 4}, {2, 902}, {5, 5255}, {6, 11235}, {7, 3551}, {8, 4090}, {11, 171}, {31, 11680}, {35, 19513}, {38, 5057}, {42, 149}, {43, 3434}, {55, 17717}, {58, 24387}, {63, 29676}, {79, 3953}, {81, 10707}, {238, 2886}, {244, 20292}, {312, 4865}, {321, 32844}, {333, 21242}, {377, 21214}, {516, 17596}, {551, 26109}, {553, 24216}, {595, 25639}, {614, 17889}, {726, 29840}, {752, 14829}, {846, 29639}, {894, 29655}, {908, 3961}, {940, 11238}, {968, 29657}, {982, 1836}, {984, 24703}, {986, 12699}, {1046, 10916}, {1110, 31633}, {1125, 4201}, {1201, 2475}, {1215, 4514}, {1279, 3838}, {1621, 29640}, {1647, 27003}, {1707, 5231}, {1757, 4847}, {1935, 10957}, {2329, 7745}, {2476, 3915}, {2548, 3501}, {2550, 16569}, {2887, 29637}, {2895, 31136}, {3006, 32930}, {3058, 3750}, {3073, 26470}, {3120, 7191}, {3208, 9596}, {3219, 29690}, {3662, 29668}, {3666, 17722}, {3679, 14555}, {3685, 29671}, {3705, 3923}, {3706, 32861}, {3729, 7774}, {3741, 4388}, {3744, 17605}, {3746, 19646}, {3749, 5219}, {3751, 24392}, {3752, 24715}, {3757, 25385}, {3782, 17598}, {3816, 17122}, {3840, 4645}, {3846, 5263}, {3873, 24725}, {3914, 29821}, {3919, 6788}, {3925, 17123}, {3936, 32943}, {3938, 31053}, {3971, 17777}, {4011, 29641}, {4307, 5274}, {4312, 18193}, {4365, 32842}, {4383, 31140}, {4414, 29680}, {4417, 32941}, {4438, 4676}, {4442, 32924}, {4450, 32918}, {4671, 32854}, {4854, 17600}, {4888, 14548}, {4972, 32944}, {5014, 32931}, {5046, 10459}, {5211, 24165}, {5247, 24390}, {5249, 29820}, {5264, 7741}, {5266, 9955}, {5293, 21616}, {5294, 29861}, {5300, 25591}, {5315, 31159}, {5530, 10624}, {5695, 32855}, {5710, 10896}, {5711, 9669}, {5741, 32945}, {5880, 17063}, {6174, 9337}, {6327, 30942}, {6682, 24723}, {7081, 17766}, {7290, 17064}, {9580, 17594}, {9599, 17754}, {9665, 17750}, {9670, 19765}, {9812, 17591}, {10453, 32946}, {10456, 30479}, {11246, 18201}, {11813, 30115}, {13740, 19879}, {14009, 28356}, {14956, 18169}, {16044, 17752}, {16056, 28364}, {16483, 17532}, {16484, 17056}, {16496, 28609}, {17126, 29662}, {17127, 24892}, {17135, 32843}, {17449, 17483}, {17592, 17723}, {17715, 17718}, {17716, 17720}, {17737, 21764}, {21443, 30660}, {22793, 24851}, {24349, 29844}, {24477, 24695}, {24552, 25760}, {24943, 25958}, {25496, 29633}, {25502, 26105}, {25527, 29660}, {25959, 29677}, {26015, 32913}, {26034, 29827}, {26060, 28257}, {27064, 29673}, {27184, 29652}, {29675, 31266}, {29824, 32949}, {29832, 32925}, {29849, 32929}


X(33107) = X(1)X(5046)∩X(2)X(31)

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

X(33107) lies on these lines: {1, 5046}, {2, 31}, {6, 11680}, {9, 29664}, {11, 81}, {38, 17484}, {42, 149}, {63, 29680}, {226, 1421}, {244, 26842}, {321, 32842}, {329, 7226}, {443, 27625}, {497, 17018}, {601, 6972}, {612, 27131}, {614, 31019}, {846, 29688}, {908, 3920}, {942, 28098}, {946, 17016}, {982, 17483}, {984, 26792}, {1064, 6840}, {1125, 26131}, {1193, 2475}, {1203, 24883}, {1215, 32844}, {1386, 17605}, {1479, 19767}, {1621, 5718}, {1699, 5256}, {1738, 17020}, {1757, 29690}, {1836, 4850}, {2476, 16466}, {2886, 32911}, {2895, 3741}, {3006, 27064}, {3060, 10473}, {3072, 6960}, {3073, 6888}, {3120, 29821}, {3218, 24239}, {3219, 29639}, {3240, 3434}, {3452, 5297}, {3618, 29868}, {3666, 5057}, {3670, 14450}, {3677, 31164}, {3705, 26223}, {3745, 5087}, {3752, 20292}, {3772, 10129}, {3822, 5315}, {3840, 32949}, {3873, 17721}, {3877, 5725}, {3914, 17012}, {3923, 29849}, {3936, 32942}, {3944, 17017}, {3971, 30578}, {3995, 17777}, {3997, 26074}, {4011, 29643}, {4184, 21321}, {4193, 5711}, {4344, 5748}, {4392, 5905}, {4415, 17726}, {4417, 24552}, {4424, 5180}, {4683, 6682}, {4865, 32931}, {4999, 16948}, {5141, 5230}, {5211, 17140}, {5219, 29665}, {5226, 26228}, {5249, 7292}, {5259, 24936}, {5262, 12047}, {5263, 5741}, {5264, 27529}, {5269, 30852}, {5272, 27186}, {5284, 17056}, {5294, 29872}, {5710, 11681}, {5712, 29814}, {6542, 31052}, {6685, 32947}, {7290, 29681}, {8616, 29678}, {9330, 18228}, {10453, 31034}, {15485, 29661}, {16057, 28239}, {16468, 24892}, {17011, 24210}, {17015, 30384}, {17025, 19785}, {17165, 29840}, {17353, 29873}, {17469, 17719}, {17491, 26840}, {17598, 32856}, {17723, 24703}, {17749, 26060}, {17778, 29824}, {19717, 29837}, {19863, 26064}, {20012, 21283}, {20086, 32919}, {21241, 29850}, {21242, 32864}, {25385, 32914}, {25527, 29666}, {29586, 31062}, {29650, 32776}, {29671, 32849}, {29676, 32912}, {29832, 32937}, {29866, 30828}, {30942, 32863}

X(33107) = anticomplement of X(32918)


X(33108) = X(1)X(3841)∩X(2)X(11)

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

X(33108) lies on these lines: {1, 3841}, {2, 11}, {4, 5260}, {5, 962}, {7, 15346}, {8, 442}, {9, 5057}, {10, 908}, {12, 3617}, {21, 4302}, {38, 17889}, {40, 6828}, {42, 32865}, {63, 4312}, {75, 3006}, {86, 29829}, {141, 25959}, {142, 11025}, {145, 25466}, {171, 24892}, {192, 4442}, {200, 31266}, {210, 3838}, {226, 3681}, {244, 29676}, {321, 3790}, {333, 6327}, {354, 27186}, {355, 6937}, {377, 2975}, {404, 26363}, {405, 9668}, {443, 5253}, {474, 26060}, {496, 5550}, {499, 17531}, {516, 10883}, {517, 6829}, {518, 31019}, {612, 17064}, {614, 26724}, {631, 26470}, {693, 3126}, {740, 29643}, {756, 3944}, {858, 4329}, {899, 17717}, {946, 6991}, {956, 17528}, {958, 2475}, {976, 24161}, {982, 29690}, {984, 3120}, {993, 4316}, {1086, 4392}, {1150, 4645}, {1211, 25958}, {1329, 5141}, {1478, 6175}, {1479, 5047}, {1538, 4002}, {1698, 4193}, {1699, 3305}, {1738, 4850}, {1757, 24725}, {1788, 26481}, {1836, 3219}, {1861, 30687}, {2177, 29640}, {2320, 10609}, {2478, 19855}, {2551, 6871}, {2887, 3775}, {2895, 4042}, {3091, 15908}, {3218, 5880}, {3240, 5718}, {3306, 5231}, {3428, 6839}, {3436, 5177}, {3528, 32633}, {3555, 3824}, {3579, 6845}, {3614, 9711}, {3616, 8728}, {3621, 15888}, {3622, 3813}, {3624, 24387}, {3634, 7741}, {3651, 18517}, {3660, 17620}, {3666, 21949}, {3679, 3822}, {3698, 25005}, {3703, 28605}, {3705, 4359}, {3706, 32858}, {3715, 26792}, {3717, 4054}, {3722, 29675}, {3740, 17605}, {3741, 25957}, {3744, 29681}, {3750, 29661}, {3752, 29680}, {3757, 5014}, {3771, 32945}, {3772, 3920}, {3782, 7226}, {3814, 19875}, {3820, 17530}, {3823, 30818}, {3836, 21242}, {3840, 25961}, {3846, 26037}, {3868, 11551}, {3870, 25525}, {3871, 10198}, {3873, 4847}, {3890, 4342}, {3897, 17647}, {3911, 30312}, {3914, 28606}, {3918, 18395}, {3927, 14450}, {3932, 4671}, {3935, 17718}, {3957, 4863}, {4187, 19877}, {4188, 4999}, {4189, 24953}, {4190, 5303}, {4294, 31420}, {4295, 11684}, {4299, 31458}, {4307, 24597}, {4345, 25962}, {4361, 32842}, {4384, 4766}, {4388, 5278}, {4414, 24715}, {4417, 4651}, {4418, 4438}, {4420, 11374}, {4463, 29667}, {4647, 30172}, {4660, 32917}, {4666, 24392}, {4678, 12607}, {4699, 31083}, {4704, 21927}, {4731, 5123}, {4756, 27549}, {4772, 7897}, {4865, 32914}, {4981, 27184}, {4989, 26723}, {5016, 16824}, {5051, 19853}, {5056, 7681}, {5080, 9708}, {5086, 5727}, {5176, 9623}, {5219, 7679}, {5220, 17484}, {5223, 31164}, {5224, 17220}, {5235, 14009}, {5251, 11114}, {5264, 24880}, {5275, 17737}, {5297, 17720}, {5433, 17572}, {5499, 18525}, {5552, 6856}, {5584, 6895}, {5587, 6932}, {5603, 6881}, {5695, 32849}, {5708, 9782}, {5711, 24883}, {5759, 8226}, {5779, 9809}, {5790, 11698}, {5818, 6842}, {5904, 11263}, {6284, 16865}, {6361, 6841}, {6666, 7678}, {6684, 6943}, {6703, 29864}, {6830, 26446}, {6852, 11248}, {6853, 11499}, {6884, 11496}, {6887, 10531}, {6888, 10310}, {6901, 11249}, {6920, 10525}, {6923, 10728}, {6930, 10724}, {6945, 10175}, {6951, 12248}, {6963, 11231}, {6975, 12700}, {6989, 12116}, {6990, 12699}, {7080, 10585}, {7191, 24789}, {7288, 10957}, {7292, 17278}, {7504, 26364}, {8580, 30852}, {8727, 9778}, {9589, 12558}, {9655, 31494}, {9669, 16842}, {9709, 27529}, {10176, 18393}, {10200, 17535}, {10453, 18139}, {10593, 17575}, {12053, 24564}, {12649, 28629}, {14795, 17566}, {14923, 24987}, {15674, 20066}, {16819, 17550}, {16825, 32844}, {16992, 20553}, {17012, 17723}, {17018, 17056}, {17025, 17366}, {17061, 29815}, {17070, 17602}, {17122, 29662}, {17135, 18134}, {17162, 17377}, {17234, 29824}, {17347, 17491}, {17592, 29682}, {17715, 29689}, {17740, 30741}, {18499, 28466}, {19755, 19865}, {20486, 29593}, {20544, 29576}, {20653, 31327}, {21020, 32778}, {21026, 29674}, {21283, 29830}, {21299, 30056}, {21381, 24342}, {24217, 30950}, {24703, 27065}, {25304, 26543}, {25352, 25378}, {25383, 25384}, {25453, 32772}, {25496, 29850}, {26013, 26540}, {26098, 32911}, {26227, 32850}, {27754, 28580}, {28612, 30171}, {29632, 32941}, {29642, 32943}, {29653, 32915}, {29671, 32860}, {29673, 32771}, {29832, 32922}, {29857, 32779}, {29873, 32777}, {30970, 32784}, {31025, 31079}, {31075, 31115}, {31237, 32783}, {32853, 32949}, {32864, 32946}, {32916, 32948}


X(33109) = X(1)X(224)∩X(2)X(902)

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

X(33109) lies on these lines: {1, 224}, {2, 902}, {6, 32865}, {8, 32946}, {10, 4388}, {11, 17122}, {35, 27622}, {38, 20292}, {43, 2550}, {55, 29640}, {57, 29676}, {75, 4865}, {142, 29820}, {149, 3720}, {171, 2886}, {226, 3961}, {238, 3925}, {321, 32847}, {333, 752}, {387, 31420}, {442, 5255}, {443, 21214}, {497, 6821}, {516, 846}, {519, 17778}, {528, 3750}, {595, 3841}, {612, 3944}, {750, 11680}, {756, 5057}, {894, 29673}, {940, 31140}, {964, 19879}, {982, 5880}, {984, 1836}, {1054, 24239}, {1086, 17598}, {1215, 32850}, {1376, 17717}, {1386, 21949}, {1699, 5268}, {1738, 29821}, {1757, 25006}, {1909, 21416}, {1961, 20539}, {2475, 10459}, {2650, 5178}, {2887, 5263}, {3006, 4418}, {3058, 16484}, {3120, 3920}, {3218, 29690}, {3662, 29652}, {3666, 24715}, {3679, 5739}, {3681, 24725}, {3685, 29653}, {3696, 32861}, {3705, 3980}, {3706, 32846}, {3741, 4645}, {3749, 25525}, {3752, 17722}, {3757, 17766}, {3772, 17716}, {3826, 17123}, {3836, 32942}, {3838, 17719}, {3915, 4197}, {3923, 29641}, {3936, 32945}, {3938, 31019}, {3979, 5853}, {4279, 28356}, {4359, 32844}, {4414, 29664}, {4425, 16830}, {4429, 25496}, {4442, 32928}, {4450, 32917}, {4514, 24325}, {4651, 32843}, {4654, 16496}, {4683, 4981}, {4732, 4886}, {4847, 32913}, {4972, 29633}, {5014, 32771}, {5247, 31419}, {5266, 24161}, {5269, 17064}, {5293, 12047}, {5814, 31327}, {5903, 26893}, {6327, 31330}, {6686, 26073}, {7081, 25385}, {7779, 17116}, {11235, 24217}, {14829, 21242}, {17063, 17721}, {17126, 24892}, {17135, 32949}, {17155, 29832}, {17289, 28595}, {17449, 26842}, {17594, 29657}, {17596, 29639}, {18134, 32941}, {18139, 32943}, {18141, 31137}, {19804, 24693}, {21301, 23825}, {21384, 31416}, {24165, 29840}, {24552, 25957}, {24692, 26840}, {24699, 25368}, {24943, 25959}, {26060, 27627}, {28599, 31025}, {28605, 32854}, {29643, 32929}, {29671, 32932}, {31134, 32782}, {31136, 32863}


X(33110) = X(1)X(27186)∩X(2)X(11)

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

X(33110) lies on these lines: {1, 27186}, {2, 11}, {4, 3617}, {7, 2890}, {8, 79}, {10, 3583}, {20, 22758}, {21, 20066}, {31, 32865}, {38, 24715}, {40, 6895}, {65, 5178}, {69, 9054}, {75, 1369}, {142, 29817}, {145, 377}, {153, 6923}, {200, 31053}, {210, 5057}, {226, 3935}, {321, 32850}, {333, 4450}, {355, 31828}, {376, 18515}, {388, 3621}, {404, 15325}, {442, 3871}, {443, 3622}, {495, 6175}, {496, 17531}, {516, 3219}, {517, 6839}, {518, 17483}, {519, 11551}, {752, 32864}, {952, 6951}, {956, 17579}, {958, 15680}, {962, 6894}, {1125, 26060}, {1279, 26724}, {1370, 19825}, {1479, 9780}, {1482, 6901}, {1699, 27131}, {1706, 25005}, {1738, 7191}, {1836, 3681}, {1858, 5086}, {2476, 5687}, {2887, 32945}, {2975, 15326}, {3006, 32932}, {3085, 31420}, {3086, 17572}, {3120, 3961}, {3146, 11827}, {3158, 31266}, {3210, 29832}, {3218, 4847}, {3240, 26098}, {3295, 4197}, {3305, 9580}, {3306, 24392}, {3410, 21293}, {3436, 4678}, {3523, 12116}, {3550, 24892}, {3585, 3626}, {3625, 5270}, {3634, 4857}, {3654, 18407}, {3679, 5080}, {3689, 3838}, {3690, 29309}, {3697, 22793}, {3741, 32948}, {3744, 21949}, {3746, 3841}, {3749, 29681}, {3755, 17011}, {3813, 5253}, {3814, 31159}, {3836, 32943}, {3870, 31019}, {3873, 4863}, {3876, 12699}, {3886, 32858}, {3914, 3920}, {3927, 31888}, {3936, 3996}, {3938, 17889}, {3957, 5249}, {4000, 17024}, {4085, 32772}, {4126, 4756}, {4188, 10527}, {4189, 19843}, {4193, 9709}, {4208, 10587}, {4294, 16865}, {4302, 15677}, {4359, 4514}, {4365, 32847}, {4386, 17737}, {4388, 4651}, {4418, 21381}, {4420, 12047}, {4440, 20068}, {4442, 32926}, {4645, 17135}, {4660, 24259}, {4671, 10327}, {4685, 32843}, {4861, 17647}, {4865, 32842}, {4894, 28612}, {4968, 5100}, {4981, 24723}, {5047, 15171}, {5056, 10531}, {5141, 5552}, {5175, 5554}, {5177, 10528}, {5180, 5692}, {5260, 6284}, {5264, 24883}, {5276, 21956}, {5278, 11330}, {5297, 24210}, {5541, 11604}, {5657, 6840}, {5659, 9778}, {5695, 32862}, {5794, 14923}, {5818, 10525}, {6063, 8047}, {6361, 16139}, {6828, 10306}, {6829, 10679}, {6852, 11849}, {6853, 32141}, {6871, 7080}, {6888, 11248}, {6900, 22791}, {6904, 10529}, {6914, 13199}, {6917, 12245}, {6940, 10943}, {6960, 11499}, {6965, 10738}, {6972, 26470}, {6975, 11928}, {7226, 24248}, {7391, 11677}, {8168, 11237}, {9708, 11114}, {9782, 18398}, {9812, 31018}, {10453, 21283}, {10586, 17580}, {12575, 24564}, {14795, 25440}, {15172, 17529}, {15584, 26985}, {15674, 19854}, {16704, 20101}, {16859, 19855}, {17064, 29665}, {17124, 24217}, {17495, 29840}, {17548, 30478}, {17577, 17757}, {17594, 29664}, {17596, 29690}, {17680, 26759}, {17764, 32936}, {17765, 32923}, {17766, 32914}, {17778, 20011}, {17781, 24393}, {18406, 28194}, {19785, 29815}, {20012, 31034}, {20020, 30699}, {21241, 29846}, {21242, 32918}, {23958, 24477}, {24342, 29685}, {24597, 30652}, {25639, 27529}, {25957, 32941}, {26015, 27003}, {26627, 29843}, {27538, 30578}, {29641, 32849}

X(33110) = anticomplement of X(1621)


X(33111) = X(1)X(442)∩X(2)X(31)

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

X(33111) lies on these lines: {1, 442}, {2, 31}, {10, 4417}, {11, 26102}, {12, 24806}, {37, 3838}, {38, 29664}, {42, 32865}, {43, 3925}, {55, 29640}, {75, 29671}, {81, 24892}, {86, 29635}, {100, 29678}, {142, 17063}, {226, 984}, {244, 27186}, {312, 25385}, {321, 29643}, {325, 10436}, {333, 32946}, {354, 29676}, {386, 3841}, {497, 16484}, {601, 6852}, {612, 17719}, {614, 17722}, {756, 31053}, {846, 1836}, {894, 4438}, {940, 31245}, {978, 8728}, {982, 5249}, {986, 12609}, {1046, 5791}, {1064, 6829}, {1086, 17591}, {1125, 16062}, {1150, 32949}, {1193, 4197}, {1215, 29641}, {1468, 26131}, {1621, 29661}, {1698, 5743}, {1699, 19542}, {1742, 8727}, {1961, 17720}, {2475, 10448}, {3006, 32771}, {3011, 17716}, {3073, 6861}, {3120, 28606}, {3219, 24725}, {3434, 3750}, {3454, 19858}, {3550, 6690}, {3624, 13728}, {3662, 6682}, {3666, 17889}, {3681, 26738}, {3705, 24325}, {3720, 11680}, {3731, 17747}, {3741, 18134}, {3744, 29675}, {3745, 29658}, {3757, 4865}, {3771, 5263}, {3792, 10473}, {3812, 25135}, {3816, 17245}, {3817, 7377}, {3822, 30116}, {3826, 16569}, {3840, 17234}, {3869, 21674}, {3873, 29690}, {3914, 17592}, {3920, 17725}, {3936, 31330}, {3961, 17718}, {3979, 4863}, {3980, 32851}, {4038, 11269}, {4138, 4357}, {4300, 6828}, {4358, 29854}, {4359, 29849}, {4414, 20292}, {4429, 6685}, {4514, 29651}, {4649, 5712}, {4650, 5745}, {4850, 29688}, {4892, 27184}, {5219, 5268}, {5247, 19854}, {5255, 10198}, {5271, 32861}, {5273, 24695}, {5275, 30755}, {5278, 32843}, {5293, 11374}, {5530, 24440}, {5741, 26037}, {5880, 17596}, {5886, 30448}, {5903, 22276}, {6173, 18193}, {7226, 32856}, {7295, 25514}, {9347, 29683}, {10026, 17275}, {10453, 21242}, {11679, 32846}, {16056, 21321}, {16601, 21856}, {16706, 29650}, {17469, 29681}, {17594, 24715}, {17600, 19785}, {17721, 29820}, {17723, 24789}, {17778, 32853}, {17782, 20095}, {18139, 30942}, {19292, 28268}, {19684, 29631}, {19786, 29644}, {21026, 29679}, {21241, 32773}, {21820, 24064}, {24160, 30142}, {24552, 29632}, {26061, 29873}, {26109, 29837}, {27267, 27518}, {28605, 32848}, {29642, 32942}, {29670, 32850}, {29830, 32943}, {29832, 32923}, {29839, 32941}, {29846, 30834}, {29857, 32780}, {29862, 32777}, {30811, 32783}, {30970, 32782}, {31034, 32864}, {31993, 32778}


X(33112) = X(1)X(149)∩X(2)X(31)

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

X(33112) lies on these lines: {1, 149}, {2, 31}, {7, 4392}, {8, 31025}, {10, 32843}, {37, 5057}, {38, 17483}, {57, 29680}, {63, 29664}, {75, 32842}, {81, 2886}, {100, 5718}, {124, 28836}, {142, 7292}, {145, 21283}, {226, 3920}, {244, 17722}, {497, 29814}, {601, 6888}, {612, 31053}, {614, 27186}, {756, 26792}, {846, 29682}, {870, 30632}, {894, 3006}, {902, 29640}, {908, 5297}, {940, 11680}, {962, 5713}, {982, 26842}, {984, 17484}, {1064, 6839}, {1086, 17726}, {1203, 3841}, {1621, 17056}, {1699, 5287}, {1738, 17012}, {1836, 28606}, {2177, 20095}, {2476, 5711}, {2550, 3240}, {2895, 31330}, {2979, 10473}, {3073, 6884}, {3216, 26060}, {3218, 29639}, {3315, 25557}, {3434, 5712}, {3550, 29678}, {3616, 17676}, {3664, 26015}, {3666, 20292}, {3741, 32863}, {3745, 3838}, {3914, 17011}, {3923, 29643}, {3925, 32911}, {3936, 5263}, {3944, 5311}, {3980, 29849}, {4000, 17025}, {4011, 29854}, {4197, 16466}, {4210, 21321}, {4300, 6895}, {4340, 10527}, {4344, 26228}, {4360, 4442}, {4414, 29657}, {4418, 29671}, {4675, 17721}, {4682, 17605}, {4709, 14459}, {4850, 5880}, {4865, 32771}, {4892, 32775}, {4956, 29574}, {5080, 30116}, {5211, 26806}, {5248, 24936}, {5249, 7191}, {5262, 12609}, {5268, 27131}, {5269, 29665}, {5294, 29873}, {5717, 17016}, {5905, 7226}, {6542, 31063}, {6625, 21220}, {6646, 17491}, {6685, 32948}, {7174, 31164}, {8025, 29837}, {8616, 29661}, {9330, 31018}, {9335, 9776}, {9345, 24217}, {9347, 10129}, {9782, 24046}, {10448, 15680}, {10459, 20060}, {10707, 17392}, {11200, 29624}, {11269, 14996}, {16830, 26580}, {16948, 24953}, {17017, 17889}, {17019, 24210}, {17135, 17778}, {17138, 26110}, {17140, 29840}, {17300, 29824}, {17379, 29829}, {17596, 29688}, {17718, 26738}, {17763, 25385}, {17777, 31035}, {18134, 24552}, {18139, 32942}, {19684, 32773}, {19858, 26064}, {20086, 32853}, {21020, 32861}, {21241, 29631}, {21242, 32919}, {21282, 29822}, {23812, 29655}, {24239, 27003}, {24325, 32844}, {24349, 29832}, {25525, 29681}, {25527, 29648}, {26223, 29641}, {29644, 32776}, {29653, 32930}, {29690, 32913}

X(33112) = anticomplement of X(32917)


X(33113) = X(1)X(6693)∩X(2)X(37)

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

X(33113) lies on these lines: {1, 6693}, {2, 37}, {8, 5791}, {9, 5741}, {10, 10448}, {21, 5016}, {31, 29671}, {35, 5300}, {38, 3771}, {42, 4438}, {55, 3006}, {57, 18139}, {63, 3936}, {71, 29981}, {100, 4224}, {171, 29643}, {190, 31053}, {226, 3977}, {238, 29849}, {244, 29642}, {304, 27187}, {306, 1150}, {319, 5361}, {354, 29830}, {498, 3701}, {614, 24542}, {740, 24892}, {750, 29653}, {846, 25760}, {896, 32946}, {902, 4865}, {982, 29632}, {984, 29846}, {1054, 25961}, {1214, 28774}, {1215, 29678}, {1465, 28776}, {1468, 3178}, {1621, 3705}, {1836, 4427}, {1930, 25581}, {1962, 29635}, {2177, 29673}, {2269, 30052}, {2476, 7283}, {2886, 3712}, {2887, 4414}, {3011, 3891}, {3085, 4696}, {3120, 32934}, {3161, 5748}, {3218, 18134}, {3219, 4417}, {3434, 30741}, {3685, 11680}, {3687, 5278}, {3695, 7483}, {3702, 26363}, {3703, 6690}, {3704, 24953}, {3710, 13411}, {3729, 31266}, {3744, 29832}, {3821, 31237}, {3868, 25650}, {3873, 29839}, {3909, 26892}, {3932, 5432}, {3944, 32936}, {3969, 11679}, {4001, 4035}, {4062, 32853}, {4189, 7270}, {4362, 32848}, {4392, 29866}, {4422, 26688}, {4429, 29873}, {4442, 17064}, {4473, 26791}, {4640, 6327}, {4641, 31034}, {4643, 31037}, {4650, 32949}, {4692, 10197}, {4884, 17724}, {4921, 17363}, {4968, 10198}, {4972, 17594}, {5218, 10327}, {5233, 27065}, {5248, 30171}, {5263, 29664}, {5273, 5739}, {5695, 31245}, {5718, 26223}, {5744, 26872}, {5794, 27690}, {5905, 30828}, {5955, 19874}, {6679, 17017}, {6682, 24943}, {6685, 26061}, {7081, 32862}, {7262, 32843}, {8616, 32844}, {9371, 27521}, {10371, 27558}, {11375, 25253}, {14829, 32858}, {15523, 32916}, {17020, 17352}, {17063, 29851}, {17122, 29854}, {17164, 28628}, {17165, 17718}, {17184, 30811}, {17234, 27003}, {17248, 31247}, {17266, 27002}, {17336, 26792}, {17355, 31281}, {17591, 29858}, {17592, 29631}, {17596, 25957}, {17598, 29638}, {17599, 26230}, {17600, 29636}, {17601, 32948}, {17717, 32930}, {17719, 32925}, {17751, 26066}, {17778, 26070}, {17889, 32845}, {18141, 24593}, {19334, 19857}, {20182, 29833}, {20896, 25080}, {22370, 30034}, {24325, 29661}, {24552, 29639}, {24614, 30173}, {24723, 25958}, {25496, 29688}, {25734, 28609}, {26128, 29865}, {27068, 27523}, {27184, 30831}, {29640, 32771}, {29657, 32772}, {29658, 32928}, {29665, 32926}, {29674, 32918}, {29675, 32923}, {29676, 32943}, {29680, 32942}, {29681, 32922}, {29690, 32941}, {29872, 32773}, {30566, 30568}, {31019, 32939}, {32778, 32917}, {32855, 32914}

X(33113) = anticomplement of X(28655)


X(33114) = X(1)X(24542)∩X(2)X(210)

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

X(33114) lies on these lines: {1, 24542}, {2, 210}, {6, 3006}, {8, 5266}, {10, 750}, {31, 5014}, {37, 29829}, {38, 25453}, {42, 4438}, {58, 5300}, {63, 4972}, {81, 29641}, {149, 4676}, {320, 25959}, {333, 29667}, {345, 3896}, {597, 17726}, {748, 29655}, {756, 29635}, {896, 4660}, {982, 29850}, {984, 29631}, {1001, 29835}, {1215, 24892}, {1386, 29832}, {1707, 4450}, {1714, 4968}, {1757, 25760}, {1999, 32862}, {2308, 4865}, {2886, 26223}, {2887, 17771}, {3011, 31229}, {3120, 32935}, {3187, 3703}, {3218, 4429}, {3219, 32773}, {3240, 32851}, {3242, 26230}, {3306, 24988}, {3338, 17674}, {3416, 16704}, {3434, 26065}, {3679, 5429}, {3701, 5292}, {3705, 32911}, {3729, 4442}, {3741, 26061}, {3751, 3936}, {3755, 3977}, {3759, 32842}, {3772, 17165}, {3791, 32854}, {3816, 26688}, {3826, 26627}, {3874, 19846}, {3914, 28526}, {3938, 6679}, {3944, 32938}, {3952, 17720}, {3966, 19742}, {3969, 17156}, {3999, 17356}, {4038, 29854}, {4085, 4414}, {4195, 5178}, {4358, 11269}, {4385, 24883}, {4392, 16706}, {4417, 29872}, {4418, 32865}, {4514, 17127}, {4641, 6327}, {4649, 29643}, {4650, 32948}, {4663, 31034}, {4696, 5230}, {4722, 32946}, {4847, 5294}, {5016, 5247}, {5057, 17350}, {5173, 28776}, {5192, 10916}, {5220, 26580}, {5284, 29843}, {5791, 26115}, {6682, 29663}, {7226, 19786}, {7262, 32947}, {7292, 17352}, {9708, 16344}, {10391, 27521}, {10394, 27542}, {11680, 27064}, {14829, 29679}, {15523, 32853}, {16468, 32844}, {16496, 29855}, {17126, 32850}, {17135, 32777}, {17140, 24789}, {17162, 17299}, {17279, 29824}, {17353, 26015}, {17598, 29852}, {17770, 31134}, {17889, 32940}, {18134, 29873}, {21241, 24725}, {24391, 25904}, {25496, 29690}, {25957, 32913}, {26128, 29867}, {29658, 32927}, {29659, 32917}, {29674, 32919}, {29676, 32944}, {29856, 32775}, {31330, 32780}, {32778, 32864}


X(33115) = X(1)X(24542)∩X(2)X(38)

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

X(33115) lies on these lines: {1, 24542}, {2, 38}, {6, 29643}, {8, 3722}, {9, 124}, {10, 21}, {11, 4422}, {31, 29641}, {37, 29631}, {44, 32843}, {57, 25961}, {63, 25957}, {81, 29653}, {88, 1224}, {120, 26933}, {121, 1054}, {149, 4432}, {190, 3120}, {210, 29846}, {226, 32938}, {238, 3006}, {239, 32848}, {306, 32864}, {312, 24892}, {333, 15523}, {334, 799}, {344, 11269}, {345, 32860}, {354, 29851}, {518, 29632}, {659, 25634}, {672, 30969}, {678, 3617}, {740, 32849}, {748, 3705}, {846, 4972}, {896, 4645}, {899, 32851}, {902, 32850}, {940, 29854}, {958, 20999}, {966, 2246}, {993, 4218}, {1089, 24880}, {1125, 3315}, {1150, 29674}, {1155, 3823}, {1220, 21674}, {1268, 4632}, {1376, 16064}, {1621, 29673}, {1635, 25633}, {1647, 25531}, {1724, 30172}, {1738, 3977}, {1757, 3936}, {2254, 26031}, {2310, 27542}, {2345, 14439}, {2611, 21254}, {2886, 32930}, {2887, 3219}, {3011, 3717}, {3035, 9458}, {3218, 3836}, {3242, 29638}, {3305, 25960}, {3666, 29850}, {3678, 25645}, {3681, 3771}, {3683, 32947}, {3695, 27368}, {3703, 32914}, {3772, 32925}, {3846, 27065}, {3873, 29642}, {3912, 32919}, {3914, 32936}, {3920, 6679}, {3925, 4418}, {3932, 17763}, {3985, 17737}, {3989, 19786}, {3992, 17734}, {4003, 17356}, {4011, 11680}, {4138, 17781}, {4201, 9780}, {4357, 30768}, {4362, 32862}, {4383, 29849}, {4414, 4429}, {4427, 24715}, {4430, 29870}, {4453, 25605}, {4473, 17777}, {4553, 18191}, {4640, 32948}, {4641, 32949}, {4655, 25959}, {4661, 29866}, {4703, 25958}, {4722, 17778}, {4756, 21093}, {4766, 30763}, {4847, 32943}, {4860, 17265}, {4865, 17127}, {4892, 17484}, {4974, 32842}, {4981, 32783}, {5014, 8616}, {5057, 21241}, {5220, 30811}, {5249, 32940}, {5273, 26034}, {5278, 8300}, {5284, 29655}, {5294, 32772}, {5745, 32918}, {6211, 8229}, {6327, 7262}, {6667, 16594}, {7174, 29855}, {7292, 31289}, {8299, 31330}, {8301, 19732}, {9345, 17244}, {11814, 31272}, {14829, 29687}, {16484, 29835}, {16704, 32846}, {17125, 17338}, {17155, 24789}, {17263, 30950}, {17279, 30942}, {17289, 30970}, {17303, 20331}, {17350, 24725}, {17353, 29639}, {17597, 29853}, {17599, 29852}, {17735, 20483}, {17776, 32915}, {17888, 20881}, {17889, 32933}, {18134, 32912}, {18139, 32913}, {18201, 31252}, {18743, 29662}, {19742, 32861}, {19877, 30577}, {21047, 21944}, {24165, 26724}, {24193, 25534}, {24318, 25344}, {24358, 24712}, {24736, 30947}, {24746, 27102}, {25006, 32945}, {25453, 28606}, {25496, 29664}, {25591, 26363}, {25611, 26042}, {26685, 30741}, {26723, 32924}, {27184, 31237}, {27628, 31339}, {29658, 31229}, {29671, 32911}, {29679, 31073}, {29681, 32920}, {29690, 32942}, {31019, 32935}, {32853, 32858}, {32865, 32929}

X(33115) = complement of X(33148)


X(33116) = X(1)X(4438)∩X(2)X(37)

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

X(33116) lies on these lines: {1, 4438}, {2, 37}, {9, 4417}, {10, 1043}, {21, 7270}, {28, 19842}, {31, 29643}, {35, 11102}, {38, 29632}, {55, 25494}, {57, 17234}, {63, 320}, {69, 5273}, {72, 25650}, {81, 1332}, {86, 2983}, {100, 4228}, {171, 29653}, {190, 226}, {209, 5208}, {222, 28965}, {238, 29671}, {244, 29851}, {306, 319}, {329, 17336}, {341, 3085}, {442, 7283}, {497, 30741}, {518, 29839}, {651, 28979}, {748, 29849}, {750, 29854}, {756, 29846}, {846, 2887}, {894, 17056}, {896, 32949}, {940, 17317}, {968, 29857}, {982, 29642}, {984, 3771}, {1001, 3705}, {1150, 32858}, {1211, 17256}, {1214, 18721}, {1215, 29640}, {1231, 17095}, {1265, 5703}, {1279, 29840}, {1330, 31445}, {1376, 19310}, {1621, 3006}, {1760, 10319}, {1962, 29631}, {1999, 17315}, {2003, 4585}, {2064, 25080}, {2275, 24663}, {2321, 31205}, {2329, 3912}, {2886, 3685}, {2899, 10588}, {2901, 24880}, {2999, 17352}, {3011, 32926}, {3101, 16568}, {3120, 32936}, {3159, 24160}, {3161, 5226}, {3178, 5247}, {3218, 18139}, {3219, 3936}, {3305, 5233}, {3452, 25101}, {3584, 3992}, {3616, 4906}, {3661, 5737}, {3683, 4388}, {3687, 17277}, {3695, 6675}, {3703, 3757}, {3704, 16824}, {3712, 3925}, {3717, 13405}, {3729, 25525}, {3746, 5100}, {3750, 29673}, {3758, 5712}, {3836, 17596}, {3873, 29830}, {3891, 29681}, {3928, 17298}, {3929, 17347}, {3932, 6690}, {3954, 25665}, {3971, 17719}, {3977, 5249}, {3989, 29865}, {3996, 25006}, {4011, 17717}, {4035, 4416}, {4062, 32864}, {4136, 4384}, {4357, 20106}, {4385, 10198}, {4387, 31245}, {4389, 25527}, {4392, 29870}, {4398, 23681}, {4414, 25957}, {4415, 17261}, {4419, 26132}, {4427, 20292}, {4429, 17594}, {4544, 17294}, {4640, 4645}, {4641, 17778}, {4670, 26109}, {4673, 19843}, {4676, 26098}, {4737, 10056}, {4865, 8616}, {4886, 5278}, {4972, 29873}, {5015, 5248}, {5016, 16865}, {5086, 27690}, {5174, 13739}, {5205, 5432}, {5219, 30568}, {5259, 30171}, {5271, 5564}, {5295, 25446}, {5316, 31333}, {5435, 6604}, {5718, 27064}, {5741, 27065}, {5743, 17260}, {5744, 17241}, {5791, 10449}, {6335, 20566}, {6350, 18750}, {6376, 18751}, {6682, 29637}, {6703, 16826}, {7191, 24542}, {7226, 29866}, {7262, 32946}, {7523, 19841}, {7535, 19845}, {8056, 32019}, {9369, 15888}, {10030, 18045}, {11375, 19582}, {11679, 17233}, {14547, 23691}, {14552, 17360}, {14555, 17335}, {15523, 32917}, {15569, 29837}, {16086, 24929}, {16484, 29655}, {16777, 29841}, {16825, 32855}, {17080, 25082}, {17240, 34255}, {17242, 31187}, {17258, 27184}, {17286, 18229}, {17592, 25453}, {17593, 24169}, {17598, 29672}, {17600, 29654}, {17605, 17777}, {17718, 32937}, {17728, 30947}, {17889, 32934}, {18739, 28742}, {19744, 29576}, {19839, 21530}, {20223, 30852}, {20367, 29474}, {20691, 27321}, {21026, 32948}, {21299, 25613}, {21361, 29531}, {23661, 27529}, {24177, 27191}, {24552, 29664}, {24892, 32915}, {25496, 29657}, {25568, 27549}, {25728, 28609}, {25734, 31164}, {25959, 32950}, {26128, 29858}, {26227, 32862}, {26580, 30831}, {26590, 30763}, {28740, 31225}, {29639, 32942}, {29661, 32771}, {29674, 32916}, {29675, 32920}, {29678, 32931}, {29682, 32772}, {29687, 32918}, {29688, 32944}, {29689, 32923}, {29690, 32943}, {30834, 31053}, {31019, 32933}, {31237, 32776}, {32848, 32914}


X(33117) = X(1)X(2)∩X(6)X(20483)

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

X(33117) lies on these lines: {1, 2}, {6, 20483}, {9, 32947}, {31, 32850}, {38, 4429}, {63, 32948}, {100, 4438}, {149, 4011}, {210, 25760}, {238, 5014}, {321, 32865}, {341, 21935}, {354, 3823}, {518, 25957}, {740, 32862}, {748, 4514}, {756, 32773}, {867, 8256}, {958, 16064}, {984, 4972}, {1376, 20999}, {1738, 17155}, {1757, 6327}, {1762, 2550}, {1836, 32938}, {1851, 1861}, {2886, 32931}, {2887, 3681}, {3058, 4422}, {3120, 32937}, {3219, 4660}, {3416, 32864}, {3434, 32930}, {3703, 32860}, {3717, 3914}, {3740, 25960}, {3751, 32949}, {3772, 30615}, {3790, 4365}, {3821, 7226}, {3836, 3873}, {3878, 26911}, {3915, 5100}, {3925, 32771}, {3932, 32915}, {3944, 3952}, {3976, 17674}, {4085, 28606}, {4090, 21241}, {4119, 26242}, {4126, 4415}, {4147, 6546}, {4383, 32844}, {4392, 24169}, {4417, 21805}, {4450, 7262}, {4645, 32912}, {4661, 25959}, {4683, 5220}, {4863, 17279}, {4865, 32911}, {4914, 17348}, {4981, 32784}, {5247, 5300}, {5263, 26061}, {5880, 32940}, {6545, 17072}, {9708, 20834}, {11238, 24709}, {17063, 24988}, {17127, 17766}, {17165, 17889}, {17715, 24542}, {18134, 21026}, {19742, 28599}, {20292, 32935}, {20962, 25306}, {24390, 25591}, {24715, 32933}, {24789, 32923}, {27918, 31337}, {28595, 32782}, {32777, 32945}

X(33117) = anticomplement of X(29672)


X(33118) = X(2)X(210)∩X(6)X(29641)

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

X(33118) lies on these lines: {2, 210}, {6, 29641}, {8, 1104}, {9, 32773}, {10, 58}, {31, 32850}, {38, 16706}, {43, 4438}, {44, 4388}, {63, 4429}, {100, 5324}, {190, 3914}, {238, 4514}, {239, 3703}, {319, 15523}, {320, 25957}, {341, 5230}, {497, 26685}, {595, 5100}, {614, 17352}, {726, 19796}, {744, 21020}, {756, 29631}, {846, 4085}, {894, 3925}, {896, 32948}, {984, 19786}, {1150, 29679}, {1714, 4385}, {1724, 5015}, {1738, 32939}, {1757, 2887}, {1836, 17350}, {1864, 27542}, {1999, 3932}, {2299, 5174}, {2550, 26065}, {2886, 27064}, {3006, 16791}, {3120, 32938}, {3187, 32862}, {3219, 4972}, {3434, 4676}, {3661, 4042}, {3701, 24883}, {3705, 4383}, {3706, 17280}, {3717, 19815}, {3720, 17263}, {3751, 18134}, {3769, 10327}, {3772, 32937}, {3791, 32847}, {3836, 32913}, {3846, 29861}, {3896, 32849}, {3923, 32865}, {3936, 29873}, {3957, 24542}, {3961, 6679}, {3966, 17349}, {3989, 17320}, {4090, 17719}, {4104, 30832}, {4126, 17602}, {4387, 17339}, {4417, 29857}, {4423, 17338}, {4641, 4645}, {4649, 29653}, {4651, 32779}, {4660, 7262}, {4663, 17778}, {4722, 21026}, {4847, 17353}, {4854, 17261}, {4865, 16468}, {4884, 17366}, {4886, 32778}, {4974, 32866}, {5014, 17127}, {5087, 26791}, {5178, 11319}, {5208, 22277}, {5220, 27184}, {5223, 25527}, {5263, 5294}, {5278, 29667}, {5284, 29835}, {5302, 26117}, {5435, 26047}, {5741, 29872}, {5904, 19846}, {7226, 32774}, {7321, 32940}, {7672, 28776}, {9330, 29864}, {10394, 27521}, {10453, 17279}, {10916, 13741}, {11019, 25531}, {11269, 18743}, {12329, 25494}, {17123, 29655}, {17140, 26724}, {17156, 17233}, {17258, 32776}, {17264, 32915}, {17289, 26061}, {17317, 29854}, {17322, 29647}, {17351, 21949}, {17356, 21342}, {17367, 17599}, {17720, 27538}, {17889, 32935}, {19742, 31079}, {20142, 30179}, {20919, 23690}, {21805, 29846}, {24349, 24789}, {24757, 29840}, {24892, 32931}, {24914, 26029}, {24988, 27003}, {25959, 32859}, {26723, 32922}, {28653, 30966}, {29665, 31229}, {29674, 32853}, {29687, 32919}, {29690, 32944}, {29820, 31289}, {29867, 32775}


X(33119) = X(1)X(6693)∩X(2)X(38)

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

X(33119) lies on these lines: {1, 6693}, {2, 38}, {6, 29849}, {9, 25960}, {10, 36}, {11, 32930}, {31, 3705}, {37, 29845}, {42, 32851}, {57, 25957}, {58, 30171}, {63, 1756}, {75, 24892}, {81, 29671}, {86, 29682}, {100, 29673}, {171, 3006}, {226, 32940}, {306, 32919}, {312, 29662}, {333, 2206}, {345, 11269}, {354, 29632}, {499, 25591}, {518, 29846}, {750, 29641}, {867, 2886}, {896, 4388}, {902, 4514}, {908, 32938}, {940, 29643}, {1150, 32778}, {1155, 32948}, {1376, 20999}, {1621, 29655}, {1698, 17674}, {1757, 5741}, {1962, 29837}, {1999, 32848}, {2352, 31330}, {2887, 3218}, {3011, 32923}, {3120, 32939}, {3187, 32855}, {3219, 3846}, {3242, 29848}, {3306, 25961}, {3315, 29672}, {3454, 6763}, {3550, 5014}, {3662, 31237}, {3666, 29631}, {3677, 29855}, {3687, 32864}, {3703, 17763}, {3741, 32779}, {3742, 29851}, {3750, 29835}, {3752, 29850}, {3769, 32854}, {3771, 3873}, {3772, 17155}, {3791, 32842}, {3836, 27003}, {3874, 25645}, {3891, 29658}, {3914, 32845}, {3923, 11680}, {3936, 32913}, {3944, 32933}, {3977, 24210}, {4011, 24709}, {4224, 5285}, {4257, 4680}, {4363, 25366}, {4376, 24712}, {4414, 32773}, {4417, 32912}, {4640, 32947}, {4641, 32843}, {4650, 6327}, {4655, 25958}, {4692, 17734}, {4847, 32945}, {4850, 25453}, {4865, 17126}, {4884, 17602}, {4892, 17483}, {4972, 17596}, {5263, 29690}, {5294, 24239}, {5484, 9780}, {5744, 26034}, {5791, 28258}, {6679, 7191}, {9340, 20101}, {13741, 28096}, {13742, 28074}, {14829, 15523}, {16704, 32861}, {16706, 29867}, {17279, 17728}, {17289, 31241}, {17351, 17605}, {17358, 24736}, {17449, 29865}, {17469, 29840}, {17591, 29856}, {17592, 29829}, {17597, 29638}, {17598, 26230}, {17599, 29636}, {17600, 29833}, {17716, 29832}, {17717, 26223}, {17720, 32925}, {17740, 32860}, {17754, 30752}, {18139, 29862}, {19335, 26446}, {19684, 29657}, {19786, 29863}, {19808, 30970}, {19846, 24046}, {20292, 21241}, {21015, 30778}, {21125, 21212}, {23958, 25959}, {24542, 29820}, {24552, 29676}, {24627, 32781}, {24914, 28386}, {25496, 29680}, {26015, 32943}, {26066, 28349}, {28606, 29635}, {29639, 32772}, {29649, 32862}, {29665, 32920}, {29667, 32916}, {29683, 32926}, {30751, 30969}, {30942, 32777}, {31053, 32935}

X(33119) = complement of X(33153)


X(33120) = X(1)X(2)∩X(6)X(4144)

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

X(33120) lies on these lines: {1, 2}, {6, 4144}, {11, 32931}, {31, 4514}, {38, 1227}, {57, 32948}, {58, 4894}, {63, 32947}, {80, 996}, {81, 4865}, {149, 3923}, {171, 5014}, {210, 25960}, {244, 4429}, {320, 31134}, {354, 3834}, {496, 25591}, {497, 16561}, {518, 25760}, {750, 32850}, {982, 4972}, {1215, 11680}, {1266, 3914}, {1376, 23858}, {1468, 5015}, {1621, 4438}, {1836, 32940}, {2177, 32851}, {2886, 32771}, {2887, 3873}, {3120, 24349}, {3218, 4660}, {3242, 32775}, {3416, 16797}, {3434, 4418}, {3662, 17449}, {3681, 3846}, {3703, 3943}, {3742, 25961}, {3751, 32843}, {3772, 32923}, {3816, 16594}, {3821, 4392}, {3896, 32855}, {3944, 4080}, {3966, 32864}, {3976, 4202}, {4085, 4850}, {4090, 27131}, {4147, 6544}, {4358, 24217}, {4359, 32865}, {4363, 24712}, {4388, 20072}, {4425, 7226}, {4430, 25958}, {4450, 4650}, {4699, 21027}, {4854, 4884}, {4863, 32945}, {5057, 32935}, {5233, 21805}, {6327, 32913}, {6545, 24720}, {9053, 17602}, {9318, 16799}, {14475, 17072}, {16796, 17721}, {17063, 24183}, {17126, 17766}, {17140, 17889}, {17145, 31017}, {17234, 17450}, {17598, 32774}, {17720, 32927}, {17774, 31264}, {21241, 31019}, {24210, 32925}, {24241, 31130}, {24477, 26034}, {24552, 32780}, {24629, 26582}, {24703, 32938}, {26061, 32942}, {32777, 32943}, {32779, 32941}


X(33121) = X(1)X(4438)∩X(2)X(210)

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

X(33121) lies on these lines: {1, 4438}, {2, 210}, {6, 3705}, {8, 3769}, {10, 14829}, {11, 27064}, {31, 4514}, {37, 29837}, {38, 19786}, {42, 32851}, {57, 4429}, {58, 5015}, {63, 24723}, {81, 3006}, {171, 29673}, {190, 24210}, {238, 29655}, {244, 29850}, {312, 11269}, {319, 32778}, {320, 2887}, {333, 6043}, {497, 4676}, {674, 3794}, {756, 29845}, {894, 2886}, {896, 32947}, {940, 29641}, {982, 16706}, {984, 29635}, {1001, 29843}, {1150, 29667}, {1220, 6734}, {1386, 29840}, {1468, 7270}, {1621, 29835}, {1757, 3846}, {1999, 3703}, {2308, 32844}, {2318, 24550}, {3120, 32940}, {3218, 4972}, {3242, 29634}, {3618, 24757}, {3741, 17289}, {3751, 4417}, {3758, 26098}, {3772, 24349}, {3779, 24678}, {3791, 32866}, {3914, 32939}, {3936, 29872}, {3944, 32935}, {3980, 32865}, {4011, 24217}, {4038, 17317}, {4085, 17596}, {4357, 10520}, {4385, 5292}, {4388, 4641}, {4392, 29868}, {4425, 17258}, {4649, 29671}, {4650, 4660}, {4684, 20106}, {4722, 32843}, {4847, 5263}, {4878, 27391}, {4886, 32864}, {4968, 24883}, {5014, 17126}, {5100, 5264}, {5178, 11115}, {5255, 8258}, {5272, 17352}, {5294, 26015}, {5712, 30741}, {6682, 29633}, {6703, 16830}, {7226, 29864}, {7247, 24995}, {7321, 17889}, {7672, 28774}, {8167, 17338}, {9345, 29854}, {10391, 27542}, {10453, 32777}, {10916, 13740}, {10980, 17282}, {11019, 17353}, {11680, 26223}, {15523, 32919}, {17135, 32779}, {17155, 19796}, {17263, 24736}, {17350, 24703}, {17449, 29867}, {17450, 29851}, {17499, 20544}, {17598, 29654}, {17720, 32937}, {18134, 29857}, {18139, 29873}, {18201, 24169}, {18398, 19846}, {19684, 29664}, {19797, 21020}, {19808, 31330}, {24542, 29817}, {24892, 32771}, {25496, 29676}, {25760, 32912}, {25958, 32859}, {26061, 30942}, {26105, 26685}, {26128, 29856}, {28606, 29829}, {29658, 32920}, {29659, 32916}, {29662, 32931}, {29681, 31229}, {29683, 32927}, {29685, 32917}, {29690, 32772}, {29863, 32775}

X(33121) = {X(2),X(4430)}-harmonic conjugate of X(33122)


X(33122) = X(1)X(3454)∩X(2)X(210)

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

X(33122) lies on these lines: {1, 3454}, {2, 210}, {6, 26230}, {9, 24542}, {31, 17770}, {37, 29830}, {38, 3771}, {42, 26128}, {55, 17184}, {69, 26228}, {81, 29634}, {100, 3662}, {141, 17724}, {171, 29848}, {226, 24552}, {238, 29638}, {306, 3891}, {320, 17126}, {333, 29681}, {551, 31179}, {612, 18139}, {614, 5741}, {740, 27476}, {748, 29672}, {756, 29642}, {902, 4655}, {964, 13407}, {982, 29846}, {984, 29632}, {1001, 26580}, {1125, 17125}, {1150, 3011}, {1215, 24943}, {1386, 29831}, {1621, 27184}, {1757, 29860}, {2177, 3821}, {2887, 3938}, {3006, 3242}, {3056, 3909}, {3120, 32941}, {3187, 17061}, {3240, 16706}, {3416, 20045}, {3434, 26132}, {3620, 26245}, {3699, 17283}, {3705, 30831}, {3722, 4660}, {3726, 26281}, {3744, 6327}, {3749, 4450}, {3750, 32776}, {3751, 29855}, {3757, 32782}, {3763, 26251}, {3769, 32863}, {3772, 17135}, {3782, 28530}, {3794, 23155}, {3811, 4202}, {3870, 4972}, {3886, 4442}, {3896, 19785}, {3920, 18134}, {3923, 32856}, {3935, 4429}, {3944, 32943}, {3952, 17279}, {3957, 32773}, {3961, 25957}, {3966, 31037}, {4038, 29847}, {4062, 32921}, {4310, 17740}, {4392, 32851}, {4417, 7191}, {4427, 17276}, {4438, 29865}, {4514, 25958}, {4649, 29636}, {4651, 24789}, {4657, 29822}, {4676, 17484}, {4683, 8616}, {4689, 17235}, {4756, 17339}, {4767, 29629}, {4966, 17602}, {5192, 21077}, {5233, 7292}, {5263, 31019}, {5297, 17234}, {6679, 32912}, {6682, 29678}, {7226, 29866}, {9330, 17263}, {9347, 17300}, {10404, 11115}, {14829, 29665}, {15523, 32920}, {16496, 29857}, {16887, 25581}, {17018, 19786}, {17123, 29853}, {17165, 32777}, {17282, 24988}, {17375, 24678}, {17469, 32946}, {17598, 29849}, {17625, 28774}, {17715, 32947}, {17716, 32949}, {17719, 30942}, {17720, 29824}, {17723, 29823}, {17725, 17763}, {17766, 31134}, {17778, 29838}, {17889, 32945}, {24349, 32779}, {24391, 25982}, {24955, 25687}, {25496, 29686}, {25557, 26627}, {25959, 32850}, {25960, 29820}, {25968, 26651}, {28606, 29839}, {29637, 32931}, {29639, 30834}, {29658, 32919}, {29660, 32944}, {29670, 32781}, {29673, 31237}, {29674, 32927}, {29675, 32917}, {29836, 32843}, {31053, 32942}, {32771, 32783}, {32778, 32923}, {32858, 32926}

X(33122) = {X(2),X(4430)}-harmonic conjugate of X(33121)


X(33123) = X(1)X(4202)∩X(2)X(38)

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

X(33123) lies on these lines: {1, 4202}, {2, 38}, {6, 29852}, {10, 26724}, {21, 36}, {31, 3662}, {37, 29851}, {42, 16706}, {55, 17290}, {57, 29855}, {75, 24943}, {81, 29654}, {86, 2206}, {100, 24169}, {141, 32914}, {142, 5285}, {171, 26230}, {210, 17356}, {226, 32944}, {238, 4683}, {306, 32924}, {312, 29677}, {320, 2308}, {321, 29637}, {334, 3112}, {350, 21415}, {354, 29631}, {518, 29850}, {612, 17282}, {614, 25527}, {748, 27184}, {750, 29634}, {846, 24542}, {896, 26840}, {940, 29636}, {968, 17304}, {1001, 16064}, {1086, 4418}, {1279, 32947}, {1376, 29848}, {1386, 32949}, {1621, 3821}, {1738, 32945}, {1848, 4211}, {1962, 17302}, {2352, 4657}, {2887, 7191}, {2895, 4974}, {3006, 17598}, {3011, 32918}, {3120, 32942}, {3218, 6679}, {3315, 29655}, {3337, 6693}, {3616, 4201}, {3663, 32936}, {3666, 29632}, {3677, 29857}, {3683, 17235}, {3705, 31237}, {3720, 19786}, {3742, 29845}, {3744, 29836}, {3745, 3834}, {3752, 29846}, {3757, 17291}, {3771, 4850}, {3772, 30942}, {3782, 32930}, {3791, 32863}, {3836, 3920}, {3846, 7292}, {3873, 25453}, {3891, 29674}, {3912, 32928}, {3914, 32943}, {3936, 29821}, {3938, 4429}, {3957, 4085}, {4000, 32860}, {4038, 29833}, {4046, 4395}, {4359, 32783}, {4365, 19796}, {4514, 29818}, {4645, 17469}, {4655, 17127}, {4672, 17483}, {4697, 26842}, {4865, 17024}, {5263, 29686}, {5272, 25960}, {5293, 17674}, {5294, 24231}, {5311, 17234}, {6533, 24931}, {6535, 17285}, {7859, 20703}, {8616, 32950}, {9345, 29841}, {9347, 29842}, {11375, 28385}, {11680, 29668}, {15523, 32922}, {16062, 28082}, {16065, 25507}, {16468, 32859}, {16787, 26085}, {16825, 32782}, {17017, 18134}, {17031, 30965}, {17061, 17763}, {17123, 26580}, {17150, 32846}, {17155, 32777}, {17278, 26037}, {17279, 32925}, {17283, 29687}, {17353, 32938}, {17370, 29663}, {17383, 24653}, {17449, 29867}, {17450, 29837}, {17591, 29858}, {17592, 29830}, {17596, 29860}, {17599, 29643}, {17716, 29831}, {17720, 30957}, {17889, 24552}, {18064, 30631}, {18398, 20083}, {19684, 29646}, {19785, 32915}, {19836, 24159}, {19864, 24160}, {24165, 32779}, {24712, 25345}, {24789, 31330}, {25378, 26105}, {25496, 29666}, {25525, 29826}, {26723, 32864}, {27003, 29874}, {27064, 32856}, {27065, 31289}, {27186, 29648}, {28606, 29642}, {29679, 32920}, {29681, 32916}, {29849, 30811}, {29865, 32851}, {31017, 32861}, {32858, 32921}


X(33124) = X(1)X(977)∩X(2)X(210)

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

X(33124) lies on these lines: {1, 977}, {2, 210}, {8, 24789}, {31, 320}, {38, 29632}, {42, 16706}, {55, 3662}, {81, 16791}, {141, 3757}, {171, 29656}, {200, 17282}, {226, 32942}, {238, 29672}, {244, 29846}, {306, 32922}, {319, 32914}, {345, 4310}, {350, 18138}, {497, 26132}, {612, 17234}, {614, 4417}, {740, 19796}, {744, 1962}, {748, 29853}, {750, 29848}, {756, 17263}, {940, 29634}, {968, 4389}, {982, 3771}, {984, 29642}, {1001, 27184}, {1043, 23536}, {1086, 32932}, {1104, 3616}, {1125, 5247}, {1150, 29681}, {1211, 16823}, {1215, 29637}, {1220, 21620}, {1279, 4388}, {1386, 17778}, {1621, 17184}, {1738, 3996}, {1909, 18052}, {1943, 15253}, {1999, 4966}, {3011, 14829}, {3035, 27002}, {3052, 7232}, {3120, 32943}, {3219, 24542}, {3242, 29641}, {3315, 30831}, {3452, 25531}, {3666, 29839}, {3683, 6646}, {3685, 3782}, {3705, 17597}, {3715, 17338}, {3720, 32775}, {3722, 32948}, {3744, 4645}, {3745, 17300}, {3750, 3821}, {3769, 26228}, {3772, 10453}, {3836, 3961}, {3840, 17719}, {3846, 29820}, {3870, 4429}, {3886, 23681}, {3891, 32858}, {3912, 32926}, {3920, 18139}, {3936, 7191}, {3938, 25957}, {3953, 25645}, {3957, 4972}, {3974, 29579}, {3979, 4085}, {4038, 29645}, {4046, 17117}, {4062, 32924}, {4195, 10404}, {4357, 14828}, {4392, 29866}, {4418, 7321}, {4420, 17674}, {4425, 16484}, {4438, 29858}, {4512, 17274}, {4640, 26840}, {4649, 29654}, {4651, 26724}, {4655, 8616}, {4660, 17715}, {4676, 5905}, {4703, 15485}, {4849, 17356}, {4883, 29837}, {4886, 16825}, {4906, 5211}, {5014, 25959}, {5233, 5272}, {5249, 5263}, {5269, 17298}, {5284, 26580}, {5311, 17317}, {5328, 26112}, {5741, 7292}, {6057, 17268}, {6679, 29860}, {6682, 29640}, {6690, 24627}, {7081, 17724}, {7226, 29870}, {7247, 24549}, {9345, 29847}, {10371, 19851}, {13407, 13740}, {13741, 21077}, {14555, 16020}, {15523, 32923}, {17018, 32774}, {17127, 32859}, {17140, 32779}, {17164, 26729}, {17227, 26034}, {17264, 32925}, {17279, 32937}, {17289, 24943}, {17315, 32928}, {17449, 29865}, {17450, 29845}, {17469, 29836}, {17598, 29671}, {17642, 27542}, {17717, 29668}, {17725, 29649}, {17889, 32941}, {19684, 29648}, {19808, 24325}, {21031, 25965}, {22769, 25494}, {24231, 32939}, {24349, 32777}, {24552, 31019}, {24657, 30945}, {25496, 29660}, {25681, 26093}, {26237, 30965}, {28606, 29830}, {29651, 32784}, {29674, 32920}, {29675, 32916}, {29677, 32931}, {29680, 30834}, {29686, 32772}, {29687, 32927}, {29689, 32917}, {29818, 32844}, {30614, 31091}, {32856, 32930}


X(33125) = X(1)X(32948)∩X(2)X(846)

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

X(33125) lies on these lines: {1, 32948}, {2, 846}, {10, 7226}, {31, 16706}, {37, 25961}, {38, 4429}, {42, 3662}, {43, 17184}, {55, 17290}, {57, 29631}, {63, 29850}, {75, 32781}, {100, 26128}, {141, 4046}, {149, 29668}, {165, 29855}, {171, 29636}, {192, 29687}, {210, 17235}, {238, 32950}, {244, 32773}, {612, 17304}, {614, 32947}, {726, 29679}, {748, 24723}, {750, 19786}, {756, 4389}, {894, 29663}, {899, 27184}, {968, 17282}, {982, 4972}, {986, 4202}, {1086, 32771}, {1125, 4188}, {1278, 6535}, {1376, 32775}, {1621, 29853}, {1738, 31330}, {1836, 32944}, {1962, 17234}, {2206, 21997}, {2308, 17367}, {2887, 4850}, {2999, 32843}, {3006, 17591}, {3210, 15523}, {3218, 25453}, {3306, 29845}, {3336, 20083}, {3416, 32924}, {3550, 26230}, {3589, 11246}, {3663, 4082}, {3666, 25957}, {3683, 17356}, {3685, 29677}, {3715, 17255}, {3735, 8041}, {3745, 17382}, {3749, 29836}, {3752, 25760}, {3772, 32918}, {3782, 32931}, {3836, 28606}, {3873, 4085}, {3914, 30942}, {3924, 4201}, {4000, 26034}, {4062, 4734}, {4357, 26037}, {4359, 32784}, {4383, 4683}, {4392, 29673}, {4645, 17017}, {4655, 32911}, {4660, 7191}, {4970, 32858}, {5014, 17598}, {5051, 24174}, {5192, 24851}, {5256, 32949}, {5269, 29834}, {5311, 17302}, {5880, 32772}, {6327, 29821}, {6685, 31019}, {6686, 27131}, {8013, 17238}, {12579, 16859}, {16062, 24443}, {16569, 26580}, {16610, 25960}, {17012, 32946}, {17024, 17766}, {17126, 29654}, {17140, 29659}, {17147, 29674}, {17276, 32938}, {17279, 32936}, {17291, 24943}, {17301, 32928}, {17495, 32778}, {17592, 18139}, {17594, 29632}, {17600, 31151}, {17763, 19785}, {20292, 25496}, {21241, 29680}, {23681, 29828}, {23958, 29868}, {24165, 29667}, {24210, 30957}, {24552, 24715}, {24627, 24892}, {24789, 32917}, {25059, 30984}, {25527, 29846}, {25959, 29671}, {25970, 26635}, {26061, 32939}, {26150, 29686}, {26223, 32857}, {26840, 32912}, {27003, 29635}, {29637, 32929}, {30631, 30964}, {31237, 32851}, {32777, 32845}


X(33126) = X(1)X(3846)∩X(2)X(210)

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

X(33126) lies on these lines: {1, 3846}, {2, 210}, {6, 29634}, {8, 3772}, {10, 26728}, {31, 29848}, {37, 29839}, {38, 29846}, {42, 19786}, {43, 16706}, {55, 24723}, {69, 3769}, {86, 6043}, {100, 17184}, {141, 7081}, {165, 17274}, {171, 320}, {200, 4429}, {226, 5263}, {238, 29656}, {239, 17061}, {306, 32926}, {319, 4362}, {329, 4676}, {333, 3011}, {612, 18134}, {614, 5233}, {748, 29638}, {756, 29632}, {846, 17258}, {902, 4683}, {908, 32942}, {976, 7270}, {984, 3771}, {1010, 13407}, {1043, 13161}, {1150, 29665}, {1155, 26840}, {1211, 3757}, {1215, 17289}, {1330, 5266}, {1376, 3662}, {1386, 29838}, {1621, 26580}, {1707, 17347}, {1757, 6679}, {1961, 17317}, {1999, 17602}, {2177, 32776}, {2550, 26132}, {2646, 5484}, {2887, 3961}, {3006, 30831}, {3120, 32945}, {3240, 32774}, {3242, 3705}, {3454, 5015}, {3550, 4655}, {3685, 4415}, {3687, 32922}, {3717, 20106}, {3722, 32947}, {3741, 17719}, {3744, 4388}, {3745, 17778}, {3750, 4425}, {3782, 32932}, {3794, 8679}, {3811, 16062}, {3816, 30867}, {3870, 32773}, {3914, 3996}, {3920, 3936}, {3935, 4972}, {3938, 4514}, {3944, 32941}, {3967, 17280}, {3971, 17264}, {3980, 7321}, {4028, 4360}, {4062, 32928}, {4104, 17277}, {4202, 4420}, {4357, 13405}, {4389, 17594}, {4418, 32856}, {4640, 6646}, {4649, 29645}, {4682, 17300}, {4703, 8616}, {4734, 17301}, {4886, 32914}, {5014, 25958}, {5268, 17234}, {5278, 29681}, {5297, 18139}, {5432, 24627}, {5564, 21085}, {5739, 26228}, {5741, 7191}, {5743, 16823}, {8580, 17282}, {9330, 29870}, {9711, 25965}, {10453, 17720}, {13740, 21077}, {15523, 32927}, {16830, 17056}, {17123, 29672}, {17125, 29853}, {17126, 32859}, {17165, 32779}, {17202, 18185}, {17256, 29675}, {17263, 29642}, {17278, 26038}, {17279, 27538}, {17320, 17592}, {17353, 21060}, {17469, 32843}, {17716, 32946}, {17717, 29652}, {18235, 21320}, {19796, 32860}, {19808, 32771}, {19832, 29647}, {20045, 31037}, {21805, 29850}, {24542, 27065}, {24552, 31053}, {24943, 32931}, {24954, 26093}, {26227, 32782}, {26230, 32911}, {29641, 30811}, {29658, 32853}, {29664, 30834}, {29670, 32784}, {29683, 32919}, {29686, 32944}, {32777, 32937}, {32778, 32920}


X(33127) = X(1)X(2476)∩X(2)X(38)

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

X(33127) lies on these lines: {1, 2476}, {2, 38}, {5, 28082}, {8, 24161}, {10, 31237}, {12, 3924}, {31, 226}, {37, 29661}, {42, 3772}, {55, 3120}, {63, 32856}, {75, 29846}, {81, 29658}, {86, 29847}, {100, 17889}, {142, 17124}, {149, 17715}, {171, 29665}, {238, 29681}, {312, 29632}, {321, 3771}, {354, 29662}, {379, 18266}, {442, 976}, {498, 24159}, {518, 24892}, {612, 25525}, {614, 5219}, {678, 17784}, {748, 908}, {750, 5249}, {894, 17003}, {896, 5905}, {899, 24789}, {902, 1836}, {940, 29683}, {946, 28027}, {1001, 29689}, {1086, 5432}, {1125, 5192}, {1149, 5886}, {1193, 11374}, {1201, 11375}, {1279, 17605}, {1376, 17783}, {1468, 13407}, {1621, 3944}, {1656, 28096}, {1707, 31164}, {1737, 26728}, {2177, 3914}, {2239, 30985}, {2292, 10198}, {2650, 3487}, {2886, 3938}, {2887, 26227}, {3006, 32920}, {3085, 4642}, {3090, 28074}, {3242, 29690}, {3434, 3722}, {3452, 17125}, {3475, 11269}, {3550, 20292}, {3662, 32918}, {3666, 29678}, {3689, 21949}, {3705, 32923}, {3720, 17720}, {3744, 3838}, {3757, 25760}, {3767, 21808}, {3769, 32949}, {3782, 4414}, {3791, 31034}, {3870, 17064}, {3891, 29671}, {3915, 12047}, {3920, 17725}, {3935, 32865}, {3936, 4362}, {3994, 17776}, {4011, 24542}, {4138, 31134}, {4197, 5293}, {4358, 29642}, {4417, 32914}, {4424, 10197}, {4650, 17483}, {4671, 29866}, {4722, 24597}, {4865, 20045}, {4892, 6327}, {4972, 29670}, {5014, 21241}, {5056, 28080}, {5057, 8616}, {5205, 25961}, {5263, 29848}, {5264, 11263}, {5272, 30852}, {5311, 17056}, {5718, 17017}, {5741, 16825}, {5748, 16020}, {5902, 17734}, {5904, 24880}, {6679, 26223}, {6685, 32774}, {6745, 9350}, {7081, 25957}, {7191, 17717}, {7262, 17484}, {7951, 30117}, {8227, 28011}, {10327, 21026}, {10448, 13161}, {10459, 28628}, {13411, 23536}, {15523, 30811}, {16569, 26724}, {16823, 25960}, {17024, 17722}, {17122, 27186}, {17123, 27131}, {17155, 32851}, {17184, 32916}, {17279, 29869}, {17469, 26098}, {17598, 29680}, {17599, 29688}, {17721, 29818}, {17723, 29819}, {17758, 20267}, {17763, 18134}, {18139, 29649}, {18743, 29851}, {19684, 29645}, {19721, 21936}, {20104, 24167}, {20254, 21326}, {21805, 25568}, {24174, 27529}, {24178, 27385}, {24214, 25581}, {24215, 27187}, {24217, 29817}, {24552, 25385}, {24653, 26971}, {25496, 26230}, {25527, 29828}, {25681, 28352}, {26034, 26132}, {26237, 30953}, {26688, 31289}, {26725, 30116}, {27184, 32917}, {27757, 32855}, {28606, 29640}, {29634, 32772}, {29638, 32942}, {29641, 32927}, {29643, 32926}, {29677, 30818}, {29839, 32915}, {29849, 32922}, {29862, 32862}, {29865, 32777}, {30831, 32778}


X(33128) = X(1)X(3841)∩X(2)X(740)

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

X(33128) lies on these lines: {1, 3841}, {2, 740}, {4, 18688}, {6, 3120}, {8, 32775}, {11, 4336}, {31, 516}, {38, 19785}, {42, 3772}, {75, 29631}, {81, 17889}, {100, 29658}, {142, 9345}, {239, 25760}, {244, 4000}, {306, 31237}, {312, 29850}, {321, 25453}, {333, 32776}, {386, 31880}, {387, 2650}, {748, 24210}, {750, 1738}, {896, 24248}, {899, 17720}, {952, 30448}, {986, 24883}, {995, 16173}, {1109, 17861}, {1150, 3821}, {1193, 5886}, {1376, 29683}, {1468, 23537}, {1699, 29043}, {1714, 2292}, {1834, 3924}, {1836, 2308}, {1992, 31177}, {1999, 25957}, {2177, 3011}, {2181, 17903}, {2321, 30768}, {2886, 17017}, {2887, 3187}, {2901, 19846}, {2999, 7988}, {3006, 32921}, {3008, 17125}, {3017, 5902}, {3240, 17719}, {3434, 17469}, {3474, 9340}, {3662, 32919}, {3666, 24892}, {3703, 28472}, {3705, 32924}, {3706, 24943}, {3720, 24789}, {3722, 26228}, {3741, 32774}, {3745, 21949}, {3750, 29681}, {3751, 32856}, {3752, 29662}, {3759, 32843}, {3769, 32948}, {3771, 3896}, {3782, 5852}, {3791, 6327}, {3875, 29857}, {3886, 29855}, {3891, 29673}, {3920, 32865}, {3923, 4442}, {3925, 5311}, {3935, 17725}, {3938, 17061}, {3944, 32911}, {3946, 29639}, {3996, 29848}, {4038, 27186}, {4062, 30811}, {4085, 26227}, {4116, 27846}, {4202, 17733}, {4359, 29635}, {4360, 29643}, {4362, 4972}, {4365, 29867}, {4425, 5278}, {4429, 17763}, {4438, 17147}, {4519, 17357}, {4642, 5230}, {4647, 20083}, {4649, 31019}, {4655, 16704}, {4657, 30970}, {4703, 19742}, {4722, 5905}, {4865, 17150}, {4892, 31034}, {5057, 16468}, {5222, 7384}, {5256, 17064}, {5263, 29636}, {5292, 24443}, {5312, 24160}, {5429, 17579}, {5587, 21935}, {5718, 17070}, {5847, 31134}, {6536, 19732}, {6679, 32929}, {7191, 31084}, {7292, 24217}, {8040, 19744}, {8229, 24257}, {11679, 32781}, {11680, 29821}, {16062, 27368}, {16706, 30942}, {17012, 17717}, {17025, 17722}, {17027, 30969}, {17126, 24715}, {17135, 26128}, {17155, 19796}, {17156, 25527}, {17162, 31017}, {17184, 32853}, {17278, 30950}, {17367, 32944}, {17599, 29690}, {17600, 29664}, {17871, 19788}, {18087, 29762}, {18147, 25611}, {19767, 24161}, {19786, 31330}, {19804, 29845}, {20182, 29682}, {21054, 23927}, {21283, 29831}, {24325, 29829}, {24552, 29654}, {25378, 29590}, {25441, 28612}, {25958, 32861}, {25959, 32846}, {26102, 26724}, {26230, 32941}, {27184, 32864}, {28605, 29868}, {29634, 32945}, {29641, 32928}, {29647, 31993}, {29688, 31245}, {29852, 32942}, {29856, 32779}, {29872, 32855}, {30632, 30940}, {30828, 31280}, {32773, 32914}


X(33129) = X(1)X(3841)∩X(2)X(37)

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

X(33129) lies on these lines: {1, 3841}, {2, 37}, {6, 31019}, {7, 24597}, {10, 32775}, {11, 858}, {21, 23537}, {27, 272}, {28, 19850}, {31, 17889}, {36, 759}, {44, 17484}, {55, 29681}, {57, 21367}, {63, 4862}, {81, 3664}, {86, 29833}, {88, 655}, {100, 1738}, {110, 5137}, {149, 1279}, {226, 26723}, {238, 3120}, {239, 3936}, {278, 15474}, {319, 31017}, {320, 16704}, {333, 17184}, {442, 5262}, {614, 11680}, {673, 675}, {905, 6591}, {740, 29632}, {748, 3944}, {750, 29658}, {896, 32857}, {899, 17719}, {902, 24715}, {908, 3008}, {940, 27186}, {942, 24883}, {982, 24892}, {990, 10883}, {1086, 3218}, {1099, 3582}, {1104, 2475}, {1111, 14206}, {1125, 14005}, {1150, 3662}, {1193, 24161}, {1203, 11263}, {1215, 29850}, {1266, 3977}, {1284, 27628}, {1376, 29665}, {1443, 6357}, {1612, 23604}, {1621, 3914}, {1714, 3868}, {1722, 11681}, {1733, 17888}, {1739, 17734}, {1743, 31164}, {1757, 32856}, {1836, 17127}, {1999, 17312}, {2177, 29675}, {2550, 26228}, {2886, 7191}, {2887, 32914}, {2975, 23536}, {2999, 31266}, {3006, 32922}, {3187, 17377}, {3216, 24160}, {3219, 3782}, {3240, 17718}, {3306, 4859}, {3315, 26015}, {3416, 25959}, {3670, 24880}, {3685, 4442}, {3686, 31143}, {3687, 30831}, {3703, 29873}, {3744, 21949}, {3750, 29689}, {3757, 4972}, {3759, 31034}, {3771, 32860}, {3791, 32949}, {3821, 32917}, {3824, 26131}, {3826, 5297}, {3836, 17763}, {3891, 29641}, {3896, 29839}, {3920, 3925}, {3924, 5086}, {3935, 17724}, {3938, 32865}, {3966, 25958}, {4001, 4921}, {4054, 17353}, {4062, 4716}, {4292, 16948}, {4318, 15253}, {4357, 5235}, {4361, 30811}, {4362, 25957}, {4365, 29869}, {4383, 31053}, {4395, 27757}, {4396, 25357}, {4415, 27065}, {4418, 6679}, {4429, 26227}, {4434, 25351}, {4438, 17155}, {4641, 17483}, {4675, 14996}, {4886, 31037}, {4892, 4974}, {5016, 19851}, {5051, 16817}, {5121, 31272}, {5205, 24988}, {5219, 7190}, {5222, 26738}, {5253, 17518}, {5256, 25525}, {5260, 13161}, {5263, 26230}, {5271, 17270}, {5278, 17331}, {5284, 24210}, {5497, 30117}, {5718, 17012}, {5721, 18444}, {5739, 26132}, {5745, 31204}, {5880, 17126}, {6687, 30578}, {8056, 31224}, {9335, 17728}, {11376, 28370}, {16468, 24725}, {16489, 21630}, {16583, 27068}, {16700, 16718}, {16714, 16743}, {16825, 25760}, {17011, 17056}, {17016, 25466}, {17021, 17245}, {17025, 17723}, {17027, 31006}, {17031, 30969}, {17063, 29662}, {17122, 29683}, {17277, 26580}, {17309, 32858}, {17361, 31303}, {17521, 19841}, {17592, 29661}, {17595, 31187}, {17598, 29690}, {17599, 29664}, {17600, 29682}, {18653, 30576}, {19720, 26746}, {20045, 32850}, {20470, 23369}, {21020, 32783}, {21026, 32847}, {21241, 32844}, {23511, 30852}, {24169, 32918}, {24175, 25580}, {24310, 27661}, {24325, 29631}, {24342, 29859}, {24596, 26282}, {24663, 26821}, {25385, 32944}, {25453, 32771}, {25496, 29852}, {25598, 32092}, {25681, 27625}, {25961, 29649}, {26128, 31330}, {26247, 26582}, {29607, 30566}, {29638, 32941}, {29642, 32915}, {29643, 32921}, {29653, 32928}, {29654, 32772}, {29656, 32945}, {29671, 32924}, {29672, 32943}, {29673, 32923}, {29680, 31245}, {29862, 32848}, {29867, 32780}, {31237, 32778}


X(33130) = X(1)X(442)∩X(2)X(38)

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

X(33130) lies on these lines: {1, 442}, {2, 38}, {7, 4650}, {10, 26728}, {11, 29820}, {31, 29681}, {43, 17718}, {55, 17889}, {75, 3771}, {86, 24241}, {142, 17122}, {171, 3011}, {226, 238}, {312, 29642}, {321, 29632}, {498, 24174}, {595, 11263}, {612, 17725}, {614, 17717}, {740, 29839}, {748, 31053}, {750, 27186}, {846, 3782}, {894, 6679}, {896, 17483}, {899, 26724}, {902, 20292}, {908, 17123}, {940, 29658}, {976, 4197}, {978, 11374}, {986, 10198}, {1001, 3944}, {1046, 6147}, {1054, 5432}, {1086, 6690}, {1125, 13161}, {1279, 3838}, {1621, 3120}, {1707, 4654}, {1738, 13405}, {1739, 3584}, {1836, 8616}, {1961, 17602}, {2476, 28082}, {2887, 3757}, {3006, 32923}, {3085, 24440}, {3219, 32856}, {3434, 17715}, {3550, 5880}, {3662, 32916}, {3666, 29640}, {3703, 29862}, {3750, 3914}, {3791, 17778}, {3822, 30117}, {3824, 5266}, {3836, 7081}, {3846, 16823}, {3870, 32865}, {3873, 24892}, {3874, 24880}, {3883, 4138}, {3891, 29643}, {3925, 3961}, {3936, 32861}, {3976, 26363}, {4028, 4716}, {4135, 17264}, {4358, 29851}, {4359, 29846}, {4362, 18134}, {4388, 4892}, {4413, 17783}, {4417, 16825}, {4418, 24395}, {4429, 29670}, {4514, 21241}, {4640, 32857}, {4666, 24217}, {4671, 29870}, {4850, 29678}, {4970, 19796}, {5219, 5272}, {5226, 16020}, {5247, 13407}, {5248, 24851}, {5255, 12609}, {5263, 29656}, {5281, 7613}, {5293, 8728}, {5718, 29821}, {5745, 24231}, {5883, 17734}, {5905, 7262}, {6685, 16706}, {6933, 28074}, {7191, 17722}, {7504, 28096}, {11375, 21214}, {13411, 24178}, {15485, 24703}, {16484, 24210}, {16569, 17278}, {17125, 27131}, {17127, 24725}, {17184, 32917}, {17234, 29649}, {17592, 19785}, {17594, 23681}, {17597, 29676}, {17598, 29639}, {17599, 29657}, {17716, 26228}, {17720, 26102}, {17763, 18139}, {19684, 29636}, {20290, 31029}, {21319, 27628}, {23383, 30362}, {23675, 24541}, {24165, 32851}, {24542, 32930}, {24552, 29638}, {24697, 27184}, {25385, 29672}, {25527, 32784}, {25957, 26227}, {26230, 32772}, {26237, 30969}, {28605, 29866}, {28606, 29661}, {29641, 32920}, {29651, 32773}, {29653, 32926}, {29667, 31237}, {29671, 32922}, {29830, 32915}, {29834, 30588}, {29849, 30834}, {29858, 32777}, {29865, 32779}, {30811, 32778}, {31993, 32783}


X(33131) = X(1)X(27186)∩X(2)X(968)

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

X(33131) lies on these lines: {1, 27186}, {2, 968}, {6, 20292}, {8, 17184}, {10, 28605}, {31, 24715}, {38, 32865}, {40, 27661}, {42, 17889}, {43, 3120}, {46, 24883}, {55, 29681}, {65, 11445}, {75, 4972}, {81, 5880}, {88, 17728}, {100, 3772}, {142, 29814}, {145, 23536}, {149, 614}, {226, 3240}, {239, 6327}, {306, 25959}, {312, 4442}, {321, 4429}, {333, 32950}, {345, 29873}, {377, 17016}, {387, 23604}, {497, 7292}, {516, 17127}, {536, 32862}, {740, 25957}, {899, 3944}, {975, 26060}, {1001, 26724}, {1054, 29662}, {1086, 3873}, {1621, 24789}, {1698, 6536}, {1722, 5046}, {1836, 32911}, {2550, 3920}, {2886, 4850}, {2887, 32860}, {3006, 3210}, {3175, 3823}, {3187, 4645}, {3219, 24248}, {3434, 4000}, {3474, 24597}, {3617, 13161}, {3622, 24178}, {3623, 23675}, {3661, 17163}, {3662, 17135}, {3663, 7226}, {3666, 21949}, {3681, 3782}, {3687, 25958}, {3696, 32782}, {3705, 17495}, {3736, 17173}, {3749, 20095}, {3751, 17483}, {3752, 11680}, {3755, 5249}, {3821, 31330}, {3826, 4854}, {3836, 32915}, {3870, 23681}, {3891, 19796}, {3896, 18134}, {3923, 29850}, {3925, 28606}, {3931, 4197}, {3959, 20859}, {3980, 29631}, {3993, 29854}, {4085, 32771}, {4359, 32773}, {4362, 32948}, {4365, 29674}, {4383, 5057}, {4389, 4981}, {4392, 4847}, {4393, 23682}, {4418, 25453}, {4425, 26037}, {4430, 24231}, {4438, 32845}, {4651, 27184}, {4655, 32864}, {4656, 9330}, {4660, 32914}, {4666, 4859}, {4716, 32852}, {4865, 32924}, {4970, 29643}, {5014, 32922}, {5263, 29648}, {5278, 24723}, {5284, 17278}, {5312, 11263}, {5432, 17070}, {5725, 6175}, {7998, 21334}, {9335, 11019}, {10327, 30699}, {11269, 27003}, {12053, 28370}, {12609, 19767}, {13576, 20242}, {16706, 24552}, {16824, 17676}, {16825, 32947}, {17012, 26098}, {17147, 29641}, {17155, 29673}, {17156, 32863}, {17363, 20290}, {17591, 29690}, {17596, 24892}, {17740, 29872}, {17777, 26688}, {17784, 26228}, {18743, 24988}, {19824, 20020}, {21020, 32784}, {21241, 29849}, {21935, 24440}, {21955, 25973}, {21956, 26242}, {24169, 30942}, {24177, 26015}, {24342, 29647}, {25351, 25961}, {26128, 32945}, {26627, 29837}, {31134, 32861}, {32857, 32912}


X(33132) = X(1)X(3925)∩X(2)X(740)

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

X(33132) lies on these lines: {1, 3925}, {2, 740}, {6, 17889}, {8, 26128}, {10, 19786}, {31, 24715}, {43, 3772}, {75, 25453}, {142, 4038}, {171, 1738}, {200, 17725}, {238, 3914}, {239, 2887}, {306, 4716}, {321, 29850}, {333, 3821}, {386, 24161}, {726, 19796}, {982, 4000}, {984, 19785}, {986, 1714}, {1086, 32913}, {1376, 29658}, {1386, 21949}, {1698, 3695}, {1724, 24851}, {1757, 3782}, {1836, 16468}, {1961, 3826}, {1999, 3836}, {2177, 29681}, {2308, 20292}, {2550, 17716}, {2886, 17366}, {2999, 17064}, {3006, 32924}, {3008, 17123}, {3017, 5883}, {3120, 32911}, {3187, 25957}, {3210, 4438}, {3662, 32853}, {3696, 32783}, {3705, 7931}, {3706, 29637}, {3720, 26724}, {3741, 16706}, {3750, 3755}, {3751, 23681}, {3757, 4085}, {3759, 32946}, {3791, 4645}, {3896, 29632}, {3944, 4383}, {3946, 17600}, {3961, 17061}, {3996, 29656}, {4011, 17352}, {4202, 27368}, {4359, 29631}, {4360, 29653}, {4361, 32778}, {4362, 4429}, {4388, 4974}, {4395, 29861}, {4425, 17277}, {4442, 32930}, {4641, 32857}, {4649, 5249}, {4650, 24597}, {4651, 32775}, {4683, 19742}, {4703, 17349}, {4722, 17483}, {4847, 17598}, {4850, 24892}, {4972, 32914}, {5222, 26098}, {5230, 24440}, {5247, 23537}, {5263, 29654}, {5271, 19834}, {5272, 24217}, {5278, 24697}, {5292, 24174}, {5429, 11112}, {5745, 17593}, {6679, 32932}, {7262, 24248}, {11269, 17063}, {14829, 24169}, {16569, 17720}, {16825, 32773}, {17070, 17779}, {17184, 32864}, {17278, 26102}, {17367, 25496}, {17380, 29644}, {18147, 24746}, {18201, 24177}, {19804, 29635}, {20083, 28612}, {24443, 24883}, {24552, 29852}, {24589, 29845}, {25441, 28611}, {25959, 32852}, {26061, 28605}, {26230, 32945}, {29633, 31993}, {29641, 32921}, {29673, 32922}, {29857, 32855}, {29867, 32779}, {29873, 32848}, {30631, 30940}, {31330, 32774}


X(33133) = X(1)X(2476)∩X(2)X(37)

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

X(33133) lies on these lines: {1, 2476}, {2, 37}, {5, 5262}, {6, 31053}, {10, 31247}, {11, 5133}, {12, 17016}, {31, 3944}, {42, 17719}, {44, 26792}, {55, 29665}, {57, 15999}, {72, 24883}, {81, 226}, {88, 24177}, {92, 17902}, {100, 3914}, {149, 3744}, {171, 3120}, {239, 5741}, {306, 30831}, {319, 31037}, {329, 24597}, {333, 26580}, {349, 16749}, {404, 23537}, {495, 17015}, {497, 26228}, {612, 17064}, {740, 29846}, {750, 17889}, {908, 32911}, {940, 31019}, {942, 26729}, {975, 4197}, {976, 5178}, {982, 29662}, {984, 24892}, {1001, 29681}, {1086, 27003}, {1104, 5046}, {1150, 27184}, {1215, 29631}, {1332, 26670}, {1386, 17605}, {1621, 3011}, {1714, 3876}, {1836, 17126}, {1909, 27793}, {1962, 29640}, {1989, 30690}, {1999, 3936}, {2886, 3920}, {2887, 17763}, {2901, 25645}, {2975, 13161}, {2999, 30852}, {3006, 32926}, {3187, 4417}, {3218, 3782}, {3219, 4415}, {3306, 23681}, {3315, 11019}, {3416, 25958}, {3452, 26723}, {3584, 4868}, {3703, 29872}, {3705, 3891}, {3741, 32775}, {3745, 3838}, {3760, 25598}, {3767, 27068}, {3769, 6327}, {3771, 32915}, {3791, 32843}, {3816, 7292}, {3821, 32918}, {3846, 32914}, {3868, 5292}, {3869, 5230}, {3873, 11269}, {3925, 5297}, {3932, 29873}, {3938, 17725}, {3954, 24899}, {3957, 17724}, {4352, 27187}, {4362, 25760}, {4383, 17796}, {4396, 25345}, {4416, 4921}, {4424, 17734}, {4425, 32917}, {4434, 32948}, {4438, 32925}, {4442, 32932}, {4514, 20045}, {4554, 16750}, {4641, 17484}, {4643, 5361}, {4656, 31204}, {4854, 6690}, {4892, 32949}, {4972, 7081}, {5012, 5137}, {5219, 5256}, {5222, 5748}, {5253, 23536}, {5286, 26690}, {5287, 25525}, {5315, 11813}, {5712, 26738}, {5716, 6871}, {5718, 17011}, {6679, 32930}, {6704, 17741}, {6708, 28836}, {7196, 16727}, {7621, 29622}, {10129, 26098}, {11374, 19767}, {11679, 32782}, {14829, 17184}, {16484, 29689}, {16698, 18601}, {16700, 16719}, {16825, 25960}, {17017, 17717}, {17018, 17718}, {17019, 17056}, {17020, 17366}, {17024, 17721}, {17095, 18600}, {17127, 24703}, {17352, 26688}, {17396, 31281}, {17592, 29678}, {17599, 29680}, {17600, 29688}, {17722, 29819}, {17884, 24026}, {19684, 29841}, {21093, 32938}, {24325, 29845}, {24552, 29634}, {24954, 27625}, {25385, 29645}, {25453, 32931}, {25496, 29636}, {25957, 29649}, {26061, 29856}, {26109, 30588}, {26128, 30942}, {26227, 32773}, {26230, 32942}, {26247, 26590}, {26978, 27006}, {29633, 31264}, {29635, 32771}, {29654, 32944}, {29655, 32923}, {29656, 32943}, {29664, 31245}, {29671, 32928}, {29673, 32927}, {29674, 31237}, {29848, 32941}, {29849, 32921}, {29857, 32862}, {29863, 32780}, {30811, 32858}, {32776, 32916}, {32856, 32913}


X(33134) = X(1)X(149)∩X(2)X(968)

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

X(33134) lies on these lines: {1, 149}, {2, 968}, {4, 17016}, {6, 5057}, {8, 26580}, {10, 4671}, {11, 4850}, {42, 3944}, {43, 27131}, {55, 29665}, {75, 3266}, {81, 1836}, {100, 17720}, {145, 13161}, {192, 3006}, {226, 17018}, {244, 24217}, {306, 25958}, {312, 4972}, {321, 29667}, {345, 29872}, {350, 30632}, {387, 11415}, {390, 26228}, {497, 1370}, {516, 17126}, {528, 17602}, {740, 25760}, {750, 24715}, {756, 32865}, {846, 24892}, {894, 29829}, {902, 29658}, {908, 3240}, {940, 20292}, {1070, 11036}, {1150, 24723}, {1468, 24851}, {1478, 17015}, {1479, 5262}, {1621, 3772}, {1698, 21027}, {1699, 5256}, {1834, 3869}, {1999, 6327}, {2177, 17719}, {2476, 3931}, {2550, 5297}, {2886, 4854}, {2887, 32858}, {2895, 17156}, {2979, 21334}, {3058, 17061}, {3124, 3959}, {3175, 32862}, {3187, 4388}, {3218, 11269}, {3332, 9812}, {3434, 3920}, {3550, 29683}, {3616, 19823}, {3622, 23536}, {3662, 29824}, {3663, 4392}, {3666, 11680}, {3673, 23989}, {3681, 4415}, {3702, 16062}, {3705, 17147}, {3706, 32782}, {3720, 17889}, {3722, 17725}, {3736, 17174}, {3741, 32776}, {3751, 17484}, {3769, 4450}, {3782, 3873}, {3790, 31079}, {3821, 30942}, {3841, 27785}, {3844, 4519}, {3846, 32860}, {3875, 32842}, {3891, 4514}, {3896, 4417}, {3912, 25959}, {3923, 29631}, {3946, 17025}, {3980, 29845}, {3993, 21241}, {3995, 29641}, {4000, 7292}, {4011, 29850}, {4085, 32931}, {4197, 6051}, {4358, 4429}, {4362, 32947}, {4365, 32778}, {4418, 29635}, {4423, 26724}, {4425, 31330}, {4438, 32936}, {4642, 25005}, {4646, 11681}, {4649, 24725}, {4655, 32919}, {4656, 25006}, {4660, 17763}, {4666, 23681}, {4683, 32853}, {4703, 32864}, {4847, 7226}, {4865, 32928}, {4868, 7951}, {4970, 29849}, {5014, 32926}, {5141, 5530}, {5249, 29814}, {5284, 24789}, {5294, 29868}, {5313, 11813}, {5695, 32779}, {5698, 24597}, {5718, 10129}, {5725, 17577}, {9335, 24177}, {10453, 17184}, {10458, 17173}, {10707, 17301}, {11235, 17599}, {12047, 19767}, {12514, 24883}, {14008, 25059}, {14009, 25060}, {14829, 32950}, {17011, 26098}, {17135, 27184}, {17140, 29843}, {17155, 29655}, {17162, 17363}, {17198, 18600}, {17364, 17491}, {17395, 17726}, {17596, 29662}, {17776, 29873}, {19786, 24552}, {21955, 24554}, {23682, 29570}, {24169, 30957}, {24349, 29835}, {24703, 32911}, {24988, 30829}, {25453, 32930}, {26128, 32943}, {27812, 29576}, {29649, 32948}, {29666, 32774}, {29673, 32925}, {29857, 32849}, {31134, 32846}, {32775, 32941}, {32844, 32921}


X(33135) = X(1)X(442)∩X(2)X(740)

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

X(33135) lies on these lines: {1, 442}, {2, 740}, {6, 3944}, {11, 7073}, {30, 5429}, {42, 17719}, {43, 17720}, {55, 29658}, {57, 1719}, {58, 24851}, {75, 29635}, {81, 3120}, {100, 29683}, {149, 17469}, {171, 3914}, {192, 4438}, {226, 4649}, {238, 2328}, {239, 3846}, {312, 25453}, {321, 29631}, {333, 4425}, {386, 5496}, {612, 32865}, {614, 24217}, {758, 3017}, {846, 4854}, {940, 17889}, {982, 11269}, {986, 5292}, {1043, 1125}, {1100, 3838}, {1150, 32776}, {1193, 14011}, {1479, 16478}, {1503, 1699}, {1698, 3704}, {1738, 17122}, {1756, 18163}, {1757, 4415}, {1961, 3925}, {1999, 2887}, {2177, 29665}, {2292, 24883}, {2308, 5057}, {2784, 3817}, {3006, 32928}, {3011, 3750}, {3187, 25760}, {3434, 17716}, {3685, 6679}, {3687, 4716}, {3703, 29861}, {3705, 32921}, {3706, 32783}, {3714, 19879}, {3741, 19786}, {3743, 24880}, {3769, 4660}, {3782, 32913}, {3791, 4388}, {3792, 21334}, {3816, 17366}, {3821, 14829}, {3840, 16706}, {3870, 17725}, {3875, 32855}, {3879, 4138}, {3896, 29846}, {3946, 24239}, {3961, 17602}, {3979, 17724}, {4000, 17063}, {4038, 5249}, {4062, 30831}, {4085, 7081}, {4267, 30362}, {4358, 29850}, {4359, 29845}, {4360, 29671}, {4362, 32773}, {4365, 29863}, {4418, 4442}, {4429, 29649}, {4451, 6682}, {4647, 25441}, {4650, 24248}, {4658, 11263}, {4671, 26061}, {4682, 21949}, {4683, 16704}, {4722, 17484}, {4850, 29662}, {4868, 17734}, {4892, 17778}, {4970, 32851}, {4972, 17763}, {5051, 27368}, {5235, 6536}, {5256, 17717}, {5263, 29645}, {5324, 24436}, {5625, 26109}, {6703, 24342}, {7018, 30940}, {7191, 31126}, {7262, 24597}, {8013, 31247}, {9345, 27186}, {10453, 26128}, {11533, 21677}, {11679, 32784}, {11680, 17017}, {16062, 17733}, {16468, 24703}, {17016, 21935}, {17027, 30953}, {17123, 26723}, {17135, 32775}, {17150, 32844}, {17162, 31037}, {17184, 32919}, {17278, 25502}, {17301, 17591}, {17380, 29650}, {17598, 26015}, {17599, 29676}, {17600, 29639}, {17715, 26228}, {17737, 21840}, {17795, 20545}, {18087, 29797}, {19796, 24165}, {20182, 29657}, {20270, 24780}, {21085, 30832}, {24325, 29837}, {24552, 29636}, {24746, 25660}, {24789, 26102}, {24892, 28606}, {25123, 25688}, {25958, 32852}, {26230, 32943}, {26580, 32864}, {26724, 30950}, {27184, 32853}, {27577, 31254}, {28605, 29864}, {29634, 32941}, {29654, 32942}, {29655, 32922}, {29673, 32926}, {29829, 32771}, {29833, 32772}, {29835, 32923}, {29856, 32777}, {29872, 32848}, {30942, 32774}, {31237, 32858}


X(33136) = X(1)X(3841)∩X(2)X(2177)

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

X(33136) lies on these lines: {1, 3841}, {2, 2177}, {5, 3214}, {6, 31140}, {8, 21935}, {10, 3702}, {11, 899}, {31, 3434}, {38, 3663}, {42, 2886}, {43, 11680}, {55, 24892}, {69, 31134}, {141, 31136}, {142, 17450}, {149, 238}, {239, 4766}, {244, 1738}, {321, 29673}, {333, 32947}, {350, 5224}, {354, 21949}, {496, 27627}, {497, 748}, {516, 896}, {518, 3120}, {519, 3936}, {528, 902}, {614, 24392}, {672, 21956}, {693, 1734}, {726, 4442}, {740, 3006}, {750, 2550}, {752, 16704}, {756, 24210}, {908, 21805}, {1086, 17449}, {1109, 23690}, {1150, 4660}, {1193, 24390}, {1201, 3813}, {1376, 29662}, {1647, 16610}, {1714, 3915}, {1737, 4695}, {1757, 5057}, {1834, 10459}, {1836, 32912}, {2239, 13576}, {2887, 17135}, {3011, 3722}, {3187, 4865}, {3216, 24387}, {3218, 24715}, {3240, 17717}, {3263, 4967}, {3293, 25639}, {3666, 29690}, {3681, 3944}, {3684, 17737}, {3703, 4365}, {3705, 32860}, {3706, 15523}, {3717, 3994}, {3720, 3925}, {3739, 21027}, {3741, 4972}, {3746, 24880}, {3748, 29689}, {3751, 24725}, {3755, 29639}, {3772, 3938}, {3773, 31079}, {3814, 31855}, {3826, 30950}, {3836, 29824}, {3846, 4651}, {3870, 17064}, {3873, 17889}, {3886, 29857}, {3896, 29671}, {3912, 21026}, {3935, 17719}, {3977, 28580}, {3989, 4854}, {3996, 29846}, {4026, 30970}, {4054, 31161}, {4062, 28581}, {4193, 6048}, {4340, 31420}, {4359, 29655}, {4362, 5014}, {4383, 11235}, {4388, 32864}, {4425, 4981}, {4427, 17764}, {4429, 30942}, {4438, 32929}, {4514, 32914}, {4516, 21326}, {4642, 6734}, {4645, 32919}, {4685, 5741}, {4693, 32849}, {4716, 32842}, {4849, 17605}, {4850, 29676}, {4859, 31146}, {4871, 24988}, {5015, 27368}, {5082, 5230}, {5255, 24883}, {5263, 29631}, {5300, 17733}, {6327, 31303}, {10448, 19843}, {10453, 17232}, {10529, 32577}, {10916, 24443}, {14829, 32948}, {16062, 19817}, {17012, 17722}, {17070, 17724}, {17143, 24995}, {17156, 32852}, {17162, 17772}, {17242, 29641}, {17249, 32776}, {17491, 17771}, {17592, 29664}, {17606, 21896}, {17715, 29681}, {17763, 32850}, {17765, 20045}, {20292, 32913}, {22072, 26475}, {23541, 26013}, {24325, 29835}, {24552, 25453}, {24592, 26590}, {24693, 26627}, {26724, 29820}, {29652, 32774}, {29678, 31245}, {29685, 31993}, {29832, 32921}, {29840, 32924}, {29850, 32942}, {29861, 32779}


X(33137) = X(1)X(2)∩X(4)X(1957)

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

X(33137) lies on these lines: {1, 2}, {4, 1957}, {6, 2886}, {7, 17889}, {9, 24210}, {11, 4383}, {31, 3434}, {38, 19785}, {44, 24703}, {46, 21370}, {55, 8731}, {56, 16056}, {57, 1738}, {63, 1711}, {69, 2887}, {92, 23690}, {149, 17127}, {171, 2550}, {193, 21241}, {210, 17720}, {212, 238}, {218, 8226}, {219, 2238}, {226, 3751}, {240, 17903}, {278, 291}, {329, 1757}, {333, 32773}, {345, 740}, {347, 23669}, {350, 3718}, {354, 24789}, {377, 1468}, {390, 8616}, {516, 1707}, {518, 3772}, {528, 3052}, {602, 12116}, {672, 1723}, {726, 30699}, {846, 5273}, {902, 20075}, {940, 3925}, {958, 1834}, {982, 4000}, {983, 6601}, {1046, 4295}, {1054, 5435}, {1108, 1575}, {1150, 4972}, {1191, 3813}, {1211, 4042}, {1214, 7235}, {1284, 20760}, {1479, 1724}, {1617, 16059}, {1699, 1743}, {1716, 27509}, {1719, 21381}, {1733, 17860}, {1754, 13478}, {1780, 14956}, {1788, 24440}, {1836, 4641}, {1838, 4196}, {1985, 16471}, {1997, 24003}, {2257, 17754}, {2276, 25074}, {2309, 27317}, {2345, 32780}, {2895, 25958}, {3120, 5905}, {3242, 17061}, {3333, 24178}, {3428, 4192}, {3436, 21935}, {3474, 4650}, {3487, 24161}, {3550, 17784}, {3618, 21242}, {3668, 8769}, {3684, 7735}, {3706, 32777}, {3742, 17278}, {3744, 4863}, {3749, 5853}, {3755, 5745}, {3767, 20544}, {3769, 32850}, {3781, 21334}, {3791, 4865}, {3836, 18141}, {3838, 4663}, {3846, 14555}, {3874, 24159}, {3923, 26065}, {3931, 5791}, {3971, 27549}, {4011, 26685}, {4026, 5737}, {4038, 4648}, {4085, 32916}, {4119, 17314}, {4191, 7742}, {4255, 4999}, {4260, 10473}, {4415, 5220}, {4425, 17257}, {4429, 14829}, {4442, 32933}, {4644, 24694}, {4646, 26066}, {4649, 5712}, {4716, 32855}, {4722, 24725}, {4859, 10980}, {5018, 18623}, {5082, 5255}, {5286, 21384}, {5324, 7295}, {5573, 24216}, {5659, 17756}, {5698, 7262}, {5706, 5788}, {5711, 31419}, {5718, 31245}, {5739, 25760}, {5744, 17596}, {5816, 17737}, {5839, 32861}, {5880, 21949}, {6327, 16704}, {6679, 32941}, {6690, 31187}, {7290, 24392}, {7613, 21454}, {8167, 17337}, {8889, 26012}, {9965, 32857}, {10441, 10822}, {10900, 15299}, {11680, 32911}, {16466, 24390}, {16571, 27334}, {16610, 17728}, {16713, 18169}, {17122, 26040}, {17123, 24217}, {17155, 19789}, {17189, 30941}, {17719, 25568}, {17740, 32860}, {17759, 25252}, {17776, 32915}, {17890, 24209}, {18193, 24177}, {19540, 22770}, {19765, 24953}, {19788, 23689}, {19822, 21020}, {20064, 21282}, {20290, 31303}, {20967, 31394}, {21257, 26041}, {23681, 24231}, {24686, 24712}, {24744, 27633}, {25934, 25973}, {25957, 32919}, {25959, 32863}


X(33138) = X(1)X(2)∩X(9)X(3944)

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

X(33138) lies on these lines: {1, 2}, {9, 3944}, {11, 17123}, {35, 8731}, {36, 16056}, {44, 3838}, {55, 32865}, {58, 3841}, {63, 17889}, {72, 24161}, {75, 4438}, {87, 27317}, {100, 31204}, {171, 3925}, {210, 17719}, {226, 1757}, {238, 2886}, {244, 26724}, {278, 17927}, {333, 2887}, {442, 5247}, {497, 15485}, {748, 11680}, {759, 4184}, {846, 3914}, {896, 20292}, {982, 24789}, {984, 3772}, {986, 5791}, {1046, 12609}, {1150, 25957}, {1247, 23604}, {1324, 4191}, {1376, 31187}, {1468, 4197}, {1575, 25075}, {1617, 16409}, {1723, 17754}, {1738, 5745}, {1780, 14009}, {1836, 7262}, {1838, 4212}, {2108, 2954}, {2550, 3550}, {3120, 3219}, {3428, 19540}, {3434, 8616}, {3678, 24160}, {3711, 17783}, {3751, 25525}, {3816, 17337}, {3826, 17122}, {3836, 14829}, {3846, 17277}, {3936, 32864}, {4000, 17591}, {4042, 30811}, {4085, 31205}, {4138, 4416}, {4199, 5251}, {4312, 16570}, {4361, 32855}, {4365, 32849}, {4383, 17717}, {4388, 21241}, {4415, 17070}, {4423, 24217}, {4429, 32916}, {4442, 32936}, {4640, 21949}, {4649, 17056}, {4650, 5880}, {4859, 18193}, {4863, 17715}, {4972, 32917}, {4981, 32775}, {5249, 32913}, {5255, 31419}, {5260, 21935}, {5263, 6679}, {5273, 24248}, {5278, 25760}, {5361, 25959}, {5712, 28650}, {5737, 32784}, {6682, 16706}, {7184, 16713}, {7186, 18191}, {7742, 16059}, {8727, 9441}, {16468, 26098}, {16704, 32949}, {17063, 17278}, {17189, 30966}, {17888, 20879}, {18134, 32853}, {18139, 32919}, {18698, 20437}, {19742, 32843}, {19808, 27798}, {21020, 32779}, {21242, 32942}, {24169, 24627}, {24440, 26066}, {24542, 32943}, {24851, 31445}, {25385, 27064}, {31019, 32912}, {31237, 32782}, {31993, 32780}


X(33139) = X(1)X(2)∩X(31)X(32865)

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

X(33139) lies on these lines: {1, 2}, {31, 32865}, {44, 5057}, {69, 25959}, {81, 3925}, {149, 238}, {190, 4442}, {291, 21907}, {333, 4972}, {354, 26724}, {672, 1731}, {740, 32849}, {896, 24715}, {902, 20095}, {1104, 5178}, {1150, 4429}, {1724, 11330}, {1738, 3218}, {1757, 3120}, {1834, 5260}, {1931, 5196}, {2238, 5375}, {2240, 5291}, {2475, 5247}, {2550, 17126}, {2886, 32911}, {2887, 2895}, {3219, 3914}, {3434, 17127}, {3676, 4608}, {3681, 3772}, {3696, 32779}, {3751, 31019}, {3836, 32919}, {3841, 26131}, {3873, 24789}, {3944, 26792}, {4000, 4392}, {4026, 5235}, {4042, 32782}, {4085, 32917}, {4383, 11680}, {4388, 19742}, {4438, 32860}, {4641, 20292}, {4645, 16704}, {4716, 32848}, {4753, 4892}, {4974, 32844}, {4981, 19786}, {5278, 32773}, {5361, 26034}, {5739, 25958}, {6679, 32945}, {6690, 31204}, {7226, 19785}, {13576, 14956}, {17064, 31053}, {17125, 24217}, {17483, 17889}, {17491, 20072}, {17719, 21805}, {20086, 32949}, {21020, 32780}, {21026, 32846}, {21027, 24342}, {21241, 32843}, {21242, 32944}, {24210, 27065}, {24387, 30980}, {24687, 24712}, {24744, 27671}, {25957, 32853}, {26842, 32913}, {27812, 28604}


X(33140) = X(1)X(2)∩X(5)X(5247)

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

X(33140) lies on these lines: {1, 2}, {5, 5247}, {6, 17717}, {11, 238}, {31, 11680}, {35, 30944}, {36, 851}, {44, 5087}, {57, 1711}, {58, 14009}, {63, 3944}, {72, 30986}, {149, 902}, {171, 2886}, {225, 4212}, {226, 32913}, {230, 3684}, {291, 2006}, {312, 4438}, {320, 4892}, {333, 3846}, {497, 8616}, {518, 17719}, {524, 27759}, {595, 24387}, {672, 2957}, {740, 32851}, {846, 5745}, {894, 25385}, {896, 5057}, {908, 1757}, {940, 31245}, {942, 24161}, {982, 3772}, {984, 17720}, {1001, 24217}, {1046, 12047}, {1054, 1738}, {1086, 17070}, {1150, 25760}, {1155, 24715}, {1326, 19642}, {1376, 32865}, {1386, 17722}, {1468, 2476}, {1479, 30943}, {1575, 8609}, {1580, 8229}, {1699, 1707}, {1724, 1985}, {1733, 24026}, {1743, 7988}, {1834, 4999}, {1836, 4650}, {2238, 2323}, {2887, 14829}, {2975, 21935}, {3052, 11235}, {3072, 26470}, {3120, 3218}, {3242, 17725}, {3434, 3550}, {3583, 14956}, {3673, 30988}, {3712, 4693}, {3749, 24392}, {3750, 6690}, {3751, 5219}, {3767, 21384}, {3769, 4865}, {3775, 30832}, {3816, 17123}, {3821, 24627}, {3835, 27845}, {3874, 24160}, {3914, 17596}, {3916, 24851}, {3925, 17122}, {3936, 32919}, {3987, 5445}, {4038, 17056}, {4184, 14794}, {4192, 11012}, {4331, 5435}, {4417, 32853}, {4434, 32850}, {4442, 32845}, {4641, 17605}, {4645, 21241}, {4649, 5718}, {4972, 32918}, {5255, 24390}, {5263, 21242}, {5278, 25960}, {5284, 31204}, {5372, 25958}, {5711, 31493}, {5741, 32864}, {5744, 24248}, {5955, 31327}, {6679, 32942}, {6682, 19786}, {7262, 24703}, {7658, 21186}, {8557, 17754}, {8758, 16610}, {10129, 24725}, {10591, 30971}, {11249, 19540}, {16058, 26357}, {16468, 24597}, {16704, 32843}, {17061, 17598}, {17063, 17728}, {17591, 19785}, {18193, 23681}, {22345, 30362}, {24440, 24914}, {24699, 25383}, {25531, 31289}, {26007, 31210}, {31053, 32912}, {32773, 32916}


X(33141) = X(1)X(442)∩X(2)X(2177)

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

X(33141) lies on these lines: {1, 442}, {2, 2177}, {6, 11235}, {8, 3846}, {10, 4673}, {11, 43}, {31, 149}, {42, 11680}, {57, 24715}, {75, 24241}, {100, 29662}, {145, 21935}, {171, 3434}, {212, 238}, {312, 29673}, {325, 3875}, {345, 4693}, {354, 17889}, {386, 24387}, {496, 978}, {516, 4650}, {518, 3944}, {519, 4417}, {528, 3550}, {740, 3705}, {940, 31140}, {982, 3914}, {984, 4656}, {986, 10916}, {1046, 12699}, {1054, 17728}, {1150, 32947}, {1210, 24440}, {1479, 5247}, {1621, 24892}, {1699, 3751}, {1707, 9580}, {1724, 4857}, {1738, 11019}, {1743, 17747}, {1757, 24703}, {1836, 32913}, {1962, 29664}, {1999, 4865}, {2280, 17737}, {2550, 17122}, {2887, 10453}, {3006, 32915}, {3011, 17715}, {3058, 8616}, {3120, 3873}, {3187, 32844}, {3214, 4193}, {3293, 7741}, {3632, 4952}, {3666, 29676}, {3673, 20935}, {3679, 5743}, {3685, 4438}, {3706, 32778}, {3722, 29665}, {3741, 32773}, {3742, 21949}, {3744, 29658}, {3748, 29675}, {3755, 24239}, {3769, 17766}, {3816, 16569}, {3826, 25502}, {3840, 4429}, {3870, 17719}, {3880, 25135}, {3896, 29849}, {3915, 24883}, {3925, 26102}, {3938, 17725}, {3961, 4863}, {3976, 23537}, {3979, 17718}, {4138, 4684}, {4187, 6048}, {4335, 6067}, {4362, 4514}, {4383, 11238}, {4388, 32853}, {4428, 31187}, {4430, 32856}, {4442, 17155}, {4649, 26098}, {4651, 25960}, {4660, 14829}, {4685, 5233}, {4734, 4743}, {4849, 5087}, {4970, 17774}, {4972, 30942}, {5014, 17763}, {5015, 17733}, {5057, 32912}, {5231, 17594}, {5255, 5292}, {5256, 17722}, {5263, 29635}, {5324, 7301}, {5697, 22276}, {6327, 32919}, {7191, 31084}, {9812, 24695}, {10707, 32911}, {16474, 31159}, {16706, 29668}, {17026, 26590}, {17135, 25760}, {17156, 32861}, {17450, 27186}, {17592, 29639}, {17598, 19785}, {17721, 29821}, {17734, 25439}, {17754, 21956}, {18134, 21241}, {18141, 31151}, {19786, 29652}, {21805, 27131}, {23681, 31146}, {24177, 24216}, {24248, 24477}, {24325, 29843}, {24366, 24652}, {24552, 29631}, {24709, 26688}, {24789, 29820}, {25453, 32942}, {25957, 29824}, {27337, 28734}, {28606, 29690}, {29640, 31245}, {29649, 32850}, {29829, 32772}, {29832, 32928}, {29835, 32771}, {29840, 32921}, {29844, 32922}, {29861, 32777}, {31134, 32863}, {31136, 32782}


X(33142) = X(1)X(2)∩X(6)X(11680)

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

X(33142) lies on these lines: {1, 2}, {6, 11680}, {11, 32911}, {31, 149}, {69, 25958}, {81, 2886}, {497, 2361}, {593, 19642}, {748, 24217}, {750, 32865}, {1150, 32773}, {1203, 24387}, {1468, 2475}, {1738, 27003}, {1757, 26792}, {1834, 2975}, {2887, 32863}, {2895, 25760}, {3120, 17483}, {3218, 3914}, {3219, 24210}, {3434, 17126}, {3550, 20095}, {3681, 17720}, {3706, 32779}, {3742, 26724}, {3751, 31053}, {3769, 5014}, {3772, 3873}, {3791, 32844}, {3822, 16474}, {3846, 32864}, {3896, 32851}, {3944, 17484}, {4085, 32918}, {4388, 16704}, {4392, 19785}, {4438, 32849}, {4442, 32939}, {4641, 5057}, {4663, 17605}, {4972, 14829}, {5046, 5247}, {5372, 26034}, {6043, 24624}, {6284, 16948}, {6679, 32943}, {17064, 31019}, {17889, 26842}, {20060, 21935}, {20086, 32946}, {20101, 21282}, {21241, 32949}, {21242, 32772}


X(33143) = X(1)X(149)∩X(2)X(726)

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

X(33143) lies on these lines: {1, 149}, {2, 726}, {6, 32856}, {31, 3782}, {38, 3772}, {42, 19785}, {57, 29683}, {75, 32775}, {100, 17725}, {192, 29632}, {226, 17017}, {244, 17720}, {312, 29677}, {321, 24943}, {345, 29865}, {497, 29818}, {612, 23681}, {740, 27476}, {748, 4415}, {750, 1086}, {756, 24789}, {846, 29681}, {894, 29636}, {896, 17276}, {899, 4000}, {902, 24248}, {968, 29689}, {976, 23537}, {982, 29662}, {1125, 4054}, {1215, 29663}, {1386, 24725}, {1836, 17469}, {1961, 27186}, {2177, 17724}, {2308, 5905}, {2887, 3891}, {3011, 3663}, {3017, 3894}, {3210, 29846}, {3218, 29658}, {3315, 24217}, {3662, 17763}, {3666, 29678}, {3673, 20940}, {3685, 29638}, {3703, 31237}, {3729, 29855}, {3757, 32776}, {3771, 17147}, {3791, 32859}, {3821, 26227}, {3875, 4062}, {3914, 3938}, {3920, 17889}, {3923, 26230}, {3924, 13161}, {3936, 32921}, {3944, 7191}, {3993, 29830}, {3994, 17279}, {3995, 29642}, {4009, 17356}, {4023, 4395}, {4310, 11269}, {4353, 29639}, {4362, 17184}, {4365, 30699}, {4389, 32917}, {4398, 32845}, {4417, 32924}, {4418, 29634}, {4429, 32927}, {4442, 32941}, {4660, 20045}, {4671, 29637}, {4850, 17719}, {4972, 32920}, {5249, 5311}, {5846, 31134}, {5850, 32912}, {6327, 28512}, {6679, 32933}, {9345, 25557}, {10129, 17722}, {11680, 17598}, {15523, 25527}, {16468, 17484}, {16475, 31164}, {16706, 32931}, {16825, 26580}, {17064, 29690}, {17126, 32857}, {17140, 29635}, {17150, 32946}, {17165, 25453}, {17301, 17718}, {17304, 29828}, {17596, 29665}, {17716, 20292}, {17776, 29869}, {18134, 32928}, {19786, 29647}, {19796, 32860}, {19846, 24068}, {21241, 29832}, {21747, 24695}, {24349, 29631}, {25525, 29682}, {25760, 32922}, {25957, 32926}, {25958, 32866}, {25959, 32847}, {26098, 29819}, {26223, 29654}, {27064, 29852}, {27184, 32914}, {28605, 32783}, {28606, 29661}, {29656, 32929}, {29688, 31266}, {29821, 31053}, {29848, 32932}, {29850, 32937}, {29858, 32849}, {30811, 32848}, {30831, 32855}, {32773, 32923}


X(33144) = X(1)X(4)∩X(2)X(38)

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

X(33144) lies on these lines: {1, 4}, {2, 38}, {3, 28108}, {6, 17061}, {7, 171}, {8, 2887}, {10, 24159}, {11, 17597}, {31, 5905}, {40, 28039}, {42, 19785}, {43, 4000}, {55, 3782}, {56, 13732}, {57, 6211}, {63, 3011}, {69, 4362}, {78, 23536}, {87, 24669}, {142, 5268}, {144, 7262}, {145, 4865}, {165, 4862}, {192, 29839}, {193, 3791}, {200, 1738}, {210, 24789}, {238, 329}, {256, 26125}, {320, 3769}, {334, 7033}, {344, 3971}, {345, 726}, {348, 24215}, {350, 21590}, {354, 17720}, {377, 976}, {390, 17715}, {443, 5293}, {495, 30448}, {498, 3670}, {499, 3953}, {516, 3749}, {518, 3772}, {519, 4138}, {527, 1707}, {612, 5249}, {613, 15253}, {614, 908}, {740, 30699}, {748, 31018}, {846, 4419}, {894, 29634}, {896, 20078}, {936, 24178}, {940, 17602}, {978, 20498}, {986, 3085}, {988, 13411}, {1001, 4415}, {1086, 1376}, {1125, 13742}, {1279, 24703}, {1284, 23853}, {1329, 17054}, {1463, 3784}, {1647, 10584}, {1714, 5904}, {1722, 21075}, {1836, 3744}, {1961, 4648}, {1997, 4871}, {2345, 21101}, {2478, 28082}, {2550, 3961}, {2886, 3242}, {3008, 21060}, {3052, 17768}, {3086, 3976}, {3120, 3434}, {3218, 29665}, {3219, 29681}, {3436, 3924}, {3452, 5272}, {3474, 3550}, {3509, 7735}, {3616, 17697}, {3617, 28595}, {3618, 29654}, {3649, 5710}, {3662, 7081}, {3663, 13405}, {3666, 17718}, {3672, 17592}, {3673, 21609}, {3677, 5219}, {3703, 30811}, {3722, 20075}, {3740, 17278}, {3750, 10578}, {3757, 27184}, {3811, 23537}, {3821, 29670}, {3840, 28808}, {3868, 5230}, {3870, 3914}, {3873, 11269}, {3874, 5292}, {3875, 4028}, {3891, 3936}, {3911, 18193}, {3915, 11415}, {3920, 26032}, {3923, 29656}, {3967, 17279}, {3974, 29674}, {3989, 29661}, {3995, 29830}, {3999, 17728}, {4011, 21093}, {4039, 21281}, {4071, 17314}, {4104, 4384}, {4193, 28074}, {4220, 28081}, {4294, 24851}, {4295, 5255}, {4307, 17716}, {4334, 7365}, {4346, 5281}, {4417, 32922}, {4418, 29848}, {4424, 10056}, {4425, 29651}, {4640, 17276}, {4642, 10528}, {4650, 9965}, {4654, 5269}, {4655, 26245}, {4675, 4682}, {4694, 10072}, {4847, 16496}, {4859, 8580}, {4906, 5087}, {4920, 17170}, {4942, 17340}, {5046, 28086}, {5121, 5573}, {5218, 17596}, {5226, 17598}, {5250, 28027}, {5294, 29855}, {5297, 27186}, {5432, 17595}, {5435, 18201}, {5552, 24443}, {5698, 8616}, {5711, 6147}, {5718, 17599}, {5724, 11237}, {5739, 32914}, {5927, 14523}, {6327, 20045}, {6557, 26112}, {6646, 16996}, {6679, 26065}, {6700, 11512}, {6745, 24177}, {6919, 28080}, {6931, 28096}, {7080, 24440}, {7174, 25525}, {7191, 31053}, {7195, 18788}, {7290, 28609}, {7292, 27131}, {9318, 24321}, {9776, 17122}, {10327, 25957}, {10453, 30953}, {10580, 24217}, {11263, 30145}, {12647, 24222}, {12649, 21935}, {14548, 24241}, {14555, 16825}, {16020, 17123}, {17126, 17483}, {17127, 17484}, {17142, 27252}, {17150, 31034}, {17155, 17740}, {17184, 26034}, {17449, 29662}, {17469, 24725}, {17491, 20064}, {17605, 17721}, {17726, 17775}, {17776, 29632}, {17784, 24715}, {18134, 32926}, {18141, 29649}, {19649, 28107}, {19789, 32860}, {19843, 24161}, {19861, 23675}, {19993, 32844}, {20103, 24175}, {20254, 21333}, {20760, 21320}, {24046, 26364}, {24160, 26363}, {24597, 32912}, {25385, 29652}, {25760, 32923}, {26105, 29820}, {26129, 28016}, {26223, 26230}, {29638, 32930}, {29639, 31266}, {29658, 32913}, {29671, 30828}, {29866, 32849}, {30393, 31183}


X(33145) = X(1)X(11015)∩X(2)X(17593)

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

X(33145) lies on these lines: {1, 11015}, {2, 17593}, {10, 4980}, {31, 19785}, {38, 3663}, {42, 3782}, {75, 32776}, {81, 32857}, {141, 4365}, {149, 17598}, {190, 29850}, {192, 25957}, {239, 4683}, {244, 24210}, {321, 3821}, {345, 31237}, {516, 17469}, {527, 4722}, {536, 15523}, {726, 4972}, {740, 17184}, {748, 4000}, {752, 17150}, {756, 1738}, {899, 4415}, {902, 17061}, {968, 23681}, {986, 21935}, {1086, 3720}, {1111, 17874}, {1155, 29683}, {1836, 17017}, {1962, 5249}, {2292, 23537}, {2308, 17768}, {2796, 29654}, {2887, 17147}, {2895, 4716}, {3017, 4880}, {3058, 29818}, {3120, 3666}, {3175, 29687}, {3187, 4655}, {3210, 25760}, {3662, 32915}, {3673, 17871}, {3706, 17235}, {3712, 29865}, {3729, 26061}, {3739, 6536}, {3741, 4442}, {3772, 4414}, {3775, 17163}, {3824, 27577}, {3836, 3995}, {3844, 6535}, {3846, 17495}, {3875, 32852}, {3891, 4660}, {3920, 24715}, {3923, 32774}, {3925, 3989}, {3936, 4970}, {3944, 4850}, {3969, 28522}, {3993, 18139}, {4038, 26842}, {4042, 17255}, {4054, 31264}, {4085, 17165}, {4357, 21020}, {4358, 24169}, {4359, 4425}, {4360, 32949}, {4362, 32950}, {4363, 29647}, {4387, 17290}, {4388, 32924}, {4389, 31330}, {4398, 17155}, {4418, 19786}, {4427, 6679}, {4429, 32925}, {4440, 32940}, {4516, 21325}, {4642, 6735}, {4645, 20069}, {4649, 17483}, {4664, 29854}, {4676, 29852}, {4697, 29833}, {4743, 20011}, {5057, 29821}, {5256, 24725}, {5262, 24851}, {5294, 28526}, {5311, 5880}, {5695, 24943}, {6327, 32921}, {6646, 32864}, {6686, 30566}, {7226, 32865}, {11680, 17591}, {13097, 27628}, {16706, 32930}, {17156, 17274}, {17276, 32912}, {17302, 32772}, {17382, 29684}, {17490, 25960}, {17592, 31019}, {17595, 29662}, {17601, 29665}, {17769, 28599}, {17772, 20290}, {17889, 28606}, {19796, 24723}, {25453, 32933}, {25958, 32855}, {26034, 30699}, {26128, 32929}, {26840, 32919}, {27184, 32860}, {28516, 28595}, {28605, 32784}, {29631, 32939}, {32775, 32932}, {32922, 32947}, {32926, 32948}


X(33146) = X(1)X(11015)∩X(2)X(45)

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

X(33146) lies on these lines: {1, 11015}, {2, 45}, {6, 17483}, {7, 27}, {8, 17678}, {9, 26724}, {21, 24159}, {31, 32857}, {37, 27186}, {38, 17889}, {43, 32856}, {57, 15999}, {63, 4862}, {69, 19789}, {75, 17184}, {86, 17587}, {141, 28605}, {149, 17597}, {192, 18139}, {226, 4850}, {229, 14015}, {239, 32859}, {244, 3944}, {306, 1266}, {319, 19820}, {320, 3187}, {321, 3662}, {497, 3315}, {527, 26723}, {536, 32858}, {614, 5057}, {726, 25957}, {894, 32774}, {908, 24177}, {940, 26842}, {942, 1900}, {982, 3120}, {1111, 14213}, {1150, 26840}, {1155, 29665}, {1211, 7263}, {1255, 4648}, {1278, 3969}, {1463, 23155}, {1621, 24248}, {1738, 3681}, {1836, 7191}, {2476, 3670}, {2796, 29672}, {2886, 4392}, {2887, 17155}, {2895, 4361}, {2999, 31164}, {3008, 17781}, {3175, 3834}, {3210, 3936}, {3218, 3772}, {3219, 17276}, {3305, 4859}, {3434, 4310}, {3474, 26228}, {3578, 4741}, {3616, 4234}, {3661, 4980}, {3663, 5249}, {3666, 31019}, {3703, 25959}, {3712, 29866}, {3752, 31053}, {3757, 32950}, {3771, 32845}, {3816, 9335}, {3821, 32771}, {3836, 32925}, {3838, 4003}, {3868, 23537}, {3869, 23536}, {3873, 3914}, {3890, 23675}, {3891, 4645}, {3920, 5880}, {3925, 7226}, {3938, 24715}, {3946, 3982}, {3948, 24190}, {3971, 25961}, {3980, 32775}, {3995, 17234}, {4000, 5905}, {4193, 24046}, {4359, 27184}, {4383, 17484}, {4398, 17147}, {4417, 17495}, {4418, 26128}, {4429, 17165}, {4432, 29853}, {4441, 30965}, {4442, 10453}, {4640, 29681}, {4654, 5256}, {4655, 32914}, {4660, 32923}, {4672, 29852}, {4675, 17019}, {4683, 16825}, {4697, 29636}, {4854, 25557}, {4892, 29849}, {4972, 24349}, {5046, 17054}, {5180, 16483}, {5271, 17274}, {5278, 6646}, {5287, 6173}, {5333, 17321}, {5741, 17490}, {6063, 16727}, {6147, 19767}, {6327, 32922}, {6354, 21454}, {7232, 32863}, {7292, 24703}, {7321, 19786}, {7741, 24167}, {9965, 24597}, {10129, 24239}, {10404, 17016}, {11114, 30117}, {11246, 17061}, {11347, 30937}, {11351, 19738}, {11681, 24443}, {14450, 16466}, {15466, 17862}, {15808, 25056}, {16086, 17679}, {16610, 27131}, {16696, 17173}, {16700, 17174}, {16706, 26223}, {16753, 17182}, {17011, 17301}, {17127, 17768}, {17140, 32773}, {17160, 20017}, {17167, 18601}, {17235, 31993}, {17255, 19732}, {17278, 27065}, {17302, 19684}, {17323, 19701}, {17347, 19742}, {17361, 19831}, {17380, 19717}, {17593, 29678}, {17720, 27003}, {17740, 26132}, {18144, 28654}, {18201, 29662}, {19804, 26580}, {19822, 31995}, {20255, 31060}, {24165, 25760}, {24169, 32931}, {24325, 32776}, {24611, 28039}, {24725, 29821}, {24851, 28082}, {24988, 27538}, {25453, 32940}, {25527, 32779}, {26747, 28395}, {27180, 28022}, {29632, 32934}, {29642, 32936}, {29685, 31178}, {29850, 32935}, {31134, 32866}, {32920, 32948}, {32921, 32949}, {32924, 32946}


X(33147) = X(1)X(224)∩X(2)X(726)

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

X(33147) lies on these lines: {1, 224}, {2, 726}, {31, 32857}, {43, 4000}, {57, 29658}, {75, 26128}, {142, 1961}, {149, 29818}, {171, 1086}, {192, 29642}, {226, 29821}, {238, 3782}, {278, 4334}, {320, 3791}, {321, 29637}, {345, 29858}, {350, 21416}, {614, 3944}, {740, 19796}, {756, 26724}, {846, 3663}, {894, 29654}, {982, 3772}, {984, 24789}, {1054, 24177}, {1125, 7283}, {1215, 16706}, {1266, 29860}, {1376, 17725}, {1707, 4862}, {1738, 3961}, {1757, 26723}, {2308, 17483}, {2650, 26729}, {2664, 24790}, {2886, 17598}, {2887, 32866}, {3011, 17596}, {3120, 7191}, {3210, 3771}, {3242, 32865}, {3550, 26228}, {3662, 4362}, {3666, 29640}, {3677, 17064}, {3685, 29672}, {3744, 24715}, {3752, 17719}, {3755, 3979}, {3757, 3821}, {3836, 32926}, {3838, 17722}, {3891, 25957}, {3936, 32924}, {3967, 17356}, {3980, 29634}, {3995, 29851}, {4038, 25557}, {4359, 32775}, {4392, 24892}, {4398, 32934}, {4414, 29681}, {4415, 17123}, {4418, 26230}, {4425, 16823}, {4429, 32920}, {4442, 32943}, {4654, 16475}, {4671, 29677}, {4697, 7321}, {4854, 16484}, {4859, 5268}, {4968, 19879}, {4970, 29839}, {4972, 32923}, {5311, 27186}, {5880, 17716}, {5905, 16468}, {6679, 32939}, {6690, 17593}, {7009, 7194}, {7081, 24169}, {7262, 17276}, {7264, 21436}, {8616, 24248}, {10180, 17320}, {16825, 27184}, {17017, 31019}, {17056, 17600}, {17063, 17720}, {17117, 21085}, {17122, 17602}, {17140, 29631}, {17147, 29632}, {17150, 32949}, {17165, 29850}, {17184, 32914}, {17301, 17592}, {17469, 20292}, {17495, 29846}, {17594, 29675}, {17862, 23689}, {17884, 17888}, {18134, 32921}, {18139, 32928}, {19786, 24325}, {20045, 32948}, {20101, 24692}, {21241, 29840}, {24210, 29820}, {24231, 32913}, {24349, 25453}, {24542, 32936}, {24943, 28605}, {25525, 29657}, {25527, 32778}, {25959, 32854}, {26223, 29852}, {26627, 29847}, {27003, 29683}, {28808, 31242}, {29633, 32771}, {29638, 32929}, {29656, 32932}, {29869, 32849}, {30811, 32855}, {32856, 32911}


X(33148) = X(1)X(149)∩X(2)X(38)

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

X(33148) lies on these lines: {1, 149}, {2, 38}, {7, 109}, {8, 24159}, {11, 3315}, {31, 17483}, {57, 29665}, {63, 29681}, {65, 26729}, {81, 17061}, {88, 3035}, {100, 1086}, {106, 835}, {142, 5297}, {171, 26842}, {190, 24542}, {192, 29830}, {210, 26724}, {226, 1421}, {238, 17484}, {345, 29866}, {388, 977}, {595, 14450}, {596, 25645}, {612, 27186}, {614, 31053}, {651, 15253}, {726, 29632}, {748, 26792}, {750, 17725}, {846, 29689}, {894, 26230}, {902, 32857}, {908, 7292}, {942, 22321}, {1072, 18444}, {1125, 21093}, {1279, 5057}, {1290, 3446}, {1621, 3782}, {5262, 13407}, {1738, 3935}, {1769, 27545}, {1772, 3085}, {1909, 18066}, {2006, 5083}, {2887, 32923}, {2895, 32914}, {3011, 3218}, {3240, 4000}, {3475, 13576}, {3617, 26727}, {3662, 26227}, {3677, 29680}, {3681, 24789}, {3699, 24988}, {3722, 20095}, {3726, 17737}, {3744, 20292}, {3756, 31272}, {3757, 17184}, {3771, 17155}, {3772, 3873}, {3791, 20086}, {3836, 32927}, {3870, 23681}, {3874, 24883}, {3891, 18134}, {3896, 19796}, {3909, 25048}, {3914, 3957}, {3920, 5249}, {3923, 29638}, {3924, 20060}, {3936, 32842}, {3938, 17889}, {3953, 24160}, {3971, 29851}, {3980, 29848}, {4011, 29853}, {4088, 21180}, {4362, 32863}, {4414, 29675}, {4415, 5284}, {4418, 29656}, {4422, 4756}, {4427, 4440}, {4645, 20045}, {4675, 9347}, {4850, 17718}, {4892, 32844}, {4906, 17605}, {5046, 28082}, {5080, 30117}, {5154, 28074}, {5187, 28080}, {5272, 27131}, {5294, 29871}, {5573, 30852}, {5905, 17127}, {5992, 29838}, {6542, 31041}, {6679, 32940}, {7290, 31164}, {7336, 14513}, {9318, 24322}, {10129, 17721}, {11680, 17597}, {11681, 17054}, {11717, 24869}, {13257, 15251}, {14413, 21297}, {14986, 24030}, {16020, 31018}, {16823, 26580}, {17016, 21620}, {17024, 26098}, {17147, 29839}, {17150, 17778}, {17291, 26251}, {17302, 29822}, {17591, 29678}, {17602, 25557}, {17723, 26738}, {17776, 29870}, {17780, 24188}, {17954, 26110}, {18004, 24955}, {18139, 32926}, {21220, 30667}, {21320, 27628}, {23354, 27295}, {24046, 27529}, {24165, 29846}, {24171, 27385}, {24210, 29817}, {24695, 30653}, {25466, 27692}, {25525, 29664}, {25527, 29667}, {25531, 30566}, {25957, 32920}, {25958, 26132}, {29642, 32925}, {29651, 32776}, {29672, 32930}

X(33148) = anticomplement of X(33115)


X(33149) = X(1)X(528)∩X(2)X(17593)

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

X(33149) lies on these lines: {1, 528}, {2, 17593}, {6, 32857}, {7, 4649}, {10, 75}, {38, 32865}, {43, 3782}, {57, 1719}, {69, 4716}, {100, 17725}, {145, 4310}, {171, 19785}, {192, 3836}, {238, 4000}, {239, 4655}, {244, 24217}, {312, 24169}, {344, 31252}, {536, 29674}, {740, 3662}, {846, 24789}, {982, 3914}, {1054, 17720}, {1125, 17399}, {1155, 29658}, {1278, 3773}, {1633, 7301}, {1698, 4364}, {1721, 29291}, {1723, 1761}, {1757, 17276}, {1770, 16478}, {1836, 29821}, {1962, 27186}, {2486, 7741}, {2796, 4676}, {2886, 17591}, {2887, 3210}, {3011, 17601}, {3120, 4850}, {3122, 24046}, {3123, 24443}, {3240, 32856}, {3336, 16548}, {3416, 3631}, {3434, 17598}, {3550, 17061}, {3616, 16484}, {3617, 4407}, {3624, 4657}, {3644, 6541}, {3666, 17889}, {3670, 4443}, {3672, 7613}, {3696, 17235}, {3712, 29858}, {3731, 17303}, {3751, 4862}, {3752, 3944}, {3755, 24231}, {3759, 17770}, {3769, 19830}, {3772, 17596}, {3775, 17236}, {3790, 28516}, {3795, 20335}, {3826, 17246}, {3842, 17247}, {3844, 4686}, {3846, 17490}, {3875, 32846}, {3891, 32948}, {3923, 16706}, {3980, 19786}, {3993, 17234}, {3995, 25961}, {4003, 29676}, {4026, 7263}, {4085, 24349}, {4312, 16475}, {4359, 32776}, {4362, 19796}, {4363, 29633}, {4384, 24697}, {4415, 16569}, {4418, 32774}, {4425, 19804}, {4440, 32935}, {4442, 30942}, {4527, 17230}, {4660, 32922}, {4672, 17367}, {4684, 4780}, {4689, 29675}, {4710, 18144}, {4751, 25354}, {4854, 26102}, {4970, 18134}, {4972, 17155}, {5137, 5197}, {5222, 16477}, {5249, 17592}, {5695, 17290}, {6327, 32924}, {6650, 14621}, {7262, 26723}, {9352, 29683}, {11269, 18201}, {11814, 31233}, {13097, 28250}, {16468, 17366}, {16825, 24723}, {16830, 24693}, {17012, 24725}, {17017, 20292}, {17063, 24177}, {17147, 25957}, {17184, 32860}, {17231, 28484}, {17233, 28522}, {17325, 19856}, {17350, 17767}, {17353, 28526}, {17365, 28650}, {17370, 24295}, {17382, 29646}, {17400, 19878}, {17495, 25760}, {17594, 23681}, {19789, 26034}, {19877, 28604}, {24165, 32773}, {24174, 24456}, {25072, 31253}, {25453, 32939}, {25959, 32848}, {26030, 26976}, {26128, 32932}, {26840, 32853}, {28605, 32781}, {29850, 32933}, {31134, 32842}, {32914, 32950}


X(33150) = X(1)X(27186)∩X(2)X(37)

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

X(33150) lies on these lines: {1, 27186}, {2, 37}, {6, 17483}, {7, 2003}, {81, 1086}, {89, 278}, {100, 17061}, {142, 17019}, {145, 5100}, {149, 3914}, {226, 17012}, {239, 2895}, {267, 3337}, {277, 27789}, {320, 20086}, {329, 14997}, {497, 16063}, {553, 18625}, {726, 29850}, {908, 17020}, {1054, 29683}, {1104, 15680}, {1111, 30690}, {1203, 14450}, {1211, 4395}, {1255, 17245}, {1266, 5294}, {1269, 27320}, {1386, 20292}, {1738, 3920}, {2006, 26740}, {2308, 32857}, {2475, 5262}, {2550, 29815}, {2887, 32842}, {2999, 31053}, {3008, 27065}, {3120, 29821}, {3187, 3662}, {3218, 21376}, {3219, 3663}, {3434, 17024}, {3474, 30652}, {3578, 17273}, {3670, 24883}, {3744, 20095}, {3755, 3957}, {3759, 32859}, {3782, 17366}, {3821, 32914}, {3836, 32928}, {3875, 32858}, {3891, 4429}, {3923, 29852}, {3945, 15474}, {3946, 5249}, {3969, 17160}, {3980, 29636}, {3993, 29851}, {4085, 32923}, {4310, 4430}, {4346, 20078}, {4353, 25006}, {4360, 18139}, {4361, 32782}, {4365, 29637}, {4383, 26792}, {4389, 5278}, {4398, 32933}, {4418, 29654}, {4442, 32942}, {4645, 17150}, {4683, 4974}, {4854, 5284}, {4859, 5287}, {4970, 29632}, {4972, 32922}, {5180, 5315}, {5222, 5905}, {5256, 23681}, {5271, 17304}, {5286, 26793}, {5333, 17045}, {5712, 17013}, {6539, 10159}, {6542, 26978}, {6646, 19742}, {6679, 32845}, {7292, 24210}, {8025, 26806}, {16704, 26840}, {16718, 18600}, {16750, 23989}, {16752, 29586}, {16825, 32776}, {16826, 24790}, {17016, 23536}, {17017, 17889}, {17021, 17067}, {17025, 26098}, {17064, 29680}, {17127, 24248}, {17155, 25453}, {17167, 17761}, {17255, 19723}, {17323, 19732}, {17367, 26223}, {17373, 20046}, {17380, 19684}, {17469, 24715}, {17591, 24892}, {17594, 29681}, {17676, 19851}, {17763, 24169}, {19767, 24159}, {20174, 27270}, {20237, 28813}, {24165, 29631}, {24176, 25441}, {24177, 27003}, {24470, 31901}, {25957, 32921}, {26060, 30142}, {26128, 32860}, {26230, 32932}, {26627, 29841}, {26801, 27163}, {27299, 31060}, {31237, 32855}


X(33151) = X(1)X(535)∩X(2)X(45)

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

X(33151) lies on these lines: {1, 535}, {2, 45}, {6, 17484}, {8, 4442}, {11, 4392}, {37, 27127}, {38, 3944}, {55, 13589}, {75, 26580}, {76, 321}, {79, 30142}, {81, 4644}, {100, 24248}, {141, 4671}, {144, 24597}, {149, 3242}, {192, 3936}, {218, 329}, {226, 17080}, {229, 27802}, {279, 1255}, {312, 17184}, {345, 30831}, {612, 20292}, {726, 25760}, {750, 32857}, {756, 17889}, {896, 29658}, {902, 17725}, {908, 3663}, {940, 17483}, {976, 24851}, {982, 1647}, {984, 3120}, {986, 11681}, {1150, 6646}, {1211, 4665}, {1215, 32776}, {1836, 3920}, {1999, 32859}, {2886, 7226}, {2887, 4439}, {3175, 32858}, {3210, 5741}, {3218, 17276}, {3219, 3772}, {3305, 23681}, {3306, 4862}, {3315, 4310}, {3616, 13735}, {3618, 19823}, {3662, 4358}, {3666, 31053}, {3670, 4193}, {3681, 3914}, {3683, 29681}, {3703, 25958}, {3729, 32779}, {3752, 27131}, {3758, 29833}, {3771, 32936}, {3797, 27476}, {3821, 21093}, {3826, 9330}, {3838, 29664}, {3846, 17155}, {3869, 13161}, {3873, 24210}, {3876, 23537}, {3891, 4388}, {3923, 32775}, {3927, 24883}, {3932, 25959}, {3943, 30991}, {3952, 4429}, {3967, 29679}, {3971, 25957}, {3994, 29674}, {3995, 18134}, {4000, 31018}, {4003, 5087}, {4054, 4357}, {4360, 31034}, {4362, 4683}, {4383, 26792}, {4398, 5233}, {4407, 31330}, {4414, 17719}, {4417, 17147}, {4425, 32771}, {4432, 29638}, {4640, 29665}, {4650, 29683}, {4654, 5287}, {4655, 17763}, {4656, 5249}, {4660, 32927}, {4672, 29636}, {4675, 17021}, {4676, 26230}, {4679, 7292}, {4697, 29847}, {4703, 32914}, {4708, 31993}, {4854, 17018}, {4892, 29643}, {4972, 32937}, {5047, 24159}, {5224, 31025}, {5230, 11684}, {5235, 17257}, {5241, 7263}, {5256, 28609}, {5273, 31204}, {5297, 5880}, {5333, 16050}, {5698, 26228}, {5711, 14450}, {5718, 17246}, {5739, 17152}, {6327, 32926}, {6702, 24223}, {7081, 32950}, {7191, 24703}, {7321, 26627}, {10129, 29639}, {11320, 19684}, {14555, 19789}, {14996, 17365}, {14997, 17366}, {16696, 17174}, {16704, 17347}, {17012, 17301}, {17013, 17395}, {17061, 17127}, {17126, 17602}, {17165, 32773}, {17182, 18601}, {17233, 31017}, {17234, 31035}, {17235, 30818}, {17262, 30811}, {17449, 24217}, {17461, 24222}, {17579, 30115}, {17605, 29680}, {17776, 26132}, {17778, 20349}, {18074, 25259}, {18139, 29572}, {19786, 26223}, {19822, 31247}, {21334, 23155}, {21997, 30905}, {24165, 25960}, {24296, 27950}, {24723, 26227}, {24789, 27065}, {24821, 29861}, {25453, 32938}, {26128, 32930}, {27064, 29630}, {29631, 32935}, {29635, 32940}, {29659, 31161}, {29846, 32934}, {30964, 30967}, {31134, 32847}, {32843, 32921}, {32920, 32947}, {32928, 32946}


X(33152) = X(1)X(4)∩X(2)X(726)

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

X(33152) lies on these lines: {1, 4}, {2, 726}, {11, 17598}, {43, 19785}, {55, 17725}, {63, 29658}, {81, 32856}, {171, 3782}, {190, 6679}, {192, 3771}, {238, 4415}, {312, 26128}, {321, 23689}, {329, 16468}, {612, 17889}, {846, 3011}, {894, 29645}, {908, 29821}, {968, 29675}, {982, 17720}, {984, 3772}, {986, 26446}, {1086, 17122}, {1215, 19786}, {1447, 3663}, {1836, 17716}, {1961, 5249}, {2308, 17484}, {2887, 32847}, {3120, 3920}, {3218, 29683}, {3550, 9778}, {3662, 29649}, {3666, 17719}, {3685, 29656}, {3750, 4854}, {3757, 4425}, {3769, 4655}, {3821, 7081}, {3846, 32922}, {3891, 25760}, {3914, 3961}, {3923, 29634}, {3936, 32928}, {3952, 29850}, {3993, 29839}, {3995, 29632}, {4000, 16569}, {4080, 29834}, {4135, 17280}, {4201, 8669}, {4353, 10171}, {4362, 27184}, {4385, 19879}, {4389, 32916}, {4392, 29662}, {4414, 29665}, {4417, 32921}, {4442, 32945}, {4650, 17276}, {4671, 24943}, {4972, 32927}, {5057, 17469}, {5205, 24169}, {5255, 28174}, {5266, 24851}, {5268, 23681}, {5293, 23537}, {5294, 29859}, {5311, 31019}, {5432, 17593}, {5718, 17600}, {5741, 32924}, {6685, 17302}, {6690, 17246}, {7174, 17064}, {7226, 24892}, {8616, 26228}, {11533, 24987}, {13097, 28353}, {16475, 28609}, {17017, 31053}, {17140, 29845}, {17147, 29846}, {17150, 32843}, {17165, 29631}, {17184, 17763}, {17592, 17718}, {17597, 24217}, {17599, 17717}, {17605, 17722}, {17776, 29858}, {17795, 20498}, {19684, 24267}, {19852, 21077}, {19856, 31993}, {20045, 32947}, {21093, 27064}, {24349, 29635}, {25453, 32937}, {25527, 29674}, {25958, 32854}, {26223, 29636}, {26227, 32776}, {26230, 32930}, {26580, 32914}, {28606, 29640}, {29657, 31266}, {29848, 32929}, {29851, 31035}, {29865, 32849}, {30831, 32848}, {31237, 32862}, {32773, 32920}, {32774, 32931}


X(33153) = X(1)X(5046)∩X(2)X(38)

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

X(33153) lies on these lines: {1, 5046}, {2, 38}, {8, 3454}, {9, 29681}, {31, 17484}, {55, 13589}, {63, 29665}, {81, 17602}, {100, 3782}, {149, 3938}, {171, 17483}, {226, 3920}, {238, 26792}, {329, 17127}, {344, 29870}, {612, 31019}, {614, 27131}, {726, 29846}, {750, 26842}, {908, 7191}, {976, 2475}, {1621, 4415}, {2887, 32927}, {2895, 4362}, {3011, 3219}, {3120, 3961}, {3240, 19785}, {3242, 11680}, {3315, 3816}, {3452, 7292}, {3475, 29814}, {3670, 27529}, {3677, 30852}, {3681, 3772}, {3703, 30831}, {3717, 29873}, {3740, 26724}, {3744, 5057}, {3757, 26580}, {3769, 32859}, {3771, 32849}, {3812, 26729}, {3846, 32923}, {3873, 17720}, {3891, 4417}, {3914, 3935}, {3923, 29848}, {3936, 32926}, {3957, 24210}, {3971, 29632}, {3989, 29640}, {3995, 29839}, {3996, 4442}, {4011, 29638}, {4090, 29850}, {4388, 20045}, {4419, 24323}, {4420, 23537}, {4430, 11269}, {5219, 29680}, {5249, 5297}, {5262, 21077}, {5264, 14450}, {5268, 27186}, {5269, 31164}, {5294, 29874}, {5741, 32922}, {5904, 24883}, {5905, 17126}, {6542, 31023}, {6679, 32938}, {7081, 17184}, {7174, 29664}, {9780, 24159}, {10327, 25959}, {17061, 32911}, {17316, 31050}, {17353, 29871}, {17491, 20101}, {17716, 24725}, {17718, 28606}, {17763, 32863}, {17776, 29866}, {20056, 28599}, {20066, 24851}, {21060, 26723}, {21093, 29656}, {24068, 25645}, {24231, 27003}, {24695, 30652}, {25527, 29679}, {25760, 32920}, {26098, 29815}, {26131, 30142}, {26223, 29634}, {26227, 27184}, {26230, 27064}, {29588, 31062}, {29658, 32912}, {29670, 32776}, {29683, 32913}, {30811, 32862}

X(33153) = anticomplement of X(33119)


X(33154) = X(1)X(30)∩X(2)X(17593)

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

X(33154) lies on these lines: {1, 30}, {2, 17593}, {7, 4038}, {11, 17591}, {37, 17889}, {43, 4415}, {55, 17725}, {75, 4425}, {171, 3474}, {190, 25453}, {192, 2887}, {226, 17592}, {238, 19785}, {239, 4703}, {256, 2997}, {312, 3821}, {321, 32776}, {497, 17598}, {516, 17716}, {536, 32778}, {612, 24715}, {726, 32773}, {740, 27184}, {846, 3772}, {940, 32857}, {982, 3663}, {984, 3914}, {986, 1737}, {1086, 26102}, {1699, 17722}, {1738, 4656}, {1961, 5880}, {1962, 31019}, {1999, 4655}, {2796, 29645}, {2886, 17246}, {3120, 28606}, {3175, 29674}, {3187, 4683}, {3210, 3846}, {3550, 17602}, {3666, 3944}, {3672, 17600}, {3685, 26128}, {3729, 32780}, {3741, 4389}, {3750, 10578}, {3790, 28595}, {3838, 29657}, {3844, 22034}, {3875, 32861}, {3891, 32947}, {3923, 19786}, {3971, 4429}, {3993, 18134}, {3994, 29679}, {3995, 25957}, {4000, 17123}, {4011, 16706}, {4085, 32937}, {4335, 8255}, {4360, 32946}, {4362, 24723}, {4365, 32782}, {4387, 29637}, {4388, 32921}, {4398, 24165}, {4417, 4970}, {4440, 29837}, {4442, 31330}, {4640, 29658}, {4649, 5905}, {4660, 32926}, {4664, 29653}, {4671, 32781}, {4676, 29654}, {4697, 29841}, {4716, 5739}, {4743, 20012}, {4972, 32925}, {5057, 17017}, {5271, 24697}, {5311, 20292}, {5695, 32783}, {5794, 11533}, {6327, 32928}, {6646, 32853}, {8616, 17061}, {9345, 26842}, {10129, 29688}, {13161, 31397}, {16825, 19796}, {17011, 24725}, {17018, 32856}, {17147, 25760}, {17184, 32915}, {17248, 27798}, {17276, 32913}, {17301, 24703}, {17302, 25496}, {17320, 29644}, {17394, 23812}, {17495, 25960}, {17594, 17719}, {17596, 17720}, {17763, 32950}, {18743, 24169}, {25958, 32848}, {25961, 31035}, {26580, 32860}, {29631, 32933}, {29635, 32939}, {29829, 32940}, {31237, 32849}, {32774, 32930}, {32775, 32929}


X(33155) = X(1)X(149)∩X(2)X(37)

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

X(33155) lies on these lines: {1, 149}, {2, 37}, {6, 17484}, {7, 14996}, {81, 3782}, {83, 4080}, {89, 4346}, {100, 17602}, {142, 17021}, {145, 5015}, {226, 7269}, {239, 26580}, {278, 6994}, {497, 7391}, {551, 4956}, {726, 29631}, {740, 32775}, {894, 29833}, {908, 3946}, {940, 26842}, {968, 29681}, {1068, 11036}, {1150, 4389}, {1211, 4399}, {1386, 5057}, {1449, 31164}, {1621, 4854}, {1738, 5297}, {1862, 12433}, {1999, 10452}, {2177, 17725}, {2887, 32928}, {2895, 3187}, {2999, 27131}, {3218, 3663}, {3434, 29815}, {3452, 17020}, {3685, 26230}, {3745, 20292}, {3755, 3935}, {3769, 32950}, {3791, 4683}, {3821, 17763}, {3846, 32924}, {3891, 32773}, {3914, 3920}, {3923, 29636}, {3936, 4360}, {3944, 17017}, {3971, 29850}, {3980, 29847}, {3993, 29632}, {4011, 29852}, {4054, 17023}, {4085, 32927}, {4353, 26015}, {4362, 32776}, {4364, 5235}, {4365, 32783}, {4388, 17150}, {4392, 11269}, {4393, 31034}, {4395, 5241}, {4414, 29658}, {4415, 26792}, {4418, 29645}, {4419, 24597}, {4425, 32914}, {4442, 5263}, {4445, 32782}, {4649, 32856}, {4654, 18625}, {4656, 26723}, {4741, 31303}, {4858, 28836}, {4970, 29846}, {4972, 32926}, {5046, 5262}, {5222, 5526}, {5249, 17019}, {5256, 31053}, {5266, 20066}, {5287, 23681}, {5311, 17889}, {5698, 30653}, {5718, 17395}, {5791, 24898}, {5880, 9347}, {6147, 31902}, {6542, 24281}, {6646, 16704}, {6679, 32936}, {7191, 24210}, {7264, 18359}, {8543, 15253}, {10129, 17723}, {11680, 17599}, {13161, 17016}, {15474, 27789}, {16719, 18600}, {16752, 29592}, {17064, 29664}, {17126, 24248}, {17140, 29837}, {17155, 29635}, {17160, 30832}, {17316, 31041}, {17318, 30811}, {17362, 31143}, {17367, 30578}, {17591, 29662}, {17594, 29665}, {17596, 29683}, {19740, 29586}, {20086, 32859}, {20170, 27252}, {24165, 29845}, {24349, 29829}, {24790, 29578}, {25453, 32925}, {25527, 32858}, {25760, 32842}, {26100, 29591}, {26128, 32915}, {26978, 29569}, {27804, 29839}, {29588, 31029}, {29634, 32929}, {29654, 32930}


X(33156) = X(1)X(32779)∩X(2)X(740)

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

X(33156) lies on these lines: {1, 32779}, {2, 740}, {6, 4062}, {8, 3722}, {10, 2177}, {31, 306}, {38, 345}, {42, 26061}, {55, 15523}, {69, 896}, {75, 29632}, {100, 29674}, {141, 3712}, {165, 29043}, {171, 32858}, {192, 32775}, {193, 4938}, {244, 17740}, {312, 17871}, {321, 3771}, {346, 3994}, {405, 20653}, {516, 31134}, {748, 3687}, {750, 3912}, {756, 17776}, {846, 32782}, {874, 30632}, {899, 17279}, {902, 3416}, {964, 3178}, {976, 3695}, {984, 32849}, {1155, 17231}, {1376, 29687}, {1621, 32778}, {1724, 21081}, {2049, 27577}, {2321, 3011}, {2550, 21026}, {2887, 17764}, {2895, 7262}, {3006, 32941}, {3120, 5695}, {3187, 6679}, {3630, 4831}, {3661, 32917}, {3662, 32845}, {3666, 24943}, {3685, 25760}, {3703, 3938}, {3704, 3924}, {3705, 32943}, {3706, 24892}, {3729, 32856}, {3744, 32854}, {3750, 29667}, {3752, 29677}, {3755, 30768}, {3759, 14459}, {3772, 4365}, {3773, 26227}, {3782, 28556}, {3790, 32927}, {3791, 20017}, {3844, 4689}, {3875, 29855}, {3886, 29857}, {3891, 29656}, {3896, 25453}, {3914, 20106}, {3923, 3936}, {3943, 17602}, {3944, 30831}, {3961, 32862}, {3969, 4362}, {3980, 18139}, {4011, 5741}, {4023, 4422}, {4028, 5294}, {4359, 29642}, {4360, 29636}, {4413, 17267}, {4417, 32930}, {4418, 18134}, {4427, 4655}, {4438, 17135}, {4650, 32863}, {4671, 17719}, {4672, 31034}, {4676, 32843}, {4703, 31037}, {4706, 17356}, {4722, 26065}, {4850, 29637}, {4970, 32774}, {5192, 17748}, {5205, 17268}, {5263, 29643}, {5278, 21085}, {6327, 28494}, {6745, 23529}, {7191, 32855}, {8013, 19732}, {11319, 27558}, {16825, 24542}, {17018, 32780}, {17126, 32846}, {17127, 32861}, {17147, 26128}, {17184, 32934}, {17233, 17763}, {17280, 32931}, {17281, 17718}, {17286, 29828}, {17594, 32781}, {17599, 29686}, {17600, 29648}, {17717, 27757}, {19804, 29851}, {24325, 29830}, {24552, 29671}, {24715, 25959}, {24789, 29869}, {24931, 27785}, {25385, 30834}, {25957, 32932}, {26230, 32921}, {27184, 32936}, {28605, 29866}, {28606, 32783}, {29634, 32928}, {29638, 32922}, {29641, 32945}, {29661, 31993}, {29839, 32771}, {29848, 32926}, {29849, 32942}, {29873, 32865}, {30942, 32851}


X(33157) = X(1)X(26061)∩X(2)X(37)

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

X(33157) lies on these lines: {1, 26061}, {2, 37}, {6, 32858}, {8, 13742}, {9, 21367}, {10, 1621}, {11, 29872}, {31, 29674}, {38, 29637}, {44, 2895}, {55, 29679}, {63, 17284}, {81, 3912}, {100, 5310}, {141, 3219}, {171, 29687}, {190, 17184}, {238, 15523}, {239, 3969}, {306, 16470}, {319, 19742}, {333, 17285}, {672, 30965}, {740, 29850}, {748, 32778}, {756, 32783}, {846, 32781}, {894, 18139}, {908, 20106}, {940, 17267}, {968, 1698}, {982, 29677}, {984, 24943}, {1001, 29667}, {1211, 2503}, {1214, 28780}, {1215, 29632}, {1376, 1995}, {1836, 25959}, {1861, 4233}, {1962, 29633}, {1999, 17268}, {2308, 32846}, {2321, 26723}, {2886, 29873}, {2887, 5057}, {3006, 32942}, {3187, 17233}, {3246, 4914}, {3416, 17127}, {3578, 17287}, {3589, 17011}, {3661, 5278}, {3662, 32933}, {3683, 3844}, {3685, 4972}, {3695, 5262}, {3703, 7191}, {3704, 25992}, {3720, 32780}, {3757, 24542}, {3759, 20017}, {3771, 32931}, {3773, 32914}, {3782, 17340}, {3790, 3891}, {3821, 32936}, {3831, 11688}, {3834, 26842}, {3836, 4418}, {3920, 3932}, {3923, 20292}, {3936, 27064}, {3944, 31237}, {3971, 32775}, {3974, 26228}, {3980, 25961}, {4011, 25760}, {4202, 7283}, {4363, 27186}, {4429, 32929}, {4432, 28595}, {4438, 30942}, {4445, 19723}, {4514, 31079}, {4641, 17231}, {4653, 19867}, {4672, 32949}, {4676, 6327}, {5016, 17697}, {5044, 24933}, {5233, 26688}, {5249, 17355}, {5271, 17286}, {5333, 5750}, {5739, 26685}, {5955, 19877}, {6057, 17061}, {6541, 29654}, {6679, 17763}, {6703, 17021}, {7270, 11319}, {7411, 12618}, {7795, 27006}, {8025, 17317}, {9591, 25440}, {11680, 29857}, {16468, 32852}, {16484, 29685}, {16585, 24036}, {17019, 17243}, {17274, 25734}, {17283, 32939}, {17293, 19732}, {17339, 27184}, {17350, 32859}, {17351, 17483}, {17354, 18134}, {17368, 19684}, {17374, 20086}, {17469, 32847}, {17592, 29663}, {17599, 29666}, {17600, 29684}, {17602, 29874}, {17718, 29866}, {17719, 29865}, {17911, 17912}, {24169, 32845}, {24210, 30768}, {24295, 29653}, {24325, 29851}, {24552, 29641}, {24597, 34255}, {24598, 30110}, {24635, 28769}, {24703, 25958}, {25453, 32915}, {25496, 29643}, {26044, 29591}, {26065, 29579}, {26128, 32925}, {26230, 32926}, {27040, 27068}, {29638, 32920}, {29640, 31264}, {29642, 32771}, {29656, 32927}, {29671, 32944}, {29672, 32923}, {29673, 32943}, {29821, 32848}, {29852, 32921}, {30811, 31053}


X(33158) = X(1)X(3695)∩X(2)X(740)

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

X(33158) lies on these lines: {1, 3695}, {2, 740}, {8, 17715}, {10, 3750}, {31, 32846}, {37, 32783}, {38, 32849}, {43, 17279}, {55, 29674}, {69, 7262}, {75, 29642}, {100, 29687}, {141, 846}, {171, 3912}, {192, 26128}, {238, 306}, {312, 3771}, {321, 29632}, {345, 982}, {597, 1051}, {614, 32855}, {874, 30631}, {896, 32863}, {968, 32784}, {984, 17776}, {1001, 32778}, {1125, 17600}, {1215, 17280}, {1279, 32866}, {1376, 17267}, {1621, 15523}, {1707, 17296}, {1961, 17243}, {1999, 6679}, {2177, 29679}, {2886, 29862}, {2887, 3685}, {3006, 32943}, {3178, 13740}, {3416, 8616}, {3661, 19224}, {3662, 32934}, {3666, 29637}, {3679, 10389}, {3687, 17123}, {3712, 17596}, {3720, 32779}, {3744, 32847}, {3757, 3773}, {3769, 17240}, {3772, 29858}, {3790, 32920}, {3791, 6542}, {3817, 27759}, {3836, 32932}, {3840, 32851}, {3886, 32865}, {3891, 29638}, {3896, 29850}, {3914, 4693}, {3923, 18134}, {3932, 3961}, {3936, 32930}, {3938, 32862}, {3943, 17061}, {3944, 4387}, {3966, 15485}, {3969, 24542}, {3971, 17264}, {3980, 17234}, {3993, 19786}, {3995, 32775}, {4011, 4417}, {4028, 17353}, {4062, 32911}, {4104, 25101}, {4358, 29846}, {4359, 29851}, {4360, 29654}, {4362, 17233}, {4365, 29869}, {4388, 4432}, {4418, 18139}, {4438, 10453}, {4640, 17231}, {4649, 5294}, {4671, 29866}, {4672, 17778}, {4676, 32946}, {4683, 31017}, {4697, 17300}, {4716, 26723}, {4850, 29677}, {4966, 32913}, {4970, 16706}, {5047, 20653}, {5263, 29653}, {5695, 17889}, {6057, 17724}, {6535, 29689}, {6541, 29656}, {7081, 17268}, {7191, 32848}, {13741, 17748}, {17018, 26061}, {17063, 17740}, {17127, 32852}, {17184, 32936}, {17242, 29634}, {17269, 29675}, {17277, 21085}, {17283, 24169}, {17284, 17594}, {17599, 29660}, {17601, 29579}, {17722, 29671}, {19792, 24161}, {19796, 28522}, {19815, 20106}, {20182, 29646}, {24552, 29643}, {24697, 32782}, {24715, 25957}, {24931, 27784}, {24943, 28606}, {26230, 32928}, {28605, 29870}, {29641, 32941}, {29672, 32922}, {29830, 32771}


X(33159) = X(1)X(3589)∩X(2)X(38)

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

X(33159) lies on these lines: {1, 3589}, {2, 38}, {5, 6211}, {6, 29674}, {8, 4974}, {9, 46}, {10, 82}, {11, 29861}, {31, 29679}, {37, 29633}, {43, 32777}, {44, 3844}, {81, 29687}, {141, 1757}, {142, 31252}, {171, 5294}, {190, 3821}, {210, 32783}, {239, 3773}, {256, 26030}, {312, 25453}, {321, 29850}, {518, 17357}, {726, 16706}, {740, 17280}, {748, 29667}, {894, 3836}, {899, 32779}, {908, 30768}, {960, 19879}, {983, 5192}, {1001, 29659}, {1125, 3717}, {1376, 7295}, {1386, 32847}, {1423, 24914}, {1716, 5955}, {1738, 17355}, {2321, 4716}, {2887, 27064}, {2999, 32855}, {3006, 17722}, {3219, 32781}, {3242, 29660}, {3416, 16468}, {3624, 7174}, {3634, 4357}, {3661, 20142}, {3662, 32935}, {3679, 7290}, {3681, 24943}, {3685, 4085}, {3696, 17359}, {3703, 29821}, {3751, 17284}, {3755, 4693}, {3763, 5220}, {3775, 17292}, {3790, 17367}, {3864, 24256}, {3873, 29677}, {3891, 29852}, {3912, 4649}, {3923, 4429}, {3971, 19786}, {3977, 17593}, {3993, 17264}, {4011, 32773}, {4026, 4422}, {4073, 5552}, {4078, 17023}, {4358, 29631}, {4360, 6541}, {4363, 25357}, {4383, 32778}, {4388, 28595}, {4413, 24320}, {4439, 29630}, {4473, 9791}, {4645, 4672}, {4650, 26065}, {4655, 17350}, {4660, 4676}, {4663, 17231}, {4722, 32863}, {4753, 29587}, {4851, 28650}, {4972, 32930}, {5044, 28275}, {5251, 19867}, {5284, 29685}, {5293, 17698}, {5480, 18788}, {5625, 29569}, {5718, 29862}, {5772, 16020}, {5791, 27626}, {5847, 16477}, {6210, 26446}, {6679, 7081}, {7083, 9709}, {7262, 26034}, {9441, 12618}, {9780, 25611}, {10022, 19876}, {10327, 17716}, {12782, 30107}, {15481, 17237}, {15523, 32861}, {16823, 31289}, {16825, 17352}, {17012, 32848}, {17017, 32862}, {17121, 17772}, {17184, 32938}, {17257, 19877}, {17288, 17771}, {17351, 32857}, {17385, 19856}, {17592, 17776}, {17602, 29859}, {17717, 29857}, {17718, 29858}, {17720, 29856}, {17724, 29860}, {17725, 29855}, {17728, 31242}, {18147, 20083}, {18743, 29635}, {19684, 29854}, {19846, 24161}, {20601, 25365}, {24169, 32939}, {24725, 25959}, {24883, 24958}, {25010, 26699}, {25441, 25660}, {25496, 29641}, {25957, 26223}, {25960, 26688}, {26115, 27032}, {26230, 32927}, {26251, 32917}, {28606, 29663}, {29654, 32926}, {29673, 32942}, {31053, 31237}, {31079, 32844}, {32774, 32925}


X(33160) = X(1)X(3704)∩X(2)X(740)

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

X(33160) lies on these lines: {1, 3704}, {2, 740}, {8, 4438}, {10, 1043}, {21, 20653}, {31, 32861}, {42, 32779}, {43, 32777}, {55, 32778}, {58, 21081}, {69, 4650}, {75, 3771}, {81, 4062}, {100, 15523}, {141, 17596}, {165, 1503}, {171, 306}, {238, 3687}, {239, 6679}, {321, 17719}, {333, 8298}, {345, 984}, {594, 6690}, {744, 27490}, {750, 32858}, {756, 32849}, {846, 1211}, {874, 7018}, {896, 2895}, {982, 17740}, {1010, 3178}, {1330, 24850}, {1376, 19329}, {1698, 1834}, {1738, 20106}, {1758, 26942}, {2177, 29667}, {2784, 10164}, {2887, 24715}, {3006, 32945}, {3120, 30831}, {3158, 3679}, {3210, 26128}, {3240, 26061}, {3416, 3550}, {3454, 24851}, {3475, 31178}, {3661, 32916}, {3666, 32783}, {3685, 3846}, {3695, 5293}, {3703, 3961}, {3705, 32941}, {3741, 32851}, {3743, 24931}, {3744, 32866}, {3752, 29637}, {3773, 7081}, {3891, 29848}, {3896, 29631}, {3912, 17122}, {3920, 32848}, {3923, 4417}, {3925, 29862}, {3936, 4418}, {3944, 5695}, {3966, 8616}, {3969, 17763}, {3980, 18134}, {3996, 29673}, {4011, 5233}, {4028, 4649}, {4359, 29632}, {4360, 29645}, {4413, 21919}, {4414, 32782}, {4425, 30832}, {4427, 4683}, {4451, 17280}, {4646, 19879}, {4647, 24161}, {4693, 24210}, {4697, 17778}, {4850, 24943}, {4918, 11533}, {4938, 20086}, {4970, 19786}, {5235, 8013}, {5263, 29671}, {5739, 7262}, {5741, 32930}, {6536, 31247}, {6685, 17289}, {11115, 27558}, {13740, 17748}, {14005, 27577}, {16569, 17279}, {17056, 24342}, {17126, 32852}, {17147, 32775}, {17184, 32845}, {17233, 29649}, {17469, 32842}, {17594, 32784}, {17601, 26034}, {17722, 24552}, {17728, 31137}, {17799, 25432}, {17889, 30811}, {18698, 25664}, {19804, 29642}, {19854, 31327}, {24325, 29839}, {24589, 29851}, {24789, 29858}, {25760, 32929}, {26230, 32924}, {26580, 32936}, {26724, 29869}, {27096, 28772}, {27184, 32934}, {29634, 32921}, {29640, 31993}, {29656, 32922}, {29857, 32865}


X(33161) = X(1)X(32849)∩X(2)X(726)

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

X(33161) lies on these lines: {1, 32849}, {2, 726}, {6, 32848}, {8, 902}, {10, 3977}, {11, 17340}, {31, 3703}, {38, 24943}, {42, 345}, {57, 29687}, {63, 15523}, {171, 32862}, {190, 25760}, {192, 29631}, {244, 17279}, {306, 32912}, {312, 29662}, {321, 4438}, {344, 30950}, {346, 11269}, {750, 3932}, {846, 29667}, {894, 29643}, {896, 3416}, {899, 17740}, {968, 29685}, {982, 29677}, {984, 32779}, {1150, 3773}, {1215, 29678}, {1468, 3695}, {2177, 3712}, {2308, 26065}, {2345, 30970}, {2887, 17767}, {3006, 3923}, {3120, 3729}, {3210, 29850}, {3218, 29674}, {3219, 32778}, {3663, 30768}, {3666, 26061}, {3679, 15677}, {3705, 32930}, {3720, 17776}, {3751, 4062}, {3771, 17165}, {3782, 31237}, {3790, 17763}, {3891, 6679}, {3914, 28557}, {3936, 32935}, {3944, 29872}, {3969, 32853}, {3993, 29829}, {3994, 17720}, {3995, 29635}, {4003, 17357}, {4392, 29637}, {4417, 32938}, {4418, 29641}, {4422, 17125}, {4427, 4660}, {4429, 32845}, {4641, 32852}, {4676, 32844}, {4860, 17267}, {4972, 32934}, {5294, 17017}, {5300, 24850}, {5880, 21026}, {6327, 28508}, {6535, 11679}, {7226, 32783}, {9345, 17243}, {14439, 17281}, {16468, 32842}, {17126, 32847}, {17127, 32866}, {17140, 29642}, {17147, 25453}, {17233, 32919}, {17280, 30942}, {17350, 32843}, {17351, 24725}, {17354, 32944}, {17355, 29639}, {17596, 29679}, {17718, 31161}, {17768, 31134}, {17889, 29873}, {18134, 32940}, {19785, 29867}, {24349, 29632}, {25957, 32939}, {25959, 32857}, {26223, 29671}, {27064, 29849}, {28595, 32950}, {28606, 29647}, {29661, 32771}, {29673, 32929}, {29846, 32937}, {29862, 31019}, {30811, 32856}, {32773, 32936}, {32851, 32931}, {32855, 32911}, {32858, 32913}


X(33162) = X(1)X(26061)∩X(2)X(17598)

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

X(33162) lies on these lines: {1, 26061}, {2, 17598}, {6, 32854}, {8, 31}, {10, 38}, {37, 29685}, {42, 3703}, {44, 4914}, {63, 484}, {81, 32847}, {190, 32947}, {226, 31161}, {321, 29673}, {345, 2177}, {354, 29687}, {518, 15523}, {519, 3969}, {537, 17184}, {594, 672}, {612, 4901}, {726, 4972}, {750, 10327}, {752, 28599}, {756, 3717}, {896, 3626}, {902, 4030}, {982, 29679}, {984, 29667}, {1109, 4712}, {1215, 3006}, {1707, 4668}, {2239, 4651}, {2308, 5846}, {2887, 17165}, {3058, 17340}, {3240, 32855}, {3242, 24943}, {3416, 32912}, {3589, 29819}, {3617, 26034}, {3681, 32778}, {3687, 21805}, {3705, 32931}, {3706, 6535}, {3720, 3932}, {3750, 32849}, {3751, 32852}, {3773, 17135}, {3790, 32915}, {3831, 28269}, {3836, 17140}, {3846, 3952}, {3873, 29674}, {3891, 25453}, {3920, 32780}, {3923, 5014}, {3938, 32777}, {3961, 32779}, {3974, 11269}, {3989, 4026}, {3994, 24210}, {3995, 4439}, {4085, 17147}, {4090, 5741}, {4126, 5743}, {4358, 29655}, {4385, 21935}, {4388, 32938}, {4418, 32850}, {4429, 17155}, {4438, 26227}, {4514, 32930}, {4645, 32940}, {4660, 32933}, {4722, 5847}, {4766, 30179}, {4863, 17281}, {4865, 26223}, {5249, 21026}, {5258, 5314}, {5282, 17275}, {5905, 31134}, {6327, 32935}, {6679, 20045}, {6682, 26251}, {7226, 32784}, {10039, 11031}, {16587, 23632}, {17061, 29867}, {17150, 17769}, {17280, 32943}, {17362, 21764}, {17597, 29677}, {17599, 29663}, {17602, 29863}, {17719, 29872}, {17724, 29865}, {17771, 20290}, {20898, 20911}, {24349, 25957}, {25496, 29832}, {25760, 32937}, {25960, 27538}, {26098, 31091}, {26842, 31151}, {27064, 32844}, {27186, 31178}, {28605, 32865}, {28606, 29659}, {29631, 32926}, {29639, 31264}, {29641, 32771}, {29840, 32944}, {29850, 32922}, {32773, 32925}, {32866, 32911}, {32939, 32948}


X(33163) = X(1)X(3710)∩X(2)X(38)

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

X(33163) lies on these lines: {1, 3710}, {2, 38}, {6, 3703}, {7, 25957}, {8, 31}, {10, 46}, {42, 345}, {43, 17740}, {44, 3966}, {69, 15523}, {81, 32862}, {144, 4683}, {145, 17469}, {171, 10327}, {190, 32773}, {193, 4722}, {226, 29857}, {306, 3751}, {312, 11269}, {329, 25760}, {333, 14012}, {344, 3720}, {346, 32915}, {354, 17279}, {497, 16561}, {518, 32777}, {594, 4042}, {612, 3717}, {614, 17353}, {672, 2345}, {726, 19785}, {748, 26685}, {846, 29659}, {894, 29641}, {896, 3617}, {940, 3932}, {958, 7085}, {966, 5282}, {993, 5314}, {996, 12647}, {1089, 5292}, {1211, 5220}, {1376, 1473}, {1707, 3679}, {1723, 4847}, {1757, 5739}, {1762, 2550}, {1836, 17351}, {1999, 3790}, {2282, 31339}, {2308, 32854}, {2321, 17156}, {2887, 5905}, {3006, 26098}, {3052, 4030}, {3085, 11031}, {3086, 25591}, {3116, 26042}, {3218, 29679}, {3219, 29667}, {3416, 4641}, {3434, 3923}, {3474, 32948}, {3475, 29632}, {3589, 4884}, {3618, 17017}, {3681, 32779}, {3697, 5955}, {3705, 27064}, {3706, 17281}, {3715, 5743}, {3729, 3914}, {3773, 32853}, {3846, 31018}, {3925, 4363}, {3944, 29861}, {3967, 17720}, {3971, 29635}, {3974, 17763}, {3977, 17594}, {3989, 17321}, {3995, 29829}, {4000, 17155}, {4011, 29655}, {4054, 17064}, {4078, 5287}, {4085, 32934}, {4138, 31164}, {4362, 24597}, {4385, 5230}, {4387, 17340}, {4388, 17350}, {4419, 32776}, {4422, 4423}, {4429, 32939}, {4514, 4676}, {4523, 20243}, {4644, 32949}, {4648, 29854}, {4655, 20078}, {4672, 4865}, {4854, 17262}, {4901, 5269}, {4972, 24248}, {5222, 32924}, {5273, 5772}, {5698, 32947}, {5712, 29643}, {5744, 32918}, {5745, 29828}, {5749, 32772}, {5793, 21677}, {5839, 21764}, {6211, 26118}, {6327, 24695}, {6679, 26228}, {7293, 25440}, {9776, 25961}, {9780, 32781}, {10453, 17280}, {13741, 28074}, {13742, 28082}, {16468, 32866}, {16567, 26063}, {17018, 32849}, {17054, 25992}, {17339, 29843}, {17354, 32942}, {17357, 21342}, {17449, 29677}, {17483, 25959}, {17484, 25958}, {17716, 20020}, {17792, 26892}, {17871, 26665}, {18141, 29687}, {18228, 25960}, {19846, 24159}, {20064, 28599}, {20083, 24068}, {24295, 29652}, {24477, 30942}, {24744, 26971}, {25527, 30768}, {25568, 29846}, {26132, 31237}, {34255, 32919}, {28808, 29662}, {29631, 32925}, {29674, 32913}, {29872, 31053}, {29873, 31019}


X(33164) = X(1)X(3710)∩X(2)X(726)

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

X(33164) lies on these lines: {1, 3710}, {2, 726}, {8, 8616}, {9, 32778}, {10, 846}, {31, 32847}, {37, 32780}, {38, 29637}, {42, 32849}, {43, 345}, {44, 32861}, {63, 29674}, {171, 3932}, {190, 2887}, {192, 25453}, {226, 29862}, {238, 3703}, {306, 1757}, {312, 4438}, {333, 3773}, {344, 26102}, {756, 32779}, {894, 23812}, {968, 29659}, {982, 17279}, {984, 32777}, {1089, 19810}, {1215, 29640}, {1698, 19822}, {1961, 4078}, {1999, 6541}, {2292, 19879}, {2325, 24210}, {2886, 17340}, {3006, 32930}, {3120, 29873}, {3218, 29687}, {3219, 15523}, {3416, 7262}, {3550, 10327}, {3589, 17600}, {3679, 4512}, {3685, 29673}, {3695, 5247}, {3705, 4011}, {3717, 3961}, {3729, 17889}, {3741, 17280}, {3749, 4901}, {3771, 32937}, {3790, 4362}, {3794, 3799}, {3836, 32939}, {3842, 19808}, {3912, 32913}, {3923, 29641}, {3936, 32938}, {3944, 29857}, {3952, 29846}, {3967, 17719}, {3969, 32864}, {3977, 17596}, {3995, 29631}, {4038, 17243}, {4066, 24880}, {4125, 17734}, {4383, 32855}, {4392, 29677}, {4414, 29679}, {4422, 17123}, {4425, 17261}, {4427, 32948}, {4429, 32934}, {4432, 4514}, {4439, 6679}, {4553, 7186}, {4641, 32846}, {4671, 24892}, {4676, 4865}, {4703, 17336}, {4756, 30831}, {4884, 17598}, {4972, 32936}, {5695, 32865}, {6651, 30179}, {7226, 24943}, {11246, 31151}, {16569, 17740}, {17127, 32854}, {17140, 29851}, {17147, 29850}, {17165, 29632}, {17233, 32853}, {17350, 32946}, {17353, 29821}, {17354, 25496}, {17368, 29644}, {18134, 32935}, {18139, 32940}, {18165, 21865}, {19796, 28516}, {20292, 21026}, {24349, 29642}, {24477, 31137}, {24542, 32923}, {24723, 28595}, {25957, 32857}, {26061, 28606}, {26223, 29643}, {27064, 29671}, {29845, 31035}, {31079, 32947}, {32848, 32911}, {32858, 32912}


X(33165) = X(1)X(3589)∩X(2)X(17598)

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

X(33165) lies on these lines: {1, 3589}, {2, 17598}, {6, 32847}, {7, 31151}, {8, 238}, {9, 80}, {10, 75}, {37, 29659}, {38, 29679}, {40, 29291}, {42, 32862}, {43, 3703}, {142, 31178}, {171, 10327}, {190, 4660}, {192, 4085}, {210, 32778}, {312, 29673}, {321, 32865}, {344, 16484}, {346, 4693}, {355, 6211}, {518, 17231}, {519, 3759}, {537, 3662}, {612, 32780}, {740, 3790}, {752, 17350}, {756, 29667}, {1125, 17341}, {1211, 4126}, {1215, 29641}, {1698, 7174}, {1757, 3416}, {2177, 32849}, {2887, 32937}, {3006, 17717}, {3240, 32848}, {3242, 29637}, {3617, 17764}, {3626, 3883}, {3632, 7290}, {3634, 25539}, {3661, 17755}, {3681, 15523}, {3729, 24715}, {3750, 17776}, {3751, 32846}, {3775, 26176}, {3831, 27680}, {3836, 24349}, {3846, 27538}, {3873, 29687}, {3891, 29850}, {3920, 26061}, {3923, 32850}, {3944, 3967}, {3952, 25760}, {3961, 30615}, {3971, 32773}, {3977, 17601}, {4007, 16970}, {4011, 4514}, {4030, 8616}, {4073, 6735}, {4082, 24210}, {4090, 4417}, {4110, 4783}, {4358, 24217}, {4383, 32866}, {4407, 17238}, {4422, 15485}, {4432, 17339}, {4437, 16496}, {4438, 7081}, {4645, 31300}, {4676, 17766}, {4733, 24697}, {4737, 17786}, {4751, 25352}, {4753, 17363}, {4865, 27064}, {4866, 15314}, {4884, 17591}, {4972, 32925}, {5014, 32930}, {5294, 17716}, {5686, 21270}, {5687, 7295}, {5690, 6210}, {5846, 16468}, {6327, 32938}, {7226, 32781}, {16669, 28538}, {17116, 24693}, {17140, 25961}, {17165, 25957}, {17257, 28542}, {17263, 24331}, {17276, 24821}, {17283, 24841}, {17306, 19875}, {17357, 29660}, {17366, 28503}, {17484, 31134}, {17602, 29856}, {17718, 29862}, {17719, 29857}, {17720, 29861}, {17724, 29858}, {18743, 29655}, {21026, 31019}, {24325, 27147}, {25005, 26567}, {25453, 32926}, {25959, 32856}, {27184, 28595}, {29664, 31264}, {29676, 30818}, {29832, 32944}, {32854, 32911}, {32933, 32948}


X(33166) = X(2)X(38)∩X(6)X(32862)

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

X(33166) lies on these lines: {2, 38}, {6, 32862}, {8, 595}, {9, 29667}, {10, 191}, {42, 32849}, {63, 29679}, {81, 3932}, {145, 16478}, {149, 29673}, {190, 4972}, {210, 32779}, {226, 29873}, {329, 25958}, {344, 29814}, {345, 3240}, {726, 29850}, {908, 29872}, {1089, 24883}, {1654, 21038}, {1757, 2895}, {2161, 3434}, {2308, 32847}, {2887, 17484}, {3006, 27064}, {3187, 3790}, {3475, 29870}, {3681, 32777}, {3703, 32842}, {3710, 17016}, {3717, 3920}, {3751, 32858}, {3773, 32864}, {3836, 26842}, {3873, 17279}, {3971, 29631}, {3974, 24597}, {3989, 29633}, {4075, 25441}, {4078, 17019}, {4085, 32936}, {4090, 29846}, {4388, 31079}, {4415, 4756}, {4422, 5284}, {4429, 32933}, {4439, 32928}, {4676, 5014}, {4683, 28595}, {4722, 20086}, {4981, 17289}, {5220, 32782}, {5905, 25959}, {6327, 17350}, {6679, 32927}, {7174, 29648}, {7191, 17353}, {9708, 26867}, {10327, 17126}, {16468, 32854}, {17018, 17776}, {17135, 17280}, {17351, 20292}, {17354, 24552}, {17355, 25006}, {17483, 25957}, {20072, 20290}, {21035, 27320}, {21217, 30667}, {25453, 32925}, {25760, 26792}, {26223, 29641}, {29674, 32863}, {29687, 32913}, {29837, 31035}, {29857, 31053}, {29861, 30578}


X(33167) = X(1)X(345)∩X(2)X(726)

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

X(33167) lies on these lines: {1, 345}, {2, 726}, {6, 32855}, {8, 3550}, {10, 4201}, {31, 32866}, {38, 32779}, {43, 17740}, {57, 29674}, {63, 32778}, {75, 4438}, {81, 32848}, {165, 376}, {171, 3703}, {190, 3846}, {192, 29635}, {306, 32913}, {344, 25502}, {519, 5429}, {750, 32862}, {846, 3977}, {894, 29671}, {982, 29637}, {986, 19879}, {1215, 32851}, {1698, 13161}, {1757, 3687}, {2108, 3741}, {2308, 32842}, {2887, 32857}, {3006, 4418}, {3099, 21085}, {3120, 29872}, {3210, 25453}, {3218, 15523}, {3416, 4650}, {3666, 29633}, {3677, 29660}, {3685, 29655}, {3705, 3923}, {3712, 3750}, {3720, 32849}, {3729, 3944}, {3771, 24349}, {3773, 14829}, {3790, 29649}, {3816, 17340}, {3840, 17280}, {3914, 29861}, {3932, 17122}, {3936, 32940}, {3966, 7262}, {3969, 32919}, {3980, 29641}, {3993, 29837}, {3995, 29845}, {4387, 24217}, {4392, 24943}, {4414, 29667}, {4417, 32935}, {4427, 32947}, {4641, 32861}, {4659, 17064}, {4671, 29662}, {4850, 26061}, {4972, 32845}, {5015, 24850}, {5249, 29862}, {5278, 24267}, {5294, 29821}, {5741, 32938}, {6679, 32922}, {6682, 17289}, {16468, 26065}, {17063, 17279}, {17126, 32854}, {17140, 29632}, {17147, 29631}, {17165, 29846}, {17284, 18193}, {17355, 24239}, {17368, 29650}, {17495, 29850}, {17594, 29659}, {17776, 26102}, {17889, 29857}, {19785, 29856}, {19797, 27798}, {19808, 19856}, {20106, 24231}, {24892, 28605}, {25760, 32933}, {26223, 29849}, {26627, 29854}, {27003, 29687}, {29640, 32771}, {29673, 32932}, {30831, 32856}, {31079, 32948}, {32773, 32934}


X(33168) = X(2)X(37)∩X(8)X(35)

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

X(33168) lies on these lines: {2, 37}, {8, 35}, {31, 32842}, {57, 32858}, {63, 2895}, {100, 3703}, {145, 5266}, {149, 3705}, {171, 32848}, {190, 5741}, {226, 27757}, {306, 3218}, {404, 3695}, {726, 29846}, {896, 32861}, {902, 32866}, {1054, 29687}, {1089, 27529}, {1376, 32862}, {1621, 3712}, {1738, 29873}, {2887, 32845}, {2975, 3704}, {2985, 16704}, {3006, 32932}, {3035, 6057}, {3219, 3687}, {3550, 32854}, {3729, 31053}, {3771, 17155}, {3773, 32918}, {3782, 30831}, {3846, 32936}, {3912, 27003}, {3914, 29872}, {3923, 29849}, {3936, 17483}, {3969, 14829}, {3980, 29643}, {3993, 29845}, {4062, 32913}, {4364, 31247}, {4388, 4427}, {4414, 32778}, {4417, 17484}, {4418, 29671}, {4438, 32860}, {4650, 32852}, {4659, 31266}, {4781, 28599}, {4873, 31231}, {4921, 17362}, {4970, 29631}, {5012, 17977}, {5014, 20095}, {5015, 20066}, {5016, 15680}, {5046, 7283}, {5294, 17012}, {5337, 6542}, {5372, 5744}, {5695, 11680}, {6292, 29587}, {6646, 31037}, {6679, 32924}, {6763, 21081}, {14552, 24616}, {15523, 17596}, {17020, 17353}, {17140, 29839}, {17268, 27002}, {17339, 26688}, {17591, 24943}, {17593, 32781}, {17594, 29667}, {17784, 31091}, {18134, 26842}, {18359, 20237}, {24165, 29632}, {24248, 25958}, {24342, 29682}, {25760, 32934}, {26745, 30701}, {26770, 26793}, {26840, 31017}, {27109, 29590}, {27131, 30578}, {27804, 29837}


X(33169) = X(1)X(3695)∩X(2)X(17598)

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

X(33169) lies on these lines: {1, 3695}, {2, 17598}, {6, 32866}, {8, 171}, {10, 982}, {38, 29667}, {42, 32855}, {57, 3679}, {75, 29673}, {81, 32854}, {244, 29679}, {291, 31330}, {312, 24217}, {345, 3750}, {354, 29674}, {518, 32778}, {519, 17716}, {537, 27184}, {594, 17754}, {726, 32773}, {894, 4865}, {940, 32847}, {956, 5329}, {985, 32864}, {1215, 3705}, {1698, 3677}, {1757, 3966}, {2275, 16587}, {2345, 4119}, {2887, 24349}, {3006, 32771}, {3210, 4085}, {3242, 32783}, {3315, 29677}, {3416, 32913}, {3509, 17275}, {3550, 4030}, {3617, 18201}, {3632, 4046}, {3661, 24631}, {3662, 28595}, {3666, 29659}, {3720, 32862}, {3751, 32861}, {3756, 31242}, {3757, 4438}, {3772, 29861}, {3773, 10453}, {3790, 29843}, {3844, 21342}, {3846, 32937}, {3873, 15523}, {3883, 7262}, {3891, 29631}, {3923, 4514}, {3932, 26102}, {3938, 32779}, {3952, 25960}, {3961, 4952}, {3980, 32850}, {4026, 4884}, {4090, 5233}, {4104, 4899}, {4126, 5241}, {4388, 32935}, {4392, 32781}, {4418, 5014}, {4429, 24165}, {4641, 4914}, {4660, 32939}, {4901, 5268}, {4906, 17357}, {4972, 17155}, {5226, 27759}, {5249, 31178}, {5258, 5285}, {5690, 20368}, {6327, 32940}, {7191, 26061}, {10327, 17122}, {16484, 17776}, {17018, 32848}, {17061, 29856}, {17140, 25957}, {17165, 25760}, {17279, 29820}, {17289, 29652}, {17483, 31134}, {17597, 29637}, {17599, 29633}, {21026, 27186}, {24325, 29641}, {25453, 32922}, {25496, 29840}, {25958, 32856}, {26223, 32844}, {28606, 29685}, {29635, 32926}, {29670, 32851}, {29680, 31264}, {29829, 32928}, {29832, 32772}, {29835, 32915}, {29844, 32942}, {30179, 31317}, {31053, 31161}, {32933, 32947}


X(33170) = X(1)X(32849)∩X(2)X(38)

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

X(33170) lies on these lines: {1, 32849}, {2, 38}, {6, 32842}, {7, 25959}, {8, 58}, {10, 3218}, {57, 29679}, {63, 29667}, {81, 3703}, {100, 4265}, {149, 3923}, {192, 29829}, {226, 29872}, {345, 17018}, {518, 32779}, {583, 2345}, {726, 29631}, {846, 29685}, {894, 3006}, {940, 32862}, {958, 11101}, {2308, 32866}, {2887, 17483}, {2895, 32778}, {3120, 29861}, {3240, 17740}, {3475, 29866}, {3618, 17025}, {3677, 29666}, {3685, 29835}, {3705, 26223}, {3717, 5297}, {3773, 32919}, {3846, 26792}, {3873, 32777}, {3971, 29845}, {3995, 29837}, {3999, 17357}, {4078, 17021}, {4085, 32845}, {4284, 5749}, {4307, 31091}, {4414, 29659}, {4418, 21381}, {4446, 27320}, {4645, 31079}, {4649, 32848}, {4671, 11269}, {4672, 32844}, {4722, 32861}, {4972, 32939}, {4981, 19808}, {5057, 17351}, {5249, 29873}, {5294, 7191}, {5744, 5772}, {5905, 25958}, {6679, 32923}, {7292, 17353}, {9709, 26866}, {15523, 32863}, {17127, 26065}, {17155, 25453}, {17280, 29824}, {17355, 26015}, {17449, 29637}, {17484, 25760}, {17491, 31300}, {17591, 29663}, {17776, 29814}, {19785, 29868}, {20066, 24850}, {20086, 32852}, {20101, 28599}, {24068, 25441}, {24165, 29850}, {24231, 30768}, {24627, 26251}, {25957, 26842}, {26131, 30172}, {29635, 32925}, {29655, 32930}, {29857, 31019}, {32773, 32933}


X(33171) = X(1)X(2)∩X(7)X(4418)

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

X(33171) lies on these lines: {1, 2}, {7, 4418}, {31, 69}, {38, 345}, {55, 141}, {149, 25958}, {193, 2308}, {210, 17279}, {238, 5739}, {329, 32930}, {344, 756}, {346, 32925}, {390, 32947}, {497, 25760}, {518, 32777}, {599, 3052}, {672, 5227}, {740, 19785}, {748, 14555}, {750, 18141}, {902, 3620}, {940, 4966}, {960, 17441}, {966, 2280}, {968, 4357}, {982, 17740}, {984, 17776}, {1001, 1211}, {1011, 8299}, {1104, 10371}, {1279, 3966}, {1479, 3454}, {1617, 26942}, {1621, 32782}, {1707, 4001}, {1848, 1851}, {1891, 4196}, {1962, 17321}, {2177, 3619}, {2187, 7494}, {2209, 28242}, {2223, 7795}, {2345, 3475}, {2550, 25957}, {2886, 30811}, {2887, 3434}, {2895, 17127}, {2900, 24388}, {3120, 26132}, {3242, 3703}, {3305, 4104}, {3416, 3744}, {3662, 32932}, {3683, 4643}, {3685, 27184}, {3696, 24789}, {3706, 3772}, {3715, 4422}, {3745, 4851}, {3750, 32784}, {3751, 5294}, {3773, 32920}, {3782, 5695}, {3873, 32779}, {3886, 3914}, {3891, 3969}, {3896, 32774}, {3923, 5905}, {3936, 24552}, {3974, 32927}, {3996, 4429}, {4000, 32860}, {4011, 31018}, {4046, 4361}, {4307, 32949}, {4310, 17155}, {4329, 30946}, {4365, 30699}, {4387, 4415}, {4417, 32942}, {4419, 32936}, {4423, 5743}, {4432, 4703}, {4441, 18697}, {4512, 17272}, {4647, 24159}, {4660, 20075}, {4673, 19803}, {4683, 5698}, {4734, 26150}, {4849, 17357}, {5218, 32918}, {5241, 8167}, {5247, 17526}, {5250, 8897}, {5263, 18134}, {5269, 17296}, {5278, 24542}, {5329, 13588}, {5439, 5955}, {5712, 32772}, {5793, 15888}, {6057, 17269}, {6327, 31017}, {6389, 23207}, {6679, 24597}, {7226, 32849}, {7232, 11246}, {11680, 30831}, {16353, 26101}, {16678, 19343}, {16800, 17349}, {17126, 32863}, {17184, 24248}, {17233, 32926}, {17280, 32937}, {17314, 32928}, {17469, 32852}, {17598, 32855}, {17716, 32846}, {17784, 32948}, {17811, 25968}, {18518, 19540}, {19822, 24325}, {20064, 20290}, {20080, 21747}, {24695, 32859}, {25568, 32931}, {25893, 26005}, {25960, 26105}, {25961, 26040}, {26065, 32912}, {32775, 32915}


X(33172) = X(1)X(32781)∩X(2)X(6)

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

X(33172) lies on these lines: {1, 32781}, {2, 6}, {8, 30614}, {10, 3873}, {11, 25958}, {31, 29637}, {38, 29674}, {57, 32779}, {63, 17284}, {76, 16703}, {171, 24943}, {222, 28780}, {238, 29677}, {244, 32778}, {306, 4850}, {312, 17184}, {320, 26223}, {321, 3662}, {354, 3844}, {518, 29679}, {750, 32783}, {980, 6292}, {982, 15523}, {984, 29687}, {1086, 28605}, {1230, 18144}, {1255, 17321}, {1330, 5192}, {1352, 19649}, {1386, 29666}, {1621, 26034}, {1999, 17291}, {2886, 25959}, {2887, 11680}, {3175, 17235}, {3187, 16706}, {3210, 3969}, {3218, 32777}, {3219, 17279}, {3305, 17272}, {3416, 7191}, {3454, 3794}, {3661, 4359}, {3666, 17231}, {3685, 32950}, {3703, 4392}, {3720, 32784}, {3741, 25957}, {3745, 29648}, {3769, 26230}, {3771, 32918}, {3773, 17155}, {3775, 26037}, {3782, 4671}, {3791, 29852}, {3821, 32915}, {3831, 11681}, {3834, 27186}, {3836, 31330}, {3840, 25760}, {3846, 30957}, {3912, 28606}, {3932, 7226}, {3966, 7292}, {3995, 4389}, {4001, 17353}, {4011, 4683}, {4026, 29814}, {4038, 29647}, {4138, 10129}, {4197, 5208}, {4202, 10449}, {4358, 27184}, {4363, 26842}, {4429, 17135}, {4434, 29848}, {4641, 17357}, {4643, 27065}, {4645, 24552}, {4649, 29663}, {4655, 32930}, {4657, 17019}, {4660, 32943}, {4851, 17011}, {4871, 25960}, {4906, 4914}, {4966, 17018}, {4972, 10453}, {5249, 21255}, {5256, 17296}, {5271, 17282}, {5287, 17306}, {5294, 29596}, {5337, 7822}, {5435, 26942}, {5846, 17024}, {6327, 32942}, {6682, 29643}, {6690, 29866}, {7232, 17483}, {7789, 21537}, {7795, 21495}, {7800, 21511}, {9534, 17674}, {9776, 19822}, {11108, 26064}, {11220, 12618}, {16948, 17526}, {17017, 32846}, {17147, 17233}, {17228, 19804}, {17244, 21802}, {17280, 26840}, {17285, 32939}, {17288, 27064}, {17295, 20017}, {17311, 20182}, {17469, 29660}, {17591, 32848}, {17598, 32854}, {17716, 29686}, {17763, 26128}, {17776, 29579}, {18136, 18137}, {18228, 26932}, {18440, 21487}, {18743, 26580}, {19273, 24936}, {19785, 34255}, {19808, 26627}, {20255, 29593}, {20653, 24174}, {24169, 32860}, {24177, 29594}, {24551, 25010}, {25453, 32919}, {25496, 32949}, {26061, 32913}, {29632, 32916}, {29642, 32917}, {29649, 32775}, {29668, 32844}, {29821, 32852}, {29824, 32773}, {29850, 32853}, {30818, 31053}, {31136, 32865}, {32941, 32948}, {32944, 32946}


X(33173) = X(1)X(2)∩X(11)X(30831)

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

X(33173) lies on these lines: {1, 2}, {11, 30831}, {31, 32863}, {38, 32849}, {69, 17127}, {81, 4966}, {141, 1621}, {149, 2887}, {238, 2895}, {333, 24542}, {345, 4392}, {350, 20932}, {354, 32779}, {497, 25958}, {757, 30941}, {1001, 32782}, {1211, 5284}, {2308, 20086}, {3242, 32862}, {3434, 25959}, {3662, 32929}, {3681, 17279}, {3685, 17184}, {3696, 26724}, {3744, 17231}, {3748, 3844}, {3750, 32781}, {3773, 32923}, {3836, 32945}, {3873, 32777}, {3891, 17233}, {3896, 16706}, {3923, 17483}, {3936, 32942}, {3969, 32922}, {3996, 17283}, {4011, 26792}, {4184, 8299}, {4388, 31017}, {4418, 26842}, {4427, 26840}, {4432, 4683}, {4676, 32859}, {4684, 5294}, {5259, 26064}, {5263, 18139}, {5347, 30945}, {6679, 32919}, {7226, 17776}, {7677, 26942}, {11680, 30811}, {17165, 17280}, {17227, 32950}, {17302, 27804}, {17469, 32846}, {17484, 32930}, {17598, 32848}, {18134, 24552}, {20095, 32948}, {24575, 27658}, {25957, 32941}, {26128, 32915}


X(33174) = X(1)X(4030)∩X(2)X(31)

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

X(33174) lies on these lines: {1, 4030}, {2, 31}, {5, 20368}, {8, 17598}, {10, 982}, {12, 57}, {35, 16299}, {38, 29679}, {43, 141}, {55, 29637}, {56, 19879}, {75, 24169}, {81, 29663}, {100, 24943}, {244, 29667}, {291, 24988}, {312, 3821}, {345, 17593}, {354, 29659}, {474, 5329}, {846, 17279}, {899, 32782}, {940, 29633}, {1122, 15568}, {1125, 17716}, {1150, 29850}, {1211, 16569}, {1213, 17754}, {1215, 3662}, {1376, 3763}, {1460, 16408}, {1621, 29677}, {1961, 4657}, {2886, 29827}, {2999, 32861}, {3210, 3773}, {3218, 26061}, {3305, 24697}, {3361, 19880}, {3416, 29821}, {3509, 17303}, {3624, 5269}, {3666, 29674}, {3677, 3679}, {3703, 17591}, {3705, 28595}, {3740, 17237}, {3741, 4429}, {3744, 29660}, {3745, 29646}, {3752, 3844}, {3769, 17370}, {3791, 17367}, {3816, 31242}, {3831, 16062}, {3840, 24217}, {3912, 17592}, {3944, 30818}, {3967, 17235}, {3971, 4389}, {3980, 17289}, {4011, 24723}, {4026, 26102}, {4038, 18141}, {4085, 10453}, {4357, 21590}, {4358, 32776}, {4362, 16706}, {4425, 18743}, {4434, 29634}, {4438, 24627}, {4514, 29668}, {4640, 17357}, {4650, 5294}, {4655, 27064}, {4660, 32942}, {4682, 17384}, {4697, 17368}, {4734, 17230}, {4850, 15523}, {4970, 17233}, {4972, 30942}, {5233, 6686}, {5255, 19836}, {5256, 32846}, {5264, 19881}, {5268, 17306}, {5285, 16415}, {5363, 17531}, {5902, 19867}, {6682, 29641}, {6685, 18134}, {6690, 29858}, {7081, 16986}, {7262, 17353}, {9316, 28780}, {9780, 18201}, {10180, 17244}, {14829, 25453}, {16587, 20284}, {17012, 32852}, {17056, 29825}, {17184, 32931}, {17228, 21085}, {17236, 27538}, {17238, 26038}, {17280, 32934}, {17283, 29642}, {17284, 17594}, {17469, 29666}, {17596, 32777}, {17599, 32847}, {17601, 29596}, {17674, 31339}, {17719, 25527}, {17763, 32774}, {18193, 19875}, {19786, 29649}, {21026, 29664}, {21214, 25914}, {24552, 32948}, {24631, 29576}, {26251, 32771}, {26840, 32935}, {28606, 29687}, {29652, 32850}, {31019, 31264}, {32930, 32950}


X(33175) = X(1)X(2)∩X(31)X(2895)

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

X(33175) lies on these lines: {1, 2}, {31, 2895}, {55, 32782}, {69, 17126}, {100, 141}, {149, 25760}, {171, 32863}, {344, 9330}, {345, 7226}, {518, 32779}, {594, 17724}, {740, 32775}, {984, 32849}, {1211, 1621}, {1897, 17918}, {2177, 32784}, {2550, 25959}, {2886, 30831}, {2887, 32945}, {3434, 25958}, {3475, 19822}, {3681, 32777}, {3685, 26580}, {3689, 3844}, {3699, 17285}, {3773, 32927}, {3775, 32917}, {3814, 30980}, {3846, 32943}, {3896, 19786}, {3923, 17484}, {3936, 5263}, {3952, 17280}, {3969, 32926}, {3980, 26842}, {3996, 4972}, {4046, 17061}, {4104, 27065}, {4388, 31037}, {4392, 17740}, {4417, 24552}, {4418, 17483}, {4427, 6646}, {4551, 28780}, {4643, 4760}, {4645, 31017}, {4660, 20095}, {4689, 17237}, {4756, 17340}, {4781, 24707}, {4851, 9347}, {5078, 11322}, {5080, 11330}, {5248, 26064}, {5284, 5743}, {5739, 17127}, {5741, 32942}, {6679, 32864}, {14513, 24250}, {17184, 32932}, {17277, 24542}, {17283, 24988}, {17469, 32861}, {17716, 32852}, {20101, 20290}, {26128, 32860}, {26792, 32930}, {27184, 32929}, {31237, 32865}


X(33176) = X(1)X(3)∩X(11)X(3244)

Barycentrics    a*(-a+b+c)*(4*a^2-(b+c)*a-5*(b-c)^2) : :
X(33176) = 5*X(1)-X(7280), 3*X(1)-X(21842)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29105.

X(33176) lies on these lines: {1, 3}, {11, 3244}, {145, 11376}, {210, 4861}, {497, 20057}, {519, 17606}, {946, 1317}, {1392, 3885}, {1483, 30384}, {1737, 17662}, {1836, 5734}, {1837, 3241}, {3585, 13274}, {3636, 5432}, {3689, 10912}, {3698, 9342}, {3881, 15558}, {3893, 4511}, {3962, 11260}, {4018, 30538}, {4342, 10543}, {4930, 7082}, {5252, 10595}, {5326, 15808}, {5433, 28234}, {5854, 27385}, {6284, 13607}, {7967, 12701}, {7972, 18480}, {10039, 10283}, {10589, 20050}, {10915, 25416}, {10944, 13464}, {12645, 23708}, {12672, 17660}, {12735, 12743}, {12758, 24475}, {14100, 15570}, {15174, 16142}

X(33176) = X(7280)-of-Mandart-incircle triangle
X(33176) = X(16868)-of-Ursa-minor triangle
X(33176) = X(21844)-of-Hutson intouch triangle
X(33176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7982, 1388), (1388, 7982, 1155), (3333, 12703, 46)


X(33177) = X(1)X(3)∩X(58)X(10703)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29105.

X(33177) lies on these lines: {1, 3}, {58, 10703}, {946, 1411}, {1201, 12740}, {1399, 2800}, {2361, 3878}, {2594, 21740}, {3073, 17638}, {3924, 11376}, {4514, 4861}, {5258, 24431}, {10950, 15955}, {11700, 18360}


X(33178) = X(1)X(3)∩X(8)X(27528)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29105.

X(33178) lies on these lines: {1, 3}, {8, 27528}, {21, 16579}, {29, 4858}, {33, 5142}, {34, 990}, {58, 2906}, {84, 1061}, {191, 2361}, {201, 13329}, {938, 9538}, {946, 1421}, {950, 3100}, {1071, 2003}, {1203, 1858}, {1210, 6198}, {1386, 12711}, {1399, 1768}, {1473, 11396}, {1717, 3583}, {1718, 3585}, {1724, 24430}, {1727, 2964}, {1789, 4282}, {1829, 3220}, {1831, 5358}, {1854, 16466}, {1870, 4292}, {1891, 12610}, {2006, 6831}, {2654, 30117}, {3474, 4347}, {3577, 15176}, {3616, 20266}, {4276, 22347}, {4303, 8555}, {4306, 20277}, {4336, 18343}, {5125, 20268}, {5136, 20320}, {5218, 30142}, {5256, 10393}, {5722, 8144}, {5727, 7221}, {6986, 16577}, {7191, 12053}, {9785, 17024}, {10395, 26723}, {22072, 30115}, {28806, 30122}

X(33178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 15803, 1060), (65, 9630, 1), (942, 18455, 1)

X(33179) = X(1)X(3)∩X(4)X(20057)

Barycentrics    a*(4*a^3-5*(b+c)*a^2-2*(2*b-c)*(b-2*c)*a+5*(b^2-c^2)*(b-c)) : :
Trilinears    5 r - R cos A : :
X(33179) = 5*X(1)-X(3), 9*X(1)-X(40), 19*X(1)-3*X(165), 3*X(1)-X(1385), 3*X(1)+X(1482), 11*X(1)-3*X(3576), 7*X(1)-X(3579), 7*X(1)+X(7982), 21*X(1)-5*X(7987), 17*X(1)-X(7991), 11*X(1)+X(8148), 7*X(1)-3*X(10246), X(1)+3*X(10247), 13*X(1)+3*X(11224), 5*X(1)+X(11278), 15*X(1)+X(11531), 13*X(1)-X(12702), 4*X(1)-X(13624), 11*X(1)+5*X(16189), X(4)+7*X(20057)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29105.

X(33179) lies on these lines: {1, 3}, {4, 20057}, {5, 3244}, {8, 5067}, {10, 10283}, {30, 13607}, {140, 3636}, {145, 5056}, {355, 3241}, {392, 5645}, {515, 3853}, {518, 5097}, {519, 547}, {546, 28236}, {548, 28228}, {551, 5690}, {632, 15808}, {944, 3543}, {946, 1483}, {952, 3850}, {962, 3655}, {971, 15570}, {1056, 10525}, {1058, 10526}, {1125, 5844}, {1317, 12047}, {1320, 22935}, {1392, 14497}, {1656, 3632}, {1699, 18526}, {1902, 13596}, {2771, 25485}, {3083, 21551}, {3084, 21544}, {3090, 20050}, {3242, 5102}, {3533, 3616}, {3555, 5694}, {3622, 26446}, {3623, 3832}, {3626, 3628}, {3633, 5790}, {3652, 28461}, {3653, 15719}, {3654, 15708}, {3827, 15580}, {3881, 14988}, {3892, 24475}, {4297, 15686}, {4301, 28146}, {4701, 10172}, {4930, 6762}, {5059, 18481}, {5270, 10738}, {5288, 7489}, {5330, 16858}, {5734, 7967}, {5881, 18493}, {5882, 22791}, {6001, 26200}, {6684, 11812}, {6924, 25439}, {7486, 20054}, {7680, 32214}, {7681, 32213}, {7743, 10950}, {7984, 11699}, {8227, 12645}, {9856, 26088}, {10106, 12735}, {10179, 31837}, {10532, 18407}, {11237, 11928}, {11238, 11929}, {11522, 18525}, {12103, 28232}, {12245, 15702}, {12737, 17661}, {15690, 28194}, {15723, 25055}, {16126, 22936}, {16854, 19860}, {16864, 19861}, {18446, 31822}, {18483, 28224}

X(33179) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 24680}, {3, 11278}, {5, 3244}, {65, 10284}, {944, 22793}, {946, 1483}, {1319, 23960}, {1320, 22935}, {1385, 1482}, {3555, 5694}, {3579, 7982}, {5882, 22791}, {7984, 11699}, {11224, 17502}, {16126, 22936}
X(33179) = reflection of X(i) in X(j) for these (i,j): (140, 3636), (3626, 3628), (5885, 5045), (9856, 26088), (9955, 13464), (9956, 5901), (13145, 13373), (13624, 15178), (15178, 1), (31663, 1385)
X(33179) = (anti-Aquila)-complement of-X(5690)
X(33179) = X(3853)-of-2nd-circumperp-triangle
X(33179) = X(3861)-of-excenters-reflections-triangle
X(33179) = X(10226)-of-intouch-triangle
X(33179) = X(11250)-of-incircle-circles-triangle
X(33179) = X(12102)-of-excentral-triangle
X(33179) = X(15178)-of-5th mixtilinear-triangle
X(33179) = X(15331)-of-Hutson intouch-triangle
X(33179) = X(24680)-of-anti-Aquila-triangle
X(33179) = X(26086)-of-2nd anti-circumperp-tangential-triangle
X(33179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7982, 10246), (1482, 11531, 11278), (11531, 16200, 1482)

leftri

Points on the Euler line: X(33180)-X(33280)

rightri

Centers X(33180)-X(33280) were contributed by Clark Kimberling, June 22, 2019.

This section consists of points having barycentrics of the form h a^2 SA + k SB SC + m (a^4 + b^4 + c^4) : : .


X(33180) = (name pending)

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

As a point on the Euler line, X(33180) has Shinagawa coefficients (2(E+F)2-S2,-2S2).

X(33180) lies on these lines: {2, 3}, {69, 7851}, {83, 32827}, {141, 32834}, {193, 7797}, {315, 5304}, {625, 31404}, {626, 5286}, {2548, 7913}, {2549, 7863}, {3096, 32828}, {3314, 6392}, {3618, 7773}, {3620, 7938}, {3767, 7853}, {3785, 7828}, {3926, 7790}, {4045, 31400}, {4293, 30103}, {4294, 30104}, {5013, 32835}, {5254, 32830}, {5319, 7818}, {7735, 7784}, {7737, 7852}, {7738, 7778}, {7739, 7821}, {7754, 10513}, {7757, 32825}, {7763, 7918}, {7774, 7923}, {7792, 32006}, {7795, 7861}, {7800, 7844}, {7803, 7858}, {7817, 14023}, {7832, 32815}, {7834, 7843}, {7881, 32840}, {7883, 9740}, {7885, 16989}, {7899, 32829}, {7928, 17008}, {7932, 20065}, {7937, 32832}, {7939, 20080}, {7942, 14907}, {7944, 11185}, {9605, 32823}, {14061, 32838}, {14986, 26561}, {15048, 32818}, {15271, 32870}, {22110, 22332}, {31859, 32841}

X(33180) = complement of X(33201)
X(33180) = anticomplement of X(14069)
X(33180) = {X(2),X(3)}-harmonic conjugate of X(33203)
X(33180) = {X(2),X(4)}-harmonic conjugate of X(33198)
X(33180) = {X(2),X(20)}-harmonic conjugate of X(33181)
X(33180) = orthocentroidal-circle-inverse of X(33198)


X(33181) = (name pending)

Barycentrics    a^2 SA - SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 2*a^2*b^2 + 3*b^4 - 2*a^2*c^2 + 2*b^2*c^2 + 3*c^4 : :

As a point on the Euler line, X(33181) has Shinagawa coefficients (2(E+F)2-3S2,2S2).

X(33181) lies on these lines: {2, 3}, {6, 32831}, {83, 32829}, {193, 7836}, {230, 32834}, {620, 31400}, {1285, 7776}, {1992, 32821}, {3620, 7793}, {3785, 7832}, {3926, 5304}, {3972, 32816}, {4293, 30104}, {4294, 30103}, {5032, 13571}, {5286, 6680}, {5305, 32817}, {5319, 7863}, {6337, 7792}, {6392, 7806}, {7735, 7789}, {7736, 32835}, {7737, 7874}, {7754, 32840}, {7763, 7878}, {7780, 7795}, {7804, 31404}, {7822, 21843}, {7828, 32815}, {7857, 32828}, {7870, 32825}, {7880, 14023}, {7881, 10513}, {7891, 16989}, {7899, 32827}, {7930, 14907}, {7945, 20065}, {14986, 26686}, {18907, 32823}, {30435, 32818}

X(33181) = complement of X(33200)
X(33181) = anticomplement of X(32951)
X(33181) = orthocentroidal-circle-inverse of X(33199)
X(33181) = {X(2),X(3)}-harmonic conjugate of X(33202)
X(33181) = {X(2),X(4)}-harmonic conjugate of X(33199)
X(33181) = {X(2),X(20)}-harmonic conjugate of X(33180)


X(33182) = (name pending)

Barycentrics    a^2 SA - SB SC + 2 (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 + 2*a^2*b^2 + 9*b^4 + 2*a^2*c^2 - 2*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(33182) has Shinagawa coefficients (4(E+F)2-3S2,-2S2).

X(33182) lies on these lines: {2, 3}, {193, 7932}, {390, 30104}, {626, 5304}, {3600, 30103}, {3785, 7942}, {3926, 7919}, {5286, 7813}, {5305, 10513}, {6392, 7931}, {7755, 9740}, {7795, 32457}, {7827, 32825}, {7828, 15589}, {7846, 32827}, {7851, 32830}, {7868, 32834}, {7878, 32816}, {7913, 31400}, {7930, 32815}, {7944, 32828}, {11148, 32820}, {14930, 32823}, {15048, 32841}, {18840, 32872}

X(33182) = anticomplement of X(32952)
X(33182) = {X(2),X(20)}-harmonic conjugate of X(33183)


X(33183) = (name pending)

Barycentrics    a^2 SA - SB SC - 2 (a^4 + b^4 + c^4) : :
Barycentrics    11*a^4 - 2*a^2*b^2 + 7*b^4 - 2*a^2*c^2 + 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33183) has Shinagawa coefficients (4(E+F)2-5S2,2S2).

X(33183) lies on these lines: {2, 3}, {193, 7945}, {390, 30103}, {3600, 30104}, {3618, 32835}, {3785, 7930}, {3926, 7856}, {5286, 7863}, {5304, 6680}, {5305, 32840}, {6392, 16984}, {7792, 32831}, {7794, 9740}, {7832, 15589}, {7846, 32829}, {7877, 7909}, {7942, 32815}, {18841, 31467}, {22253, 32879}, {31406, 32873}

X(33183) = anticomplement of X(32953)
X(33183) = {X(2),X(20)}-harmonic conjugate of X(33182)


X(33184) = (name pending)

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

As a point on the Euler line, X(33184) has Shinagawa coefficients (2(E+F)2-S2,-3S2).

X(33184) lies on these lines: {2, 3}, {115, 141}, {148, 7931}, {230, 7761}, {315, 5305}, {316, 7792}, {325, 7757}, {385, 14929}, {495, 26590}, {496, 26561}, {524, 5028}, {538, 626}, {543, 7880}, {597, 1692}, {625, 3815}, {754, 5306}, {1007, 5024}, {2549, 6390}, {3054, 6722}, {3055, 15482}, {3589, 5033}, {3618, 15484}, {3629, 5355}, {3631, 17131}, {3649, 30119}, {3767, 7767}, {3788, 7872}, {3793, 7735}, {3820, 26582}, {3849, 19661}, {5085, 7694}, {5182, 6033}, {5286, 7776}, {5461, 11168}, {5485, 32869}, {6284, 30104}, {6680, 7842}, {7354, 30103}, {7603, 15491}, {7615, 21358}, {7619, 10150}, {7739, 9766}, {7745, 7825}, {7746, 7935}, {7747, 7852}, {7748, 7789}, {7750, 7828}, {7752, 7918}, {7755, 7873}, {7756, 7874}, {7759, 7902}, {7762, 7797}, {7764, 9607}, {7765, 7821}, {7773, 7803}, {7775, 9300}, {7785, 7923}, {7794, 14711}, {7796, 11055}, {7800, 8556}, {7801, 11648}, {7802, 7942}, {7806, 7898}, {7809, 7827}, {7810, 13468}, {7811, 22329}, {7812, 7884}, {7823, 7932}, {7829, 7843}, {7830, 7886}, {7831, 14061}, {7832, 32819}, {7847, 7899}, {7856, 7860}, {7857, 7910}, {7864, 7912}, {7868, 11185}, {7883, 14568}, {7900, 7920}, {7909, 32820}, {8589, 31274}, {9166, 9478}, {9605, 32816}, {9734, 10256}, {10008, 21356}, {10543, 30123}, {10592, 27020}, {10593, 26959}, {10748, 30789}, {11165, 32837}, {14712, 16984}, {14971, 15597}, {15819, 23514}, {21850, 22486}, {21969, 27374}, {26558, 31419}, {30435, 32006}

X(33184) = midpoint of X(2) and X(7841)
X(33184) = reflection of X(2) in X(8360)
X(33184) = reflection of X(8369) in X(2)
X(33184) = complement of X(1003)
X(33184) = anticomplement of X(8368)
X(33184) = {X(2),X(4)}-harmonic conjugate of X(11286)
X(33184) = {X(2),X(20)}-harmonic conjugate of X(33191)
X(33184) = orthocentroidal-circle-inverse of X(11286)


X(33185) = (name pending)

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

As a point on the Euler line, X(33185) has Shinagawa coefficients (4(E+F)2-3S2,S2).

X(33185) lies on these lines: {2, 3}, {32, 14929}, {141, 6680}, {230, 7822}, {325, 7846}, {495, 30104}, {496, 30103}, {524, 7869}, {597, 7764}, {626, 18907}, {2023, 31274}, {3054, 31239}, {3589, 3788}, {3629, 7895}, {3793, 7879}, {3815, 7874}, {3933, 7760}, {5254, 7820}, {5305, 7795}, {5306, 7794}, {6390, 7803}, {6683, 24256}, {6704, 15491}, {7745, 7867}, {7750, 7944}, {7762, 7931}, {7767, 7868}, {7781, 7789}, {7827, 32820}, {7829, 7880}, {7835, 7943}, {7863, 9607}, {7875, 7945}, {7881, 16989}, {7883, 19661}, {7888, 9300}, {7916, 32455}, {7919, 32819}, {10386, 26590}, {14482, 32841}, {14535, 31404}, {19846, 26007}

X(33185) = complement of X(7866)
X(33185) = {X(2),X(3)}-harmonic conjugate of X(8364)
X(33185) = {X(2),X(5)}-harmonic conjugate of X(33186)
X(33185) = {X(2),X(20)}-harmonic conjugate of X(33194)


X(33186) = (name pending)

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

As a point on the Euler line, X(33186) has Shinagawa coefficients (4(E+F)2-5S2,-S2).

X(33186) lies on these lines: {2, 3}, {141, 7886}, {230, 7854}, {325, 7856}, {495, 30103}, {496, 30104}, {626, 14929}, {2023, 31239}, {2030, 5031}, {3054, 6292}, {3589, 7862}, {3763, 10542}, {3788, 7902}, {3815, 7852}, {3933, 7828}, {5254, 7863}, {5305, 7758}, {5306, 7821}, {6390, 7851}, {6680, 7843}, {6722, 7915}, {7762, 16984}, {7772, 22110}, {7789, 7844}, {7792, 7858}, {7806, 7946}, {7834, 31406}, {7849, 13468}, {7857, 7936}, {7872, 32459}, {7889, 31275}, {7922, 22329}, {10386, 26629}

X(33186) = complement of X(32954)
X(33186) = {X(2),X(5)}-harmonic conjugate of X(33185)
X(33186) = {X(2),X(20)}-harmonic conjugate of X(33195)


X(33187) = (name pending)

Barycentrics    8 a^2 SA - 16 SB SC - 3 (a^4 + b^4 + c^4) : :
Barycentrics    11*a^4 - 4*a^2*b^2 - b^4 - 4*a^2*c^2 + 8*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33187) has Shinagawa coefficients (3(E+F)2-7S2,12S2).

X(33187) lies on these lines: {2, 3}, {3972, 7739}, {4027, 8591}, {5032, 5969}, {5304, 8289}, {6645, 10385}, {6781, 7865}, {7737, 7799}, {7763, 14537}, {7785, 32837}, {7795, 11057}, {7816, 7855}, {7836, 19569}, {19570, 32815}

X(33187) = reflection of X(2) in X(33255)
X(33187) = reflection of X(33278) in X(2)
X(33187) = anticomplement of X(33251)
X(33187) = {X(2),X(20)}-harmonic conjugate of X(33263)


X(33188) = (name pending)

Barycentrics    24 a^2 SA+ 16 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 12*a^2*b^2 + 3*b^4 - 12*a^2*c^2 - 8*b^2*c^2 + 3*c^4 : :

As a point on the Euler line, X(33188) has Shinagawa coefficients ((E+F)2+11S2,-4S2).

X(33188) lies on these lines: {2, 3}, {148, 32867}, {2896, 32839}, {6179, 31401}, {7619, 7888}, {7738, 17006}, {8860, 9607}, {20065, 31455}, {22329, 31492}

X(33188) = {X(2),X(3)}-harmonic conjugate of X(32962)
X(33188) = {X(2),X(20)}-harmonic conjugate of X(33009)


X(33189) = (name pending)

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

As a point on the Euler line, X(33189) has Shinagawa coefficients (2(E+F)2-4S2,S2).

X(33189) lies on these lines: {2, 3}, {32, 32823}, {69, 7857}, {620, 7738}, {1007, 7858}, {1056, 26686}, {1058, 26629}, {1285, 32816}, {2030, 3619}, {3589, 10542}, {3618, 7769}, {3767, 7863}, {3788, 7735}, {5007, 9770}, {5218, 30103}, {5305, 32831}, {6337, 7828}, {6680, 7736}, {7288, 30104}, {7763, 7856}, {7792, 32829}, {7832, 18840}, {7846, 8781}, {7854, 7874}, {7867, 21843}, {7871, 11008}, {7886, 32822}, {7899, 32006}, {7945, 17008}, {9605, 32835}, {11174, 32839}, {14482, 16984}, {14614, 32825}, {22253, 32841}, {31274, 31401}, {31467, 32871}

X(33189) = complement of X(33199)
X(33189) = {X(2),X(3)}-harmonic conjugate of X(32951)
X(33189) = {X(2),X(4)}-harmonic conjugate of X(32955)
X(33189) = {X(2),X(5)}-harmonic conjugate of X(32958)
X(33189) = {X(2),X(384)}-harmonic conjugate of X(32969)
X(33189) = orthocentroidal-circle-inverse of X(32955)


X(33190) = (name pending)

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

As a point on the Euler line, X(33190) has Shinagawa coefficients (2(E+F)2,-3S2).

X(33190) lies on these lines: {2, 3}, {39, 9770}, {69, 7790}, {76, 5485}, {83, 18842}, {315, 1992}, {316, 2030}, {524, 5286}, {543, 7795}, {598, 7859}, {599, 5254}, {626, 7738}, {671, 3096}, {1007, 7934}, {1056, 26590}, {1058, 26561}, {1078, 23055}, {1285, 7792}, {2482, 7867}, {2548, 31173}, {2549, 7801}, {3619, 7937}, {3767, 7810}, {3785, 7851}, {3788, 7618}, {3849, 7834}, {3926, 9741}, {3934, 7615}, {4045, 7736}, {5013, 22110}, {5032, 7762}, {5319, 7873}, {5461, 7815}, {5523, 32000}, {5569, 7886}, {6337, 7847}, {6392, 7879}, {6683, 8176}, {7620, 21358}, {7735, 7761}, {7737, 7913}, {7739, 7818}, {7745, 23334}, {7746, 15810}, {7754, 11160}, {7767, 9740}, {7774, 14482}, {7797, 9939}, {7800, 7861}, {7803, 7812}, {7830, 8182}, {7836, 32480}, {7840, 7864}, {7850, 11008}, {7868, 32815}, {7898, 16989}, {7902, 14023}, {7904, 8859}, {7915, 32479}, {7919, 14907}, {7923, 20065}, {7942, 26613}, {8744, 26206}, {9166, 32832}, {9167, 15515}, {10159, 32532}, {10513, 22253}, {11148, 32840}, {11163, 32816}, {11165, 32831}, {11168, 13881}, {11174, 32827}, {11184, 31400}, {12040, 32835}, {13161, 29573}

X(33190) = midpoint of X(2) and X(33210)
X(33190) = reflection of X(14039) in X(2)
X(33190) = anticomplement of X(33237)
X(33190) = {X(2),X(20)}-harmonic conjugate of X(8369)


X(33191) = (name pending)

Barycentrics    2 a^2 SA - SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 4*a^2*b^2 + 3*b^4 - 4*a^2*c^2 + 2*b^2*c^2 + 3*c^4 : :

As a point on the Euler line, X(33191) has Shinagawa coefficients (2(E+F)2-4S2,3S2).

X(33191) lies on these lines: {2, 3}, {32, 32818}, {69, 7835}, {325, 1285}, {538, 7735}, {620, 7736}, {1007, 3972}, {1056, 26629}, {1058, 26686}, {1078, 18840}, {1992, 7799}, {2482, 7739}, {3619, 7771}, {3767, 32822}, {3788, 32823}, {3793, 10513}, {3926, 14614}, {5182, 14912}, {5286, 8716}, {5304, 6390}, {5485, 14568}, {6680, 7738}, {7763, 12150}, {7786, 18841}, {7789, 8667}, {7820, 21843}, {7865, 8182}, {8860, 32885}, {9764, 13357}, {14482, 16989}, {21356, 26613}, {22329, 32836}, {30435, 32831}, {31274, 31415}

X(33191) = reflection of X(33285) in X(2)
X(33191) = anticomplement of X(33240)
X(33191) = {X(2),X(20)}-harmonic conjugate of X(33184)


X(33192) = (name pending)

Barycentrics    8 a^2 SA - 16 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 4*a^2*b^2 - 5*b^4 - 4*a^2*c^2 + 8*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(33192) has Shinagawa coefficients ((E+F)2+3S2,-12S2).

X(33192) lies on these lines: {2, 3}, {148, 9939}, {193, 8586}, {315, 543}, {598, 7847}, {599, 32819}, {671, 7802}, {1078, 7615}, {1992, 7823}, {2482, 7825}, {2549, 7812}, {2896, 32826}, {3785, 7620}, {3849, 7748}, {3926, 8591}, {5032, 20088}, {5171, 9880}, {5206, 5461}, {5485, 17129}, {5969, 8596}, {7618, 7752}, {7737, 7827}, {7756, 7775}, {7763, 31173}, {7783, 9770}, {7785, 23334}, {7789, 11164}, {7801, 7842}, {7810, 11185}, {7840, 32006}, {7898, 32815}, {7906, 9741}, {7939, 32822}, {11054, 14023}, {14976, 19570}, {17128, 21356}

X(33192) = reflection of X(2) in X(33017)
X(33192) = reflection of X(33193) in X(2)
X(33192) = anticomplement of X(33007)
X(33192) = {X(2),X(20)}-harmonic conjugate of X(33208)


X(33193) = (name pending)

Barycentrics    8 a^2 SA - 16 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 4*a^2*b^2 - 3*b^4 - 4*a^2*c^2 + 8*b^2*c^2 - 3*c^4 : :

As a point on the Euler line, X(33193) has Shinagawa coefficients ((E+F)2-5S2,12S2).

X(33193) lies on these lines: {2, 3}, {193, 5969}, {538, 20065}, {2549, 12150}, {3849, 32833}, {5182, 31670}, {5309, 32479}, {6781, 11185}, {7737, 7757}, {7774, 8716}, {7793, 32826}, {7802, 32027}, {7893, 32822}, {7946, 32824}, {8667, 32819}, {9466, 14907}, {9939, 32836}, {11152, 13172}, {14135, 21849}, {14712, 22564}, {23334, 32837}

X(33193) = reflection of X(2) in X(33007)
X(33193) = reflection of X(33192) in X(2)
X(33193) = anticomplement of X(33017)
X(33193) = {X(2),X(20)}-harmonic conjugate of X(33207)


X(33194) = (name pending)

Barycentrics    2 a^2 SA + SB SC + 2 (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 + 4*a^2*b^2 + 7*b^4 + 4*a^2*c^2 + 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33194) has Shinagawa coefficients (4(E+F)2-2S2,-S2).

X(33194) lies on these lines: {2, 3}, {69, 7856}, {1007, 7859}, {1285, 7784}, {1992, 7922}, {2548, 18841}, {3618, 7858}, {3619, 7828}, {3767, 18840}, {6337, 7930}, {7735, 7852}, {7736, 7867}, {7738, 7863}, {7758, 7834}, {7790, 32822}, {7795, 7902}, {7803, 7909}, {7832, 32817}, {7846, 32006}, {7946, 16989}

X(33194) = {X(2),X(3)}-harmonic conjugate of X(32952)
X(33194) = {X(2),X(20)}-harmonic conjugate of X(33185)


X(33195) = (name pending)

Barycentrics    2 a^2 SA + SB SC - 2 (a^4 + b^4 + c^4) : :
Barycentrics    11*a^4 - 4*a^2*b^2 + 9*b^4 - 4*a^2*c^2 - 2*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(33195) has Shinagawa coefficients (4(E+F)2-6S2,S2).

X(33195) lies on these lines: {2, 3}, {1007, 7878}, {3618, 7940}, {7735, 7855}, {7760, 32818}, {7763, 14482}, {7828, 32817}, {7835, 32822}, {7926, 32823}

X(33195) = {X(2),X(3)}-harmonic conjugate of X(32953)
X(33195) = {X(2),X(20)}-harmonic conjugate of X(33186)


X(33196) = (name pending)

Barycentrics    2 a^2 SA - SB SC + 2 (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 + 4*a^2*b^2 + 9*b^4 + 4*a^2*c^2 - 2*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(33196) has Shinagawa coefficients (4(E+F)2-2S2,-3S2).

X(33196) lies on these lines: {2, 3}, {69, 7919}, {325, 14482}, {1992, 7884}, {3618, 7934}, {6337, 7918}, {7735, 7853}, {7736, 7913}, {7738, 7867}, {7757, 32818}, {7790, 32817}, {7803, 32823}, {7832, 32822}, {9466, 18840}, {12150, 32006}, {14568, 21356}, {18842, 31173}

X(33196) = {X(2),X(3)}-harmonic conjugate of X(33231)
X(33196) = {X(2),X(20)}-harmonic conjugate of X(8368)


X(33197) = (name pending)

Barycentrics    2 a^2 SA - SB SC - 2 (a^4 + b^4 + c^4) : :
Barycentrics    13*a^4 - 4*a^2*b^2 + 7*b^4 - 4*a^2*c^2 + 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33197) has Shinagawa coefficients (4(E+F)2-6S2,3S2).

X(33197) lies on these lines: {2, 3}, {1285, 7778}, {1992, 7870}, {2482, 7738}, {2548, 18842}, {3767, 5485}, {3788, 9770}, {5215, 7822}, {5286, 9741}, {5503, 9167}, {5569, 7915}, {6337, 7827}, {7615, 7886}, {7618, 7834}, {7735, 7801}, {7776, 19661}, {7792, 14482}, {7808, 22247}, {7812, 32823}, {7817, 15301}, {7828, 32822}, {7832, 21356}, {7835, 32817}, {7857, 23055}, {7881, 11160}, {7930, 26613}

X(33197) = {X(2),X(3)}-harmonic conjugate of X(33230)
X(33197) = {X(2),X(20)}-harmonic conjugate of X(8360)


X(33198) = (name pending)

Barycentrics    a^2 SA + 3 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 + 2*a^2*b^2 + b^4 + 2*a^2*c^2 + 6*b^2*c^2 + c^4 : :

As a point on the Euler line, X(33198) has Shinagawa coefficients (2(E+F)2-S2,2S2).

X(33198) lies on these lines: {2, 3}, {6, 32830}, {32, 15589}, {76, 5304}, {83, 3926}, {193, 5039}, {577, 26224}, {1285, 7767}, {1975, 3618}, {2482, 31450}, {2548, 7820}, {2549, 7889}, {3172, 32000}, {3589, 7738}, {3619, 7750}, {3620, 20065}, {3734, 5286}, {3785, 3972}, {3788, 31404}, {3815, 32835}, {3912, 4339}, {5265, 26959}, {5281, 27020}, {5306, 32874}, {5319, 17130}, {5395, 7785}, {6179, 9740}, {6337, 11174}, {6392, 16989}, {7735, 32834}, {7736, 7789}, {7737, 7822}, {7757, 32824}, {7759, 7795}, {7760, 32836}, {7762, 10513}, {7790, 32826}, {7803, 32815}, {7808, 31400}, {7832, 32816}, {7835, 32829}, {7846, 11185}, {7857, 32838}, {7858, 32825}, {7868, 32006}, {7874, 31415}, {7878, 32833}, {9605, 32817}, {10519, 12110}, {10590, 30104}, {10591, 30103}, {14535, 31406}, {14930, 32840}, {15048, 32822}, {15484, 32823}, {18221, 30139}, {21843, 31239}, {31489, 32871}

X(33198) = complement of X(33025)
X(33198) = anticomplement of X(32956)
X(33198) = {X(2),X(4)}-harmonic conjugate of X(33180)
X(33198) = orthocentroidal-circle-inverse of X(33180)


X(33199) = (name pending)

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

As a point on the Euler line, X(33199) has Shinagawa coefficients (2(E+F)2-3S2,-2S2).

X(33199) lies on these lines: {2, 3}, {193, 7912}, {626, 15589}, {1007, 7851}, {3096, 32838}, {3767, 7821}, {3785, 7934}, {3788, 15301}, {3926, 7899}, {5254, 32831}, {5286, 7764}, {5304, 7828}, {5305, 32823}, {5395, 10583}, {5461, 7869}, {6722, 7800}, {7738, 32835}, {7768, 9740}, {7778, 32830}, {7790, 32829}, {7834, 31404}, {7835, 32826}, {7852, 31415}, {7862, 31400}, {7870, 32824}, {7909, 32836}, {10590, 30103}, {10591, 30104}, {13881, 32834}, {14061, 32458}, {31275, 31401}

X(33199) = complement of X(33205)
X(33199) = anticomplement of X(33189)
X(33199) = {X(2),X(4)}-harmonic conjugate of X(33181)
X(33199) = {X(2),X(20)}-harmonic conjugate of X(33203)
X(33199) = orthocentroidal-circle-inverse of X(33181)


X(33200) = (name pending)

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

As a point on the Euler line, X(33200) has Shinagawa coefficients (2(E+F)2-S2,-4S2).

X(33200) lies on these lines: {2, 3}, {115, 32834}, {193, 7885}, {625, 31400}, {626, 32830}, {2549, 7888}, {3767, 7873}, {3785, 7911}, {3926, 7934}, {4045, 31404}, {5261, 26590}, {5274, 26561}, {5286, 7759}, {5304, 7851}, {5395, 7875}, {6392, 10513}, {7620, 17130}, {7784, 15589}, {7785, 14930}, {7790, 32816}, {7794, 32869}, {7803, 32827}, {7825, 7829}, {7831, 32838}, {7832, 32826}, {7847, 32829}, {7862, 32871}, {7865, 32893}, {7872, 32835}, {7909, 32824}, {7922, 32836}, {7935, 32870}, {8165, 26582}, {9607, 9770}, {15048, 32823}, {16990, 32872}

X(33200) = anticomplement of X(33181)
X(33200) = {X(2),X(20)}-harmonic conjugate of X(33205)


X(33201) = (name pending)

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

As a point on the Euler line, X(33201) has Shinagawa coefficients (2(E+F)2-3S2,4S2).

X(33201) lies on these lines: {2, 3}, {32, 32830}, {193, 32840}, {620, 31404}, {1285, 3933}, {1506, 32871}, {1975, 5304}, {1992, 32820}, {2548, 32835}, {2996, 7806}, {3053, 15589}, {3734, 32834}, {3926, 3972}, {5261, 26629}, {5274, 26686}, {5286, 7816}, {5305, 32822}, {5395, 7777}, {6179, 32836}, {7737, 7821}, {7751, 32869}, {7760, 32824}, {7764, 32831}, {7774, 32841}, {7787, 14930}, {7795, 7848}, {7804, 31400}, {7812, 32825}, {7828, 32826}, {7835, 32816}, {7858, 32837}, {8778, 32000}, {10513, 20065}, {17008, 32872}, {17129, 32882}, {17130, 32874}, {18907, 32818}, {30435, 32817}

X(33201) = anticomplement of X(33180)


X(33202) = (name pending)

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

As a point on the Euler line, X(33202) has Shinagawa coefficients (2(E+F)2+S2,-2S2).

X(33202) lies on these lines: {2, 3}, {141, 7738}, {193, 2896}, {194, 3620}, {253, 31360}, {599, 9607}, {626, 31400}, {1968, 26224}, {1975, 3619}, {2548, 7935}, {2549, 6292}, {3096, 3926}, {3424, 12203}, {3618, 7750}, {3785, 5304}, {4045, 5286}, {4339, 17023}, {4352, 4869}, {4419, 32034}, {5013, 32831}, {5024, 32818}, {5254, 32834}, {5261, 27020}, {5274, 26959}, {5319, 7810}, {6392, 7864}, {6683, 31404}, {7736, 7784}, {7739, 7854}, {7758, 7865}, {7762, 14930}, {7763, 7937}, {7774, 7928}, {7775, 31407}, {7778, 32835}, {7786, 32816}, {7790, 32828}, {7827, 9740}, {7839, 20080}, {7847, 32815}, {7852, 21843}, {7853, 31401}, {7859, 14907}, {7879, 10513}, {7881, 32841}, {7888, 31450}, {7899, 32839}, {7904, 16989}, {7909, 32837}, {7911, 32827}, {7918, 32832}, {7922, 32825}, {7923, 17008}, {8165, 27091}, {9606, 9770}, {11174, 32006}, {13881, 32870}, {14061, 32867}, {14986, 26590}, {20081, 32476}, {22110, 31492}, {31173, 31417}, {31406, 32823}, {31859, 32840}

X(33202) = anticomplement of X(16045)
X(33202) = {X(2),X(3)}-harmonic conjugate of X(33181)


X(33203) = (name pending)

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

As a point on the Euler line, X(33203) has Shinagawa coefficients (2(E+F)2-5S2,2S2).

X(33203) lies on these lines: {2, 3}, {6, 32835}, {83, 32839}, {230, 32830}, {620, 5286}, {1384, 32823}, {2030, 3620}, {2548, 31274}, {3618, 10542}, {3785, 7922}, {3788, 7882}, {3815, 32871}, {3926, 7857}, {5215, 7854}, {5304, 7763}, {6179, 32825}, {6392, 7891}, {6680, 31400}, {7618, 7902}, {7735, 32831}, {7754, 32841}, {7760, 32837}, {7772, 9167}, {7789, 32834}, {7794, 15589}, {7835, 32828}, {7870, 9740}, {7874, 21843}, {7940, 32816}, {7947, 20080}, {9748, 10256}, {14061, 32826}, {14568, 32824}, {14930, 32873}, {14986, 26629}, {22110, 22331}, {32458, 32829} /p>

X(33203) = anticomplement of X(32955)
X(33203) = {X(2),X(3)}-harmonic conjugate of X(33180)
X(33203) = {X(2),X(20)}-harmonic conjugate of X(33199)


X(33204) = (name pending)

Barycentrics    24 a^2 SA + 16 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 12*a^2*b^2 + 5*b^4 - 12*a^2*c^2 - 8*b^2*c^2 + 5*c^4 : :

As a point on the Euler line, X(33204) has Shinagawa coefficients ((E+F)2-13S2,4S2).

X(33204) lies on these lines: {2, 3}, {1153, 7854}, {3620, 10485}, {6337, 17006}, {7619, 7772}, {7749, 7798}, {7769, 7949}, {7793, 32839}

X(33204) = {X(2),X(3)}-harmonic conjugate of X(32963)
X(33204) = {X(2),X(20)}-harmonic conjugate of X(33270)


X(33205) = (name pending)

Barycentrics    3 a^2 SA - SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    11*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 + 2*b^2*c^2 + 3*c^4 : :

As a point on the Euler line, X(33205) has Shinagawa coefficients (2(E+F)2-5S2,4S2).

X(33205) lies on these lines: {2, 3}, {32, 32831}, {193, 7891}, {385, 32840}, {390, 26686}, {620, 32835}, {1384, 32818}, {2482, 5319}, {3600, 26629}, {3785, 7835}, {3926, 6179}, {3972, 32829}, {5304, 6337}, {7618, 7829}, {7738, 32459}, {7749, 32870}, {7751, 32830}, {7777, 32873}, {7789, 15589}, {7836, 10513}, {7849, 8182}, {7857, 32815}, {7940, 32827}, {9737, 9748}, {17128, 32872}, {17129, 32880}, {17130, 32834}, {31404, 32871}

X(33205) = anticomplement of X(33199)
X(33205) = {X(2),X(20)}-harmonic conjugate of X(33200)


X(33206) = (name pending)

Barycentrics    16 a^2 SA + 8 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 8*a^2*b^2 + 3*b^4 - 8*a^2*c^2 - 4*b^2*c^2 + 3*c^4 : :

As a point on the Euler line, X(33206) has Shinagawa coefficients ((E+F)2-9S2,4S2).

X(33206) lies on these lines: {2, 3}, {5569, 7821}, {6337, 17004}, {7610, 32820}, {7622, 7755}, {7749, 7781}, {7763, 7780}, {7769, 7926}, {7779, 32835}, {7785, 32839}, {7793, 32829}, {7856, 31450}, {7860, 8182}, {7869, 9167}, {7878, 31401}

X(33206) = anticomplement of X(32998)
X(33206) = {X(2),X(3)}-harmonic conjugate of X(14063)
X(33206) = {X(2),X(4)}-harmonic conjugate of X(33270)
X(33206) = {X(2),X(20)}-harmonic conjugate of X(32963)
X(33206) = orthocentroidal-circle-inverse of X(33270)


X(33207) = (name pending)

Barycentrics    16 a^2 SA - 8 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 8*a^2*b^2 - 3*b^4 - 8*a^2*c^2 + 4*b^2*c^2 - 3*c^4 : :

As a point on the Euler line, X(33207) has Shinagawa coefficients ((E+F)2+7S2,-12S2).

X(33207) lies on these lines: {2, 3}, {538, 14907}, {5032, 5111}, {7618, 7809}, {7750, 8716}, {7757, 20065}, {8182, 14568}, {8556, 32819}, {8591, 32836}, {9862, 11152}, {9983, 32474}, {11055, 14023}, {11742, 15271}, {15589, 20094}

X(33207) = reflection of X(2) in X(33008)
X(33207) = anticomplement of X(33016)
X(33207) = {X(2),X(20)}-harmonic conjugate of X(33193)


X(33208) = (name pending)

Barycentrics    16 a^2 SA - 8 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    11*a^4 - 8*a^2*b^2 - b^4 - 8*a^2*c^2 + 4*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33208) has Shinagawa coefficients ((E+F)2-9S2,12S2).

X(33208) lies on these lines: {2, 3}, {76, 8182}, {193, 5104}, {194, 22564}, {315, 2482}, {543, 5206}, {598, 31401}, {1992, 7783}, {8587, 8596}, {3767, 26613}, {3849, 7763}, {3926, 9939}, {5032, 13330}, {5210, 17008}, {5237, 12154}, {5238, 12155}, {5286, 32480}, {5395, 10484}, {5569, 32832}, {5939, 20094}, {6781, 7775}, {7610, 32819}, {7618, 7812}, {7622, 7747}, {7746, 32479}, {7751, 15300}, {7762, 11165}, {7782, 7905}, {7793, 8591}, {7801, 7848}, {7823, 9770}, {7825, 9167}, {7904, 21356}, {8588, 11185}, {9740, 20081}, {11147, 32006}, {11148, 20105}, {11152, 12251}, {15533, 32820}, {23334, 32829}

X(33208) = anticomplement of X(33006)
X(33208) = {X(2),X(20)}-harmonic conjugate of X(33192)


X(33209) = (name pending)

Barycentrics    16 a^2 SA - 16 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    11*a^4 - 8*a^2*b^2 - 5*b^4 - 8*a^2*c^2 + 8*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(33209) has Shinagawa coefficients ((E+F)2+7S2,-16S2).

X(33209) lies on these lines: {2, 3}, {315, 14148}, {6781, 7902}, {7756, 7798}, {7758, 7802}

X(33209) = anticomplement of X(14068)
X(33209) = {X(2),X(20)}-harmonic conjugate of X(33214)


X(33210) = (name pending)

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

As a point on the Euler line, X(33210) has Shinagawa coefficients (2(E+F)2+S2,-6S2).

X(33210) lies on these lines: {2, 3}, {148, 3620}, {193, 7898}, {599, 32869}, {754, 5286}, {2549, 7813}, {2896, 2996}, {3096, 32826}, {3785, 7910}, {3926, 7911}, {5304, 7790}, {7620, 9466}, {7738, 9766}, {7753, 23334}, {7761, 15589}, {7784, 32830}, {7797, 14976}, {7800, 18546}, {7811, 9740}, {7825, 31400}, {7847, 32816}, {7883, 32836}, {7922, 32824}, {11185, 31168}

X(33210) = reflection of X(2) in X(33190)
X(33210) = anticomplement of X(14039)


X(33211) = (name pending)

Barycentrics    a^2 SA + 2 SB SC + 4 (a^4 + b^4 + c^4) : :
As a point on the Euler line, X(33211) has Shinagawa coefficients (8(E+F)2-7S2,S2).

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

X(33211) lies on these lines: {2, 3}, {3933, 7856}, {6680, 7848}, {7789, 7902}, {7792, 7905}, {7852, 7863}, {7867, 18907}, {7874, 31406}

X(33211) = {X(2),X(5)}-harmonic conjugate of X(33212)


X(33212) = (name pending)

Barycentrics    a^2 SA + 2 SB SC - 4 (a^4 + b^4 + c^4) : :
Barycentrics    8*a^4 - a^2*b^2 + 9*b^4 - a^2*c^2 - 2*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(33212) has Shinagawa coefficients (8(E+F)2-9S2,-S2).

X(33212) lies on these lines: {2, 3}, {3933, 7942}, {7852, 31406}, {7860, 19661}, {7874, 15048}

X(33212) = {X(2),X(5)}-harmonic conjugate of X(33211)


X(33213) = (name pending)

Barycentrics    a^2 SA - 2 SB SC + 4 (a^4 + b^4 + c^4) : :
Barycentrics    6*a^4 + a^2*b^2 + 9*b^4 + a^2*c^2 - 2*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(33213) has Shinagawa coefficients (8(E+F)2-7S2,-3S2).

X(33213) lies on these lines: {2, 3}, {3793, 16984}, {5305, 7855}, {5969, 6722}, {6390, 7919}, {7767, 7942}, {7792, 7926}, {15172, 30104}

X(33213) = midpoint of X(2) and X(8360)
X(33213) = reflection of X(8365) in X(2)
X(33213) = complement of X(8368)


X(33214) = (name pending)

Barycentrics    16 a^2 SA - 16 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    13*a^4 - 8*a^2*b^2 - 3*b^4 - 8*a^2*c^2 + 8*b^2*c^2 - 3*c^4 : :

As a point on the Euler line, X(33214) has Shinagawa coefficients ((E+F)2-9S2,16S2).

X(33214) lies on these lines: {2, 3}, {6781, 7781}, {9939, 32824}

X(33214) = anticomplement of X(32996)
X(33214) = {X(2),X(20)}-harmonic conjugate of X(33209)


X(33215) = (name pending)

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

As a point on the Euler line, X(33215) has Shinagawa coefficients ((E+F)2+3S2,-3S2).

X(33215) lies on these lines: {2, 3}, {32, 8182}, {39, 1992}, {69, 574}, {76, 11172}, {187, 3618}, {193, 5024}, {315, 9770}, {524, 3785}, {543, 7815}, {597, 3053}, {599, 3926}, {626, 7622}, {671, 32832}, {988, 29574}, {1007, 7761}, {1078, 7738}, {1153, 7861}, {1285, 3329}, {2482, 7795}, {2548, 3849}, {2549, 32457}, {2896, 32818}, {3589, 5210}, {3619, 8589}, {3620, 6390}, {3763, 32459}, {3767, 23055}, {3933, 11165}, {4045, 21843}, {5032, 9605}, {5171, 20423}, {5188, 22486}, {5254, 7610}, {5286, 22329}, {5461, 7872}, {5485, 32480}, {5569, 7817}, {6292, 11147}, {6337, 7618}, {7615, 7748}, {7619, 7862}, {7735, 7771}, {7736, 7812}, {7737, 15482}, {7746, 23053}, {7750, 11163}, {7754, 9740}, {7758, 31652}, {7759, 31450}, {7763, 7883}, {7766, 14482}, {7767, 11160}, {7774, 9939}, {7775, 7830}, {7783, 9741}, {7784, 22110}, {7789, 21358}, {7831, 7870}, {7840, 7904}, {7842, 8176}, {7864, 8859}, {7867, 9167}, {7873, 31457}, {7879, 32831}, {7930, 11149}, {8591, 31276}, {8593, 10991}, {8716, 32836}, {11161, 14981}, {11168, 32828}, {11171, 14912}, {11177, 32522}, {11179, 13334}, {11184, 32816}, {13881, 15597}, {15271, 32815}, {15300, 17130}, {15534, 22332}, {15589, 31859}, {16990, 32817}, {21163, 25406}, {23334, 31404}, {31173, 31455}, {31489, 32827}

X(33215) = reflection of X(32983) in X(2)
X(33215) = {X(2),X(3)}-harmonic conjugate of X(32985)
X(33215) = {X(2),X(20)}-harmonic conjugate of X(8370)
X(33215) = {X(37172),X(37173)}-harmonic conjugate of X(631)


X(33216) = (name pending)

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

As a point on the Euler line, X(33216) has Shinagawa coefficients ((E+F)2-5S2,3S2).

X(33216) lies on these lines: {2, 3}, {69, 620}, {187, 1007}, {230, 8716}, {524, 10008}, {538, 6337}, {543, 11147}, {1285, 7777}, {1692, 1992}, {2482, 23055}, {2782, 7612}, {3053, 32829}, {3618, 22486}, {3926, 8667}, {5028, 7622}, {5032, 12040}, {5206, 32006}, {5215, 5309}, {5569, 7880}, {7735, 7757}, {7736, 12150}, {7738, 7857}, {7745, 32839}, {7762, 32835}, {7763, 7877}, {7789, 8556}, {7793, 32818}, {7818, 8182}, {8588, 31274}, {8859, 9741}, {9754, 21166}, {9770, 26613}, {10796, 14494}, {13468, 32836}, {17008, 32817}, {32459, 32815}

X(33216) = reflection of X(32984) in X(2)
X(33216) = {X(2),X(3)}-harmonic conjugate of X(32986)
X(33216) = {X(2),X(20)}-harmonic conjugate of X(33228)


X(33217) = (name pending)

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

As a point on the Euler line, X(33217) has Shinagawa coefficients (3(E+F)2-2S2,S2).

X(33217) lies on these lines: {2, 3}, {6, 7796}, {32, 7848}, {83, 7778}, {99, 7943}, {183, 6680}, {187, 7914}, {599, 6179}, {620, 31457}, {1007, 31407}, {1078, 3763}, {1384, 2896}, {1975, 7765}, {3053, 3096}, {3314, 10583}, {3329, 7945}, {3589, 7763}, {3734, 7851}, {3788, 7889}, {3933, 16989}, {3972, 7784}, {4309, 26590}, {4317, 26561}, {5007, 7788}, {5008, 7896}, {5013, 7835}, {5023, 7831}, {5024, 7891}, {5041, 7908}, {5319, 7754}, {6704, 31455}, {7739, 32820}, {7772, 7880}, {7773, 7804}, {7776, 7787}, {7786, 24256}, {7789, 7803}, {7794, 14614}, {7801, 7829}, {7808, 7874}, {7811, 22331}, {7816, 7913}, {7817, 17130}, {7836, 7875}, {7857, 15271}, {7878, 7909}, {7888, 11163}, {7893, 21309}, {7912, 15484}, {7920, 22253}, {7922, 12150}, {7932, 17128}, {7940, 31489}, {7942, 13881}, {10333, 11842}, {10335, 16987}, {16984, 31276}, {26629, 31452}

X(33217) = {X(2),X(4)}-harmonic conjugate of X(8363)
X(33217) = {X(2),X(5)}-harmonic conjugate of X(33218)
X(33217) = {X(2),X(20)}-harmonic conjugate of X(33221)
X(33217) = orthocentroidal-circle-inverse of X(8363)


X(33218) = (name pending)

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

As a point on the Euler line, X(33218) has Shinagawa coefficients (3(E+F)2-4S2,-S2).

X(33218) lies on these lines: {2, 3}, {6, 7814}, {183, 7849}, {230, 7879}, {325, 5319}, {1384, 7885}, {1975, 7844}, {3053, 7934}, {3618, 31407}, {3767, 7881}, {3788, 7765}, {4045, 31457}, {4309, 26629}, {4317, 26686}, {5013, 7919}, {5023, 7911}, {5024, 7923}, {5210, 7910}, {5309, 32821}, {6680, 7773}, {6722, 7822}, {7746, 7868}, {7754, 7778}, {7755, 7788}, {7763, 9607}, {7769, 31492}, {7776, 7806}, {7784, 7857}, {7803, 9606}, {7808, 31275}, {7817, 7888}, {7821, 14614}, {7829, 11163}, {7832, 13881}, {7834, 9698}, {7852, 7862}, {7856, 9766}, {7859, 31489}, {7860, 22331}, {7900, 21309}, {7912, 16984}, {7918, 15815}, {7922, 8667}, {7925, 7932}, {7930, 14061}, {7944, 15271}, {7947, 22253}, {10583, 15484}, {26558, 31458}, {26590, 31452}

X(33218) = {X(2),X(5)}-harmonic conjugate of X(33217)
X(33218) = {X(2),X(20)}-harmonic conjugate of X(33222)


X(33219) = (name pending)

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

As a point on the Euler line, X(33219) has Shinagawa coefficients (3(E+F)2-2S2,-3S2).

X(33219) lies on these lines: {2, 3}, {6, 7809}, {115, 7868}, {183, 7844}, {315, 5306}, {325, 7739}, {599, 14568}, {625, 7913}, {626, 5309}, {1384, 7898}, {1975, 7861}, {3053, 7911}, {3096, 13881}, {3314, 19570}, {3767, 7879}, {3934, 18362}, {5013, 7899}, {5023, 7910}, {5024, 7925}, {5254, 7881}, {5969, 9166}, {7738, 32837}, {7753, 7773}, {7765, 32821}, {7776, 7797}, {7778, 7790}, {7784, 7811}, {7803, 9300}, {7817, 7818}, {7821, 7902}, {7825, 7852}, {7827, 9766}, {7870, 8716}, {7872, 7874}, {7875, 15484}, {7883, 8667}, {7885, 7932}, {7886, 7935}, {7897, 22253}, {7912, 7923}, {7937, 14061}, {7940, 15815}, {8556, 31168}, {10056, 26590}, {10072, 26561}, {10352, 22566}, {14535, 16987}, {15482, 31275}

X(33219) = midpoint of X(2) and X(33251)
X(33219) = reflection of X(33220) in X(2)
X(33219) = complement of X(33255)
X(33219) = {X(2),X(4)}-harmonic conjugate of X(6661)
X(33219) = {X(2),X(20)}-harmonic conjugate of X(33224)
X(33219) = orthocentroidal-circle-inverse of X(6661)


X(33220) = (name pending)

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

As a point on the Euler line, X(33220) has Shinagawa coefficients (3(E+F)2-4S2,3S2).

X(33220) lies on these lines: {2, 3}, {6, 7799}, {32, 7788}, {99, 7884}, {183, 7820}, {187, 7865}, {620, 11174}, {1384, 3314}, {1975, 5309}, {3053, 7811}, {3096, 5023}, {3763, 7771}, {3788, 7753}, {3972, 7778}, {5007, 32821}, {5008, 7908}, {5013, 7846}, {5024, 7875}, {5206, 7915}, {5210, 7831}, {5306, 7754}, {5319, 32820}, {6390, 16989}, {7735, 32836}, {7739, 7792}, {7763, 9300}, {7768, 22331}, {7773, 7874}, {7776, 7945}, {7779, 21309}, {7784, 7930}, {7801, 14614}, {7806, 19570}, {7816, 7851}, {7827, 8716}, {7836, 7837}, {7859, 15815}, {7870, 9766}, {7885, 19569}, {7886, 18362}, {7891, 9605}, {7913, 32456}, {7914, 15513}, {7925, 15484}, {10056, 26629}, {10072, 26686}, {10334, 11842}, {10335, 11165}, {21358, 26613}

X(33220) = midpoint of X(2) and X(33255)
X(33220) = reflection of X(33219) in X(2)
X(33220) = complement of X(33251)
X(33220) = {X(2),X(20)}-harmonic conjugate of X(33223)


X(33221) = (name pending)

Barycentrics    4 a^2 SA + 2 SB SC + 3 (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 + 4*a^2*b^2 + 5*b^4 + 4*a^2*c^2 + 2*b^2*c^2 + 5*c^4 : :

As a point on the Euler line, X(33221) has Shinagawa coefficients (3(E+F)2-S2,-S2).

X(33221) lies on these lines: {2, 3}, {69, 5319}, {315, 7943}, {626, 3618}, {1007, 7867}, {1285, 10583}, {1992, 7829}, {2549, 7915}, {3096, 7735}, {3329, 32823}, {3589, 32816}, {3619, 3767}, {3620, 5305}, {3763, 32828}, {3788, 31450}, {3926, 9607}, {4045, 6337}, {5286, 7868}, {5304, 7879}, {6704, 31415}, {7736, 7814}, {7738, 7832}, {7739, 7869}, {7751, 21356}, {7765, 7795}, {7778, 9606}, {7796, 7803}, {7800, 7852}, {7808, 31417}, {7853, 32006}, {7864, 32817}, {7874, 31457}, {7896, 11008}, {7906, 14482}, {7931, 32818}, {7932, 10336}, {7938, 16989}, {11174, 31407}, {16987, 18841}, {20172, 31420}, {22332, 32837}, {30104, 31452}, {31492, 32829}

X(33221) = {X(2),X(20)}-harmonic conjugate of X(33217)


X(33222) = (name pending)

Barycentrics    4 a^2 SA + 2 SB SC - 3 (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 4*a^2*b^2 + 7*b^4 - 4*a^2*c^2 - 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33222) has Shinagawa coefficients (3(E+F)2-5S2,S2).

X(33222) lies on these lines: {2, 3}, {69, 7874}, {1007, 6680}, {1285, 7912}, {1992, 7888}, {3589, 32839}, {3618, 9698}, {3619, 7749}, {3788, 5319}, {5306, 32825}, {6337, 7765}, {7735, 7796}, {7736, 7940}, {7738, 7942}, {7806, 32818}, {7834, 31450}, {7852, 31457}, {7857, 32027}, {7862, 31417}, {9606, 32829}, {15491, 32884}, {17004, 18840}, {30103, 31452}

X(33222) = {X(2),X(20)}-harmonic conjugate of X(33218)


X(33223) = (name pending)

Barycentrics    4 a^2 SA - 2 SB SC + 3 (a^4 + b^4 + c^4) : :
Barycentrics    a^4 + 4*a^2*b^2 + 7*b^4 + 4*a^2*c^2 - 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33223) has Shinagawa coefficients (3(E+F)2-S2,-3S2).

X(33223) lies on these lines: {2, 3}, {69, 5309}, {115, 3619}, {315, 7884}, {626, 7739}, {1007, 4045}, {1285, 7898}, {1992, 7818}, {2549, 7880}, {3589, 32827}, {3618, 7753}, {3767, 7865}, {5254, 32836}, {5286, 7788}, {5306, 7784}, {5355, 11008}, {6292, 18362}, {6337, 7867}, {7735, 7811}, {7736, 7934}, {7738, 7799}, {7778, 32837}, {7790, 32833}, {7795, 11648}, {7803, 7809}, {7834, 32006}, {7837, 7923}, {7864, 32818}, {7931, 32817}, {7938, 19570}, {9300, 32816}, {9607, 32825}, {10583, 19569}, {13881, 32885}

X(33223) = midpoint of X(2) and X(32974)
X(33223) = reflection of X(2) in X(7866)
X(33223) = reflection of X(14001) in X(2)
X(33223) = {X(2),X(20)}-harmonic conjugate of X(33220)
X(33223) = {X(37170),X(37171)}-harmonic conjugate of X(4)


X(33224) = (name pending)

Barycentrics    4 a^2 SA - 2 SB SC - 3 (a^4 + b^4 + c^4) : :
Barycentrics    11*a^4 - 4*a^2*b^2 + 5*b^4 - 4*a^2*c^2 + 2*b^2*c^2 + 5*c^4 : :

As a point on the Euler line, X(33224) has Shinagawa coefficients (3(E+F)2-5S2,3S2).

X(33224) lies on these lines: {2, 3}, {6, 32837}, {69, 7880}, {620, 3618}, {1007, 7753}, {3619, 21843}, {3926, 5306}, {6337, 6680}, {7735, 7835}, {7738, 7884}, {7789, 32836}, {7799, 7894}, {7806, 32817}, {7837, 32818}, {7874, 32006}, {7908, 11008}, {9466, 23055}, {9770, 12150}

X(33224) = midpoint of X(2) and X(32973)
X(33224) = reflection of X(2) in X(32954)
X(33224) = reflection of X(14064) in X(2)
X(33224) = {X(2),X(20)}-harmonic conjugate of X(33219)


X(33225) = (name pending)

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

As a point on the Euler line, X(33225) has Shinagawa coefficients (3(E+F)2-5S2,4S2).

X(33225) lies on these lines: {2, 3}, {6, 7891}, {32, 7779}, {39, 8782}, {83, 620}, {99, 6680}, {147, 13335}, {148, 7816}, {187, 2896}, {194, 5319}, {230, 17128}, {315, 7945}, {316, 7874}, {325, 20088}, {385, 7789}, {574, 7846}, {626, 14712}, {754, 7909}, {1078, 7820}, {1384, 7881}, {1975, 7806}, {2080, 10333}, {2482, 7829}, {2549, 7932}, {3053, 3314}, {3096, 5206}, {3329, 9606}, {3398, 10353}, {3734, 7857}, {3788, 3972}, {3926, 7766}, {4027, 14981}, {4325, 30104}, {4330, 30103}, {4366, 26686}, {5007, 7799}, {5008, 7905}, {5013, 7875}, {7868, 7904}, {5152, 11606}, {5254, 16984}, {5306, 32820}, {5368, 14148}, {5475, 7940}, {6179, 7801}, {6337, 10335}, {6390, 7839}, {6645, 15888}, {6722, 15031}, {6781, 7911}, {7735, 20081}, {7737, 7912}, {7745, 7925}, {7747, 7899}, {7748, 7942}, {7750, 7931}, {7755, 19570}, {7756, 7919}, {7759, 7870}, {7760, 7863}, {7761, 7930}, {7762, 7947}, {7763, 7787}, {7764, 12150}, {7768, 7880}, {7769, 7804}, {7771, 7822}, {7778, 7823}, {7781, 7856}, {7782, 7834}, {7783, 7792}, {7786, 31457}, {7788, 22331}, {7793, 7795}, {7802, 7867}, {7811, 7869}, {7812, 7888}, {7817, 8591}, {7830, 7944}, {7831, 7915}, {7837, 32821}, {7847, 7852}, {7897, 20065}, {7906, 30435}, {7914, 8588}, {7920, 31859}, {7938, 14907}, {7941, 18907}, {8259, 30472}, {8260, 30471}, {9865, 13357}, {9998, 14820}, {10351, 11842}, {11174, 31492}, {17277, 24384}, {20105, 32817}, {31407, 32829}

X(33225) = anticomplement of X(7901)
X(33225) = {X(2),X(3)}-harmonic conjugate of X(33021)
X(33225) = {X(2),X(20)}-harmonic conjugate of X(7933)


X(33226) = (name pending)

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

As a point on the Euler line, X(33226) has Shinagawa coefficients ((E+F)2+3S2,-5S2).

X(33226) lies on these lines: {2, 3}, {69, 7781}, {574, 32006}, {599, 32824}, {2549, 7780}, {2896, 32817}, {3619, 7816}, {3631, 10008}, {6337, 7761}, {7618, 7821}, {7735, 7847}, {7736, 7802}, {7738, 7760}, {7755, 8182}, {7843, 31450}, {7860, 9770}, {7872, 21843}, {7898, 32823}, {11008, 32450}, {15271, 32826}, {15598, 32868}, {15815, 32816}, {16990, 32822}

X(33226) = {X(2),X(20)}-harmonic conjugate of X(19687)


X(33227) = (name pending)

Barycentrics    9 a^2 SA - 2 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    12*a^4 - 9*a^2*b^2 + b^4 - 9*a^2*c^2 + 2*b^2*c^2 + c^4 : :

As a point on the Euler line, X(33227) has Shinagawa coefficients (2(E+F)2-11S2,11S2).

X(33227) lies on these lines: {2, 3}, {187, 7890}, {3793, 6337}, {3926, 15655}, {3933, 5206}, {6390, 14023}, {5210, 7767}, {5585, 7800}, {7772, 19661}, {7789, 8588}, {7794, 15513}, {7858, 12040}, {7891, 14929}


X(33228) = (name pending)

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

As a point on the Euler line, X(33228) has Shinagawa coefficients ((E+F)2-2S2,-3S2).

X(33228) lies on these lines: {2, 3}, {115, 325}, {141, 7934}, {148, 6390}, {187, 6722}, {230, 316}, {315, 8667}, {511, 23514}, {524, 5103}, {597, 7884}, {599, 21399}, {620, 31275}, {626, 9466}, {671, 7799}, {754, 5461}, {1007, 31859}, {1503, 5182}, {1506, 7861}, {2548, 7851}, {3054, 7771}, {3564, 14651}, {3583, 26629}, {3585, 26686}, {3589, 7919}, {3614, 27020}, {3629, 7926}, {3734, 18424}, {3767, 7762}, {3788, 32819}, {3814, 26582}, {3815, 7790}, {3849, 14971}, {3933, 7912}, {4045, 7603}, {5031, 5969}, {5254, 7752}, {5305, 7785}, {5306, 7812}, {5309, 7775}, {5475, 7792}, {5480, 22486}, {6036, 13449}, {6392, 32823}, {7173, 26959}, {7617, 7865}, {7735, 32827}, {7739, 11163}, {7741, 26561}, {7745, 7828}, {7746, 7750}, {7747, 7886}, {7748, 7862}, {7749, 7842}, {7753, 7817}, {7754, 32816}, {7755, 7843}, {7763, 8716}, {7767, 7885}, {7777, 15048}, {7778, 11185}, {7784, 8556}, {7789, 7899}, {7801, 18546}, {7806, 18907}, {7811, 13468}, {7814, 11055}, {7818, 18362}, {7821, 14711}, {7827, 9300}, {7832, 15031}, {7840, 19570}, {7864, 31406}, {7872, 31455}, {7879, 32828}, {7888, 32820}, {7898, 17004}, {7951, 26590}, {9167, 10150}, {10256, 21166}, {11174, 31415}, {11646, 12151}, {12040, 32480}, {13850, 32808}, {13932, 32809}, {15484, 16989}, {21849, 27374}, {25639, 26558}, {31274, 32456}

X(33228) = midpoint of X(2) and X(14041)
X(33228) = complement of X(13586)
X(33228) = {X(2),X(4)}-harmonic conjugate of X(1003)
X(33228) = {X(2),X(20)}-harmonic conjugate of X(33216)
X(33228) = {X(3),X(14063)}-harmonic conjugate of X(33229)
X(33228) = orthocentroidal-circle-inverse of X(1003)


X(33229) = (name pending)

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

As a point on the Euler line, X(33229) has Shinagawa coefficients ((E+F)2,-5S2).

X(33229) lies on these lines: {2, 3}, {76, 3631}, {115, 7750}, {141, 7911}, {148, 3933}, {230, 7802}, {316, 3629}, {325, 7748}, {524, 7860}, {543, 7821}, {625, 7756}, {626, 32819}, {671, 7768}, {2549, 7773}, {3398, 10242}, {3583, 26561}, {3585, 26590}, {3589, 7918}, {3815, 7847}, {3849, 7755}, {5305, 7823}, {5395, 18843}, {5475, 7872}, {6329, 7745}, {6390, 7912}, {6722, 15513}, {6781, 7886}, {7737, 7851}, {7738, 32827}, {7747, 7792}, {7754, 11008}, {7759, 11648}, {7764, 31173}, {7765, 7843}, {7767, 7898}, {7784, 11185}, {7785, 15048}, {7789, 7934}, {7797, 18907}, {7812, 20583}, {7815, 18424}, {7826, 32457}, {7829, 14537}, {7831, 15031}, {7854, 18546}, {7858, 9607}, {7881, 32815}, {7940, 32459}, {7947, 20094}, {10483, 26686}, {13881, 14907}, {14929, 17129}, {31859, 32816}

X(33229) = reflection of X(7807) in X(5025)
X(33229) = complement of X(33257)
X(33229) = {X(3),X(14063)}-harmonic conjugate of X(33228)


X(33230) = (name pending)

Barycentrics    4 a^2 SA + SB SC + 2 (a^4 + b^4 + c^4) : :
Barycentrics    a^4 + 8*a^2*b^2 + 7*b^4 + 8*a^2*c^2 + 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33230) has Shinagawa coefficients (4(E+F)2,-3S2).

X(33230) lies on these lines: {2, 3}, {69, 7827}, {543, 7914}, {597, 7784}, {599, 5286}, {626, 9770}, {1285, 7761}, {1992, 7803}, {3096, 21356}, {3618, 7812}, {3619, 7790}, {4045, 7908}, {5254, 5485}, {5305, 9740}, {6337, 7944}, {6680, 8182}, {7615, 7861}, {7735, 7810}, {7736, 7853}, {7738, 7801}, {7745, 18841}, {7800, 7817}, {7828, 23055}, {7859, 32006}, {7868, 32817}, {7879, 11160}, {9939, 16989}, {11163, 32823}, {22110, 31400}

X(33230) = {X(2),X(3)}-harmonic conjugate of X(33197)
X(33230) = {X(2),X(20)}-harmonic conjugate of X(33237)


X(33231) = (name pending)

Barycentrics    4 a^2 SA + SB SC - 2 (a^4 + b^4 + c^4) : :
Barycentrics    15*a^4 - 8*a^2*b^2 + 9*b^4 - 8*a^2*c^2 - 2*b^2*c^2 + 9*c^4 : :

As a point on the Euler line, X(33231) has Shinagawa coefficients (4(E+F)2-8S2,3S2).

X(33231) lies on these lines: {2, 3}, {1007, 12150}, {5309, 9741}, {7735, 7813}, {8556, 18840}, {14614, 32818}

X(33231) = {X(2),X(3)}-harmonic conjugate of X(33196)
X(33231) = {X(2),X(20)}-harmonic conjugate of X(33240)


X(33232) = (name pending)

Barycentrics    4 a^2 SA - SB SC + 2 (a^4 + b^4 + c^4) : :
Barycentrics    a^4 - 8*a^2*b^2 - 9*b^4 - 8*a^2*c^2 + 2*b^2*c^2 - 9*c^4 : :

As a point on the Euler line, X(33232) has Shinagawa coefficients (4(E+F)2,-5S2).

X(33232) lies on these lines: {2, 3}, {69, 7918}, {1285, 7834}, {3618, 7911}, {3629, 7784}, {7735, 7935}, {7738, 7853}, {7760, 11008}, {7776, 14482}, {7868, 32822}, {7878, 32006}, {18841, 18843}

X(33232) = {X(2),X(20)}-harmonic conjugate of X(33242)


X(33233) = (name pending)

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

As a point on the Euler line, X(33233) has Shinagawa coefficients ((E+F)2-4S2,S2).

X(33233) lies on these lines: {2, 3}, {6, 7769}, {83, 31489}, {99, 13881}, {183, 3788}, {187, 7773}, {230, 7754}, {316, 5023}, {325, 14023}, {498, 26686}, {499, 26629}, {574, 7851}, {599, 7909}, {620, 1975}, {625, 5206}, {1007, 7762}, {1078, 7778}, {1384, 7785}, {3053, 7752}, {3054, 7789}, {3329, 31467}, {3763, 7930}, {3767, 31859}, {3933, 17008}, {5007, 11163}, {5013, 7828}, {5024, 7797}, {5182, 15069}, {5210, 7802}, {5215, 7775}, {5444, 30124}, {5445, 30120}, {6179, 9766}, {6645, 31479}, {6680, 11174}, {6683, 32452}, {6722, 7748}, {7610, 7870}, {7622, 7902}, {7735, 32829}, {7736, 32839}, {7750, 21843}, {7751, 32821}, {7758, 22329}, {7764, 14614}, {7771, 7784}, {7776, 7793}, {7777, 30435}, {7780, 7788}, {7782, 14061}, {7787, 17005}, {7790, 15815}, {7792, 31401}, {7796, 8667}, {7801, 8860}, {7806, 9605}, {7812, 22331}, {7815, 7868}, {7825, 15513}, {7827, 22332}, {7832, 15271}, {7836, 17004}, {7842, 8588}, {7852, 15482}, {7858, 11184}, {7861, 15515}, {7863, 9167}, {7872, 8589}, {7921, 21309}, {9754, 10256}, {10104, 10352}, {16989, 31406}, {17006, 31276}

X(33233) = complement of X(32961)
X(33233) = {X(2),X(3)}-harmonic conjugate of X(7887)
X(33233) = {X(2),X(4)}-harmonic conjugate of X(33249)
X(33233) = {X(2),X(20)}-harmonic conjugate of X(32969)
X(33233) = orthocentroidal-circle-inverse of X(33249)


X(33234) = (name pending)

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

As a point on the Euler line, X(33234) has Shinagawa coefficients ((E+F)2+2S2,-5S2).

X(33234) lies on these lines: {2, 3}, {6, 7802}, {99, 7784}, {148, 7904}, {183, 7748}, {187, 7851}, {315, 31859}, {316, 5013}, {543, 7854}, {574, 7773}, {599, 7936}, {625, 15515}, {1384, 7797}, {1975, 7756}, {2549, 7750}, {3053, 7790}, {3620, 32822}, {3849, 7772}, {4299, 26590}, {4302, 26561}, {5024, 7785}, {5206, 7861}, {5210, 7857}, {5254, 14907}, {6781, 7834}, {7738, 7762}, {7747, 11174}, {7752, 15815}, {7760, 11057}, {7765, 14614}, {7771, 13881}, {7775, 31652}, {7776, 7783}, {7778, 7782}, {7780, 11648}, {7781, 7788}, {7796, 8716}, {7800, 32819}, {7816, 7868}, {7818, 32821}, {7823, 9605}, {7843, 11163}, {7844, 15513}, {7856, 22331}, {7858, 22332}, {7860, 9766}, {7862, 8589}, {7864, 14712}, {7867, 32456}, {7886, 8588}, {7893, 22253}, {7920, 21309}, {7944, 11742}, {7946, 32480}, {12943, 27020}, {12953, 26959}, {15048, 20065}, {15228, 30124}, {32450, 32452}

X(33234) = complement of X(33280)
X(33234) = {X(2),X(20)}-harmonic conjugate of X(33239)


X(33235) = (name pending)

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

As a point on the Euler line, X(33235) has Shinagawa coefficients ((E+F)2-4S2,5S2).

X(33235) lies on these lines: {2, 3}, {6, 7782}, {32, 31859}, {76, 5023}, {83, 15815}, {99, 3053}, {183, 5206}, {187, 1975}, {194, 1384}, {620, 7773}, {754, 32821}, {1078, 5210}, {2482, 7759}, {3411, 12154}, {3412, 12155}, {3629, 5017}, {3631, 4048}, {3734, 15513}, {3788, 6781}, {3849, 7888}, {3934, 8588}, {3972, 5013}, {4299, 26629}, {4302, 26686}, {5024, 7787}, {5182, 11477}, {5267, 20172}, {6337, 7762}, {6390, 20065}, {7750, 7881}, {7756, 7851}, {7760, 8716}, {7763, 32459}, {7776, 7891}, {7778, 7802}, {7781, 14614}, {7783, 30435}, {7784, 7835}, {7788, 7863}, {7789, 7879}, {7804, 15515}, {7808, 8589}, {7830, 7868}, {7839, 21309}, {7878, 22332}, {7909, 11057}, {8719, 12203}, {10131, 11842}, {10788, 10983}, {11008, 12215}, {14023, 32820}, {15228, 30120}

X(33235) = complement of X(33279)
X(33235) = {X(2),X(20)}-harmonic conjugate of X(33238)


X(33236) = (name pending)

Barycentrics    4 a^2 SA - SB SC - 2 (a^4 + b^4 + c^4) : :
Barycentrics    17*a^4 - 8*a^2*b^2 + 7*b^4 - 8*a^2*c^2 + 2*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33236) has Shinagawa coefficients (4(E+F)2-8S2,5S2).

X(33236) lies on these lines: {2, 3}, {1285, 3788}, {6337, 7856}, {7735, 7863}

X(33236) = {X(2),X(20)}-harmonic conjugate of X(33241)


X(33237) = (name pending)

Barycentrics    a^2 SA + 4 SB SC + 2 (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 + a^2*b^2 + 2*b^4 + a^2*c^2 + 4*b^2*c^2 + 2*c^4 : :

As a point on the Euler line, X(33237) has Shinagawa coefficients (4(E+F)2-3S2,3S2).

X(33237) lies on these lines: {2, 3}, {6, 7801}, {32, 599}, {39, 11165}, {69, 21309}, {83, 7870}, {141, 1384}, {187, 3763}, {524, 7795}, {543, 7834}, {597, 7789}, {598, 7773}, {671, 7851}, {1285, 14929}, {1975, 7827}, {1992, 3933}, {2482, 5013}, {2548, 22110}, {3053, 7810}, {3095, 14848}, {3589, 5024}, {3618, 6390}, {3620, 3793}, {3734, 7817}, {3788, 11184}, {3815, 14535}, {3849, 7784}, {3934, 7610}, {3972, 7868}, {5007, 15534}, {5023, 6292}, {5206, 15810}, {5215, 31239}, {5266, 29573}, {6683, 7622}, {7617, 7886}, {7754, 10583}, {7758, 8584}, {7767, 19661}, {7775, 7778}, {7776, 7812}, {7787, 7840}, {7788, 12150}, {7794, 15533}, {7800, 20582}, {7808, 31467}, {7835, 11174}, {7854, 22331}, {7856, 11054}, {7857, 8860}, {7864, 8591}, {7867, 31173}, {7872, 32479}, {7875, 31859}, {7878, 32821}, {7879, 9939}, {7880, 9766}, {7942, 9166}, {7943, 11164}, {8859, 31276}, {9167, 16508}, {9466, 13357}, {9654, 30104}, {9669, 30103}, {10991, 19662}, {11178, 13335}, {11842, 11898}, {12040, 31400}, {13085, 24256}, {13663, 13921}, {13783, 13880}, {14023, 22165}, {16989, 22253}, {18440, 26316}, {18584, 31275}, {22121, 26206}

X(33237) = midpoint of X(2) and X(14039)
X(33237) = complement of X(33190)
X(33237) = {X(2),X(4)}-harmonic conjugate of X(8360)
X(33237) = {X(2),X(20)}-harmonic conjugate of X(33230)
X(33237) = orthocentroidal-circle-inverse of X(8360)
X(33237) = {X(37340),X(37341)}-harmonic conjugate of X(4)


X(33238) = (name pending)

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

As a point on the Euler line, X(33238) has Shinagawa coefficients ((E+F)2+S2,-5S2).

X(33238) lies on these lines: {2, 3}, {69, 7748}, {141, 32826}, {316, 7738}, {1007, 7825}, {1285, 7797}, {1992, 7765}, {2549, 7759}, {3314, 32822}, {3618, 7747}, {3619, 7935}, {3849, 5319}, {5013, 32827}, {7756, 7888}, {7735, 7802}, {7736, 7847}, {7737, 7829}, {7783, 32823}, {7784, 32815}, {7885, 32818}, {7910, 11185}, {7921, 14482}, {7928, 18840}, {8716, 32825}, {9674, 32806}, {11648, 14023}, {15598, 32886}, {17130, 21356}

X(33238) = {X(2),X(20)}-harmonic conjugate of X(33235)


X(33239) = (name pending)

Barycentrics    4 a^2 SA - 6 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 4*a^2*b^2 - b^4 - 4*a^2*c^2 + 6*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33239) has Shinagawa coefficients ((E+F)2-3S2,5S2).

X(33239) lies on these lines: {2, 3}, {69, 7816}, {194, 1285}, {230, 32826}, {385, 32822}, {524, 32824}, {1007, 7747}, {1384, 6392}, {1992, 7781}, {2548, 32456}, {3053, 32815}, {3619, 7830}, {3972, 7738}, {5023, 32828}, {5052, 32450}, {5395, 31406}, {6337, 7737}, {6781, 7795}, {7736, 7782}, {7821, 32006}, {7823, 32818}, {7891, 32823}, {7904, 18840}, {20065, 32817}, {32459, 32829}

X(33239) = {X(2),X(20)}-harmonic conjugate of X(33234)


X(33240) = (name pending)

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

As a point on the Euler line, X(33240) has Shinagawa coefficients (4(E+F)2-5S2,-3S2).

X(33240) lies on these lines: {2, 3}, {538, 7778}, {599, 5028}, {625, 15484}, {626, 8667}, {3788, 8716}, {5033, 7603}, {6034, 14971}, {6722, 15271}, {7610, 7865}, {7739, 22110}, {7746, 8556}, {7757, 7851}, {7773, 7942}, {7776, 7828}, {7784, 7886}, {7817, 9766}, {7862, 31467}, {7867, 9466}, {7868, 14061}, {7884, 11163}, {7913, 31275}, {9654, 30103}, {9669, 30104}, {10008, 32885}, {11055, 32821}, {14535, 31415}

X(33240) = midpoint of X(2) and X(33285)
X(33240) = complement of X(33191)
X(33240) = {X(2),X(4)}-harmonic conjugate of X(8368)
X(33240) = {X(2),X(20)}-harmonic conjugate of X(33231)
X(33240) = orthocentroidal-circle-inverse of X(8368)


X(33241) = (name pending)

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

As a point on the Euler line, X(33241) has Shinagawa coefficients (4(E+F)2-3S2,-5S2).

X(33241) lies on these lines: {2, 3}, {4045, 31467}, {7760, 7776}, {7773, 7878}, {7778, 7781}, {7780, 7784}, {7834, 15484}, {7853, 13881}, {7902, 9766}, {9655, 30103}, {9668, 30104}, {10008, 32886}, {21309, 32006}

X(33241) = {X(2),X(4)}-harmonic conjugate of X(19697)
X(33241) = {X(2),X(20)}-harmonic conjugate of X(33236)
X(33241) = orthocentroidal-circle-inverse of X(19697)


X(33242) = (name pending)

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

As a point on the Euler line, X(33242) has Shinagawa coefficients (4(E+F)2-5S2,5S2).

X(33242) lies on these lines: {2, 3}, {6, 7863}, {620, 31467}, {1384, 3631}, {1975, 7856}, {2482, 22332}, {3053, 7820}, {3629, 7758}, {3763, 5206}, {3788, 15484}, {3933, 11008}, {3972, 7776}, {5210, 6292}, {5266, 29602}, {6329, 9605}, {7778, 7843}, {7794, 22331}, {7816, 7902}, {7829, 8716}, {7835, 7858}, {7868, 7936}, {7881, 7946}, {7889, 15815}, {9655, 30104}, {9668, 30103}, {10583, 31859}, {12150, 32821}, {14535, 31401}

X(33242) = {X(2),X(20)}-harmonic conjugate of X(33232)


X(33243) = (name pending)

Barycentrics    24 a^2 SA - 16 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    15*a^4 - 12*a^2*b^2 - 5*b^4 - 12*a^2*c^2 + 8*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(33243) has Shinagawa coefficients ((E+F)2+11S2,-20S2).

X(33243) lies on these lines: {2, 3}, {11742, 32819}, {20065, 32450}


X(33244) = (name pending)

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

As a point on the Euler line, X(33244) has Shinagawa coefficients ((E+F)2-5S2,8S2).

X(33244) lies on these lines: {2, 3}, {99, 7758}, {315, 6781}, {1285, 7839}, {2549, 7856}, {3926, 7946}, {5023, 17008}, {5104, 20080}, {5206, 11185}, {6392, 20094}, {7737, 7782}, {7756, 7902}, {7763, 7843}, {7773, 32459}, {7793, 32815}, {7795, 7936}, {7802, 7909}, {7816, 7854}, {7891, 32006}, {7893, 32817}, {7900, 32831}, {8782, 20105}, {10131, 10788}, {15513, 32832}, {17129, 32822}, {19569, 32837}

X(33244) = anticomplement of X(14063)
X(33244) = {X(2),X(20)}-harmonic conjugate of X(32997)


X(33245) = (name pending)

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

As a point on the Euler line, X(33245) has Shinagawa coefficients (3(E+F)2-7S2,2S2).

X(33245) lies on these lines: {2, 3}, {32, 7814}, {39, 16984}, {83, 17005}, {99, 7886}, {183, 7945}, {187, 7885}, {230, 7836}, {385, 3788}, {574, 7923}, {620, 7765}, {1007, 7921}, {1078, 7849}, {1384, 7900}, {3053, 7912}, {3329, 6680}, {3767, 7891}, {3815, 10583}, {3934, 17006}, {3972, 7862}, {5013, 7932}, {5023, 7898}, {5206, 7934}, {5215, 7883}, {5306, 13571}, {5319, 7763}, {6179, 7840}, {6683, 16987}, {7735, 7906}, {7746, 7835}, {7749, 7832}, {7751, 7870}, {7755, 7799}, {7771, 7867}, {7778, 7793}, {7780, 7909}, {7782, 7844}, {7786, 18806}, {7792, 9606}, {7795, 17004}, {7797, 9607}, {7803, 31450}, {7815, 7930}, {7816, 14061}, {7827, 9167}, {7829, 22247}, {7834, 31457}, {7846, 31455}, {7863, 14568}, {7875, 31401}, {7904, 21843}, {7910, 8588}, {7911, 15513}, {7915, 16988}, {7918, 15515}, {7943, 15482}, {10104, 10334}, {15888, 26686}, {16989, 32829}, {19570, 32820}

X(33245) = {X(2),X(3)}-harmonic conjugate of X(7901)
X(33245) = {X(2),X(20)}-harmonic conjugate of X(33248)
X(33245) = {X(2),X(384)}-harmonic conjugate of X(32967)


X(33246) = (name pending)

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

As a point on the Euler line, X(33246) has Shinagawa coefficients (3(E+F)2-7S2,6S2).

X(33246) lies on these lines: {2, 3}, {6, 14972}, {32, 7799}, {99, 5309}, {187, 3314}, {194, 5306}, {298, 19781}, {299, 19780}, {385, 32833}, {574, 7875}, {598, 9167}, {620, 3972}, {626, 11057}, {754, 7870}, {1384, 7779}, {1975, 19570}, {2080, 10334}, {2482, 7757}, {2549, 16984}, {2896, 5023}, {3053, 7788}, {3058, 26686}, {3096, 15513}, {3734, 17004}, {3788, 7809}, {4027, 8724}, {4366, 10072}, {5013, 10583}, {5171, 10333}, {5206, 7832}, {5210, 7868}, {5434, 26629}, {6179, 7863}, {6337, 7839}, {6390, 7766}, {6645, 10056}, {6680, 7782}, {6781, 7934}, {7737, 7925}, {7739, 7783}, {7747, 7940}, {7750, 7945}, {7752, 14537}, {7756, 7942}, {7763, 7921}, {7771, 7820}, {7774, 32837}, {7778, 14712}, {7787, 9300}, {7789, 7793}, {7790, 32456}, {7792, 32459}, {7802, 7874}, {7816, 7857}, {7828, 11648}, {7830, 7930}, {7831, 8588}, {7859, 15515}, {7912, 19569}, {7931, 14907}, {7947, 20065}, {10352, 12150}, {10353, 11842}, {11152, 11156}, {17129, 32836}, {22331, 32821}

X(33246) = midpoint of X(2) and X(3552)
X(33246) = reflection of X(2) in X(7807)
X(33246) = reflection of X(5025) in X(2)
X(33246) = {X(2),X(20)}-harmonic conjugate of X(33251)


X(33247) = (name pending)

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

As a point on the Euler line, X(33247) has Shinagawa coefficients ((E+F)2+3S2,-7S2).

X(33247) lies on these lines: {2, 3}, {69, 7756}, {1007, 7842}, {1285, 7864}, {2549, 7805}, {2896, 32822}, {6337, 7821}, {7738, 7802}, {7764, 32006}, {7898, 32818}, {14482, 20088}, {15815, 32827}

X(33247) = {X(2),X(20)}-harmonic conjugate of X(33250)


X(33248) = (name pending)

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

As a point on the Euler line, X(33248) has Shinagawa coefficients (3(E+F)2-5S2,-2S2).

X(33248) lines on these lines: {2, 3}, {83, 31417}, {315, 7886}, {626, 17008}, {1007, 7797}, {2023, 31276}, {2548, 7942}, {2549, 7940}, {3329, 31407}, {3618, 5031}, {3767, 7796}, {5286, 7925}, {5304, 7941}, {5319, 7774}, {5461, 17130}, {6392, 7947}, {6645, 31410}, {6722, 7867}, {7735, 7912}, {7736, 7932}, {7746, 7849}, {7752, 16989}, {7763, 7765}, {7766, 32823}, {7769, 31450}, {7795, 14061}, {7803, 7862}, {7806, 32816}, {7834, 31275}, {7846, 31415}, {7851, 9607}, {7864, 32829}, {7872, 31274}, {7874, 11185}, {7875, 31404}, {7911, 21843}, {7919, 31401}, {7923, 31400}, {7931, 32828}, {9657, 26686}, {9670, 26629}, {16986, 32838}

X(33248) = {X(2),X(5)}-harmonic conjugate of X(16898)
X(33248) = {X(2),X(20)}-harmonic conjugate of X(33245)


X(33249) = (name pending)

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

As a point on the Euler line, X(33249) has Shinagawa coefficients ((E+F)2-4S2,-S2).

X(33249) lies on these lines: {2, 3}, {39, 6722}, {141, 5111}, {230, 6179}, {325, 7746}, {524, 7814}, {620, 32819}, {625, 7749}, {626, 31275}, {1007, 7754}, {1078, 3054}, {1506, 7792}, {2896, 17006}, {3055, 7786}, {3589, 7942}, {3788, 17130}, {3793, 7900}, {3815, 7828}, {3933, 7925}, {4366, 10593}, {5254, 7769}, {5305, 7777}, {5306, 7858}, {5319, 11163}, {5742, 25687}, {6248, 6721}, {6645, 10592}, {6668, 27255}, {6680, 7603}, {7738, 32839}, {7741, 26629}, {7745, 7857}, {7759, 22329}, {7763, 13881}, {7765, 14971}, {7767, 7912}, {7768, 13468}, {7776, 17008}, {7778, 32832}, {7789, 7940}, {7794, 12815}, {7796, 22110}, {7797, 17005}, {7803, 31489}, {7816, 31274}, {7817, 9698}, {7827, 9606}, {7844, 31455}, {7849, 10150}, {7851, 31401}, {7856, 9300}, {7859, 15491}, {7881, 32828}, {7883, 15597}, {7949, 15480}, {7951, 26686}, {8259, 33475}, {8260, 33474}, {15079, 30123}, {15598, 32027}, {15850, 20398}, {18806, 31239}, {31859, 32829}

X(33249) = complement of X(7907)
X(33249) = {X(2),X(4)}-harmonic conjugate of X(33233)
X(33249) = {X(2),X(5)}-harmonic conjugate of X(7807)
X(33249) = {X(2),X(20)}-harmonic conjugate of X(32977)
X(33249) = orthocentroidal-circle-inverse of X(33233)


X(33250) = (name pending)

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

As a point on the Euler line, X(33250) has Shinagawa coefficients ((E+F)2-4S2,7S2).

X(33250) lies on these lines: {2, 3}, {99, 7762}, {187, 32819}, {754, 32820}, {1975, 14023}, {2482, 7843}, {3054, 15031}, {3630, 5104}, {3793, 20081}, {3849, 7863}, {3933, 14712}, {4316, 26561}, {4324, 26590}, {5210, 32832}, {6390, 7823}, {6781, 7750}, {7745, 7782}, {7747, 32456}, {7752, 32459}, {7756, 7792}, {7783, 18907}, {7789, 7802}, {7890, 15301}, {9607, 12150}, {10131, 32134}, {10483, 26629}, {13330, 32449}, {14135, 27374}

X(33250) = {X(2),X(20)}-harmonic conjugate of X(33247)


X(33251) = (name pending)

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

As a point on the Euler line, X(33251) has Shinagawa coefficients (3(E+F)2-S2,-6S2).

X(33251) lies on these lines: {2, 3}, {69, 19570}, {115, 7865}, {315, 5309}, {316, 7884}, {626, 11648}, {2548, 7918}, {2549, 7799}, {3314, 32836}, {3329, 32827}, {3620, 32874}, {3767, 7811}, {5254, 7788}, {5286, 7837}, {5306, 7851}, {5319, 7860}, {5969, 21356}, {6392, 7939}, {7735, 7898}, {7737, 7919}, {7738, 7912}, {7739, 7774}, {7748, 7880}, {7753, 7803}, {7761, 17008}, {7763, 7872}, {7773, 9300}, {7783, 32837}, {7797, 32006}, {7828, 11057}, {7834, 14537}, {7844, 14907}, {7853, 11185}, {7864, 32816}, {7928, 32828}, {7931, 32815}, {7932, 19569}, {7935, 18362}, {11237, 26590}, {11238, 26561}

X(33251) = midpoint of X(2) and X(33278)
X(33251) = reflection of X(2) in X(33219)
X(33251) = reflection of X(33255) in X(2)
X(33251) = complement of X(33187)
X(33251) = anticomplement of X(33220)
X(33251) = {X(2),X(20)}-harmonic conjugate of X(33246)


X(33252) = (name pending)

Barycentrics    24 a^2 SA - 16 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    17*a^4 - 12*a^2*b^2 - 3*b^4 - 12*a^2*c^2 + 8*b^2*c^2 - 3*c^4 : :

As a point on the Euler line, X(33252) has Shinagawa coefficients ((E+F)2-13S2,20S2).

X(33252) lies on these lines: {2, 3}, {14976, 32825}


X(33253) = (name pending)

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

As a point on the Euler line, X(33253) has Shinagawa coefficients ((E+F)2+5S2,-10S2).

X(33253) lies on these lines: {2, 3}, {194, 11008}, {1975, 3631}, {2549, 6179}, {3629, 20065}, {5111, 7738}, {6337, 7898}, {6781, 7803}, {7618, 7814}, {7748, 17008}, {7751, 7756}, {7758, 11057}, {7774, 7802}, {7830, 16990}, {7847, 16989}, {7904, 32815}, {7929, 32817}, {9607, 20583}, {13571, 14976}

X(33253) = {X(2),X(20)}-harmonic conjugate of X(33257)
X(33253) = {X(2),X(550)}-harmonic conjugate of X(33254)


X(33254) = (name pending)

Barycentrics    12 a^2 SA - 8 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 6*a^2*b^2 - b^4 - 6*a^2*c^2 + 4*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33254) has Shinagawa coefficients ((E+F)2-7S2,10S2).

X(33254) lies on these lines: {2, 3}, {99, 14023}, {315, 32456}, {5104, 11008}, {5206, 17008}, {5210, 32819}, {6781, 7763}, {7618, 7858}, {7774, 7782}, {7794, 14907}, {7816, 16990}, {8588, 32832}, {11185, 15513}, {17004, 32826}

X(33254) = {X(2),X(20)}-harmonic conjugate of X(33256)
X(33254) = {X(2),X(550)}-harmonic conjugate of X(33253)


X(33255) = (name pending)

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

As a point on the Euler line, X(33255) has Shinagawa coefficients (3(E+F)2-5S2,6S2).

X(33255) lies on these lines: {2, 3}, {32, 32833}, {99, 7739}, {187, 16990}, {315, 7880}, {385, 32836}, {1285, 7779}, {1975, 5306}, {1992, 12151}, {2482, 10352}, {2549, 7884}, {3618, 12055}, {3734, 17008}, {3788, 14537}, {3926, 7837}, {3972, 7774}, {5309, 7816}, {5395, 32835}, {5969, 13331}, {6337, 7787}, {6680, 11648}, {7735, 19570}, {7737, 7809}, {7738, 10583}, {7753, 7763}, {7766, 32817}, {7788, 7789}, {7795, 7811}, {7806, 32815}, {7820, 7865}, {7832, 11057}, {7891, 32837}, {7921, 32831}, {7945, 19569}, {10334, 10788}, {11174, 32459}, {11237, 26629}, {11238, 26686}, {14561, 21166}, {17004, 32885}, {17129, 32869}, {20088, 32818}

X(33255) = midpoint of X(2) and X(33187)
X(33255) = reflection of X(2) in X(33220)
X(33255) = reflection of X(33251) in X(2)
X(33255) = complement of X(33278)
X(33255) = anticomplement of X(33219)
X(33255) = {X(2),X(20)}-harmonic conjugate of X(7924)


X(33256) = (name pending)

Barycentrics    8 a^2 SA - 12 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 - 2*a^2*b^2 - 2*b^4 - 2*a^2*c^2 + 3*b^2*c^2 - 2*c^4 : :

As a point on the Euler line, X(33256) has Shinagawa coefficients ((E+F)2+3S2,-10S2).

X(33256) lies on these lines: {2, 3}, {99, 7821}, {148, 7750}, {316, 7756}, {385, 7748}, {543, 7768}, {671, 7780}, {1975, 7898}, {2549, 7823}, {2896, 32819}, {3329, 7747}, {3629, 15514}, {3734, 7910}, {3849, 7760}, {3933, 20094}, {3972, 7872}, {5188, 10723}, {5254, 14712}, {6179, 11648}, {6645, 10483}, {6781, 7828}, {7737, 7864}, {7738, 7921}, {7751, 11057}, {7761, 17128}, {7781, 7840}, {7782, 7825}, {7816, 7911}, {7861, 16984}, {7883, 32479}, {7899, 32456}, {7900, 31859}, {7904, 11185}, {7906, 32006}, {7936, 17130}, {8591, 32820}, {14061, 15513}, {15048, 20088}, {16990, 32826}

X(33256) = anticomplement of X(19687)
X(33256) = pole of Napoleon axis wrt conic {{X(13),X(14),X(15),X(16),X(76)}}
X(33256) = {X(2),X(20)}-harmonic conjugate of X(33254)
X(33256) = {X(2),X(3529)}-harmonic conjugate of X(33257)


X(33257) = (name pending)

Barycentrics    8 a^2 SA - 12 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    4*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 3*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33257) has Shinagawa coefficients ((E+F)2-5S2,10S2).

X(33257) lies on these lines: {2, 3}, {76, 6781}, {99, 7759}, {148, 3053}, {194, 3629}, {316, 7888}, {543, 6179}, {598, 9698}, {1975, 7893}, {2482, 7814}, {2549, 7920}, {3314, 7802}, {3631, 7750}, {3734, 7904}, {3849, 7796}, {3972, 7756}, {4299, 4366}, {4302, 6645}, {5206, 17004}, {6329, 7787}, {6390, 7900}, {7737, 7783}, {7747, 7777}, {7748, 7806}, {7752, 32456}, {7754, 20094}, {7781, 7837}, {7789, 7898}, {7793, 32819}, {7794, 11057}, {7820, 7910}, {7830, 16986}, {7835, 7842}, {7847, 7875}, {7860, 7863}, {7946, 32820}, {7947, 32006}, {7949, 14148}, {8716, 13571}, {9607, 32480}, {10131, 12110}, {10992, 11152}, {11008, 20065}, {14907, 17128}, {15228, 30136}, {17008, 32826}, {17129, 32815}, {20088, 31859}

X(33257) = anticomplement of X(33229)
X(33257) = {X(2),X(20)}-harmonic conjugate of X(33253)
X(33257) = {X(2),X(3529)}-harmonic conjugate of X(33256)


X(33258) = (name pending)

Barycentrics    16 a^2 SA + 8 SB SC + 3 (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 - 8*a^2*b^2 - b^4 - 8*a^2*c^2 - 4*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33258) has Shinagawa coefficients (3(E+F)2+5S2,-4S2).

X(33258) lies on these lines: {2, 3}, {183, 9607}, {193, 13331}, {315, 9698}, {316, 31417}, {325, 31492}, {1007, 7928}, {1078, 5319}, {2896, 31400}, {3619, 7891}, {3620, 12055}, {4309, 26959}, {4317, 27020}, {5013, 16990}, {6337, 16986}, {6683, 14907}, {6704, 8588}, {7736, 7904}, {7759, 15810}, {7763, 7849}, {7765, 7815}, {7774, 9606}, {7785, 31407}, {7786, 20065}, {7796, 7800}, {7814, 7831}, {7859, 21843}, {7898, 31404}, {7910, 31415}, {7938, 32829}, {14135, 15082}, {31652, 32833}


X(33259) = (name pending)

Barycentrics    12 a^2 SA + 4 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 - 3*a^2*b^2 + b^4 - 3*a^2*c^2 - b^2*c^2 + c^4 : :

As a point on the Euler line, X(33259) has Shinagawa coefficients ((E+F)2-7S2,4S2).

X(33259) lies on these lines: {2, 3}, {69, 13196}, {99, 7749}, {148, 7746}, {183, 7891}, {187, 7769}, {230, 7783}, {316, 15513}, {574, 7797}, {620, 1078}, {1007, 7900}, {1384, 7921}, {1975, 17004}, {2896, 3788}, {3053, 7777}, {3054, 32819}, {3785, 7897}, {3972, 31455}, {4366, 5433}, {5013, 7806}, {5023, 7823}, {5024, 7920}, {5206, 7752}, {5210, 7773}, {5215, 7827}, {5432, 6645}, {5569, 7854}, {6179, 13571}, {6337, 17008}, {6390, 17129}, {7622, 7772}, {7745, 17005}, {7750, 7925}, {7756, 14061}, {7761, 7940}, {7763, 7779}, {7767, 7947}, {7778, 7904}, {7780, 7799}, {7781, 19570}, {7786, 10583}, {7787, 31401}, {7790, 15515}, {7800, 7945}, {7802, 7862}, {7810, 7909}, {7811, 7888}, {7815, 7835}, {7830, 7899}, {7831, 7874}, {7846, 15482}, {7847, 7886}, {7858, 26613}, {7864, 15815}, {7883, 9167}, {7912, 14907}, {8591, 11149}, {9698, 12150}, {10104, 10131}, {10349, 10357}, {11163, 22331}, {13468, 32820}, {17006, 32459}, {20065, 32829}

X(33259) = complement of X(32993)
X(33259) = anticomplement of X(32967)
X(33259) = {X(2),X(3)}-harmonic conjugate of X(6655)
X(33259) = {X(2),X(20)}-harmonic conjugate of X(32966)


X(33260) = (name pending)

Barycentrics    12 a^2 SA - 4 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 - 3*a^2*b^2 - b^4 - 3*a^2*c^2 + b^2*c^2 - c^4 : :

As a point on the Euler line, X(33260) has Shinagawa coefficients ((E+F)2+5S2,-8S2).

X(33260) lies on these lines: {2, 3}, {39, 14712}, {76, 20094}, {83, 6781}, {99, 2896}, {147, 32152}, {148, 1078}, {187, 7797}, {193, 32449}, {194, 14023}, {574, 7785}, {620, 7911}, {754, 13571}, {1384, 7920}, {1975, 7904}, {2482, 7909}, {2549, 7793}, {2975, 6653}, {3053, 7864}, {3785, 20081}, {3788, 7910}, {3849, 7858}, {3917, 14135}, {3926, 7929}, {4045, 10583}, {4316, 27020}, {4324, 26959}, {4366, 15338}, {5013, 7823}, {5023, 7806}, {5024, 7921}, {5206, 7790}, {5210, 7851}, {5984, 11257}, {6337, 7897}, {6390, 7939}, {6645, 15326}, {7738, 7766}, {7748, 7771}, {7750, 7779}, {7752, 15515}, {7758, 9939}, {7759, 11057}, {7761, 7782}, {7763, 7898}, {7769, 7842}, {7777, 15815}, {7780, 19570}, {7781, 7811}, {7784, 7891}, {7789, 7928}, {7799, 7873}, {7801, 7936}, {7810, 8591}, {7816, 7831}, {7828, 15513}, {7832, 32456}, {7835, 7935}, {7857, 7872}, {7863, 7883}, {7893, 31859}, {10350, 10353}, {11574, 32529}, {14824, 31299}, {20065, 32452}

X(33260) = anticomplement of X(16044)
X(33260) = {X(2),X(4)}-harmonic conjugate of X(33024)
X(33260) = {X(2),X(20)}-harmonic conjugate of X(6658)
X(33260) = orthocentroidal-circle-inverse of X(33024)


X(33261) = (name pending)

Barycentrics    16 a^2 SA + 24 SB SC + 3 (a^4 + b^4 + c^4) : :
Barycentrics    a^4 + 8*a^2*b^2 - 3*b^4 + 8*a^2*c^2 + 12*b^2*c^2 - 3*c^4 : :

As a point on the Euler line, X(33261) has Shinagawa coefficients (3(E+F)2+5S2,4S2).

X(33261) lies on these lines: {2, 3}, {1506, 7908}, {2548, 7877}, {3620, 13330}, {5007, 32832}, {7768, 31417}, {7787, 32838}, {10352, 20398}, {13571, 31407}, {31276, 31404}


X(33262) = (name pending)

Barycentrics    16 a^2 SA + 8 SB SC - 3 (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 8*a^2*b^2 + 5*b^4 - 8*a^2*c^2 - 4*b^2*c^2 + 5*c^4 : :

As a point on the Euler line, X(33262) has Shinagawa coefficients (3(E+F)2-11S2,4S2).

X(33262) lies on these lines: {2, 3}, {315, 31274}, {3972, 31417}, {5215, 7759}, {5319, 7857}, {7751, 9167}, {7763, 7805}, {7766, 32835}, {7787, 31407}, {7792, 31492}, {7803, 31457}, {7814, 20065}, {7888, 22247}, {7940, 21843}, {9606, 16989}


X(33263) = (name pending)

Barycentrics    16 a^2 SA - 8 SB SC + 3 (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 8*a^2*b^2 - 5*b^4 - 8*a^2*c^2 + 4*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(33263) has Shinagawa coefficients (3(E+F)2+5S2,-12S2).

X(33263) lies on these lines: {2, 3}, {732, 11160}, {2549, 7811}, {2896, 32836}, {3620, 11646}, {3785, 19570}, {5309, 14907}, {7738, 7837}, {7739, 7847}, {7756, 7865}, {7761, 32833}, {7799, 7910}, {7830, 11648}

X(33263) = midpoint of X(2) and X(32997)
X(33263) = reflection of X(2) in X(7791)
X(33263) = reflection of X(14035) in X(2)
X(33263) = {X(2),X(20)}-harmonic conjugate of X(33187)


X(33264) = (name pending)

Barycentrics    12 a^2 SA - 12 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    4*a^4 - 3*a^2*b^2 - 2*b^4 - 3*a^2*c^2 + 3*b^2*c^2 - 2*c^4 : :

As a point on the Euler line, X(33264) has Shinagawa coefficients ((E+F)2+5S2,-12S2).

X(33264) lies on these lines: {2, 3}, {69, 20094}, {99, 7818}, {148, 14907}, {194, 754}, {538, 9939}, {543, 7811}, {1078, 18546}, {1975, 7929}, {1992, 15514}, {2549, 7766}, {3734, 31168}, {3849, 7757}, {5309, 10631}, {6031, 31125}, {6194, 23698}, {6781, 7790}, {7738, 20088}, {7748, 7793}, {7750, 20081}, {7772, 12156}, {7778, 11742}, {7781, 7946}, {7782, 7842}, {7783, 7900}, {7787, 7847}, {7812, 19569}, {7816, 7910}, {7830, 31276}, {7840, 8716}, {7872, 7932}, {7893, 20105}, {7904, 32819}, {7911, 7945}, {7934, 32456}, {8588, 14061}, {8591, 32833}, {8722, 10723}, {9466, 32479}, {9890, 32528}, {16118, 30135}

X(33264) = reflection of X(2) in X(7833)
X(33264) = anticomplement of X(11361)
X(33264) = {X(2),X(20)}-harmonic conjugate of X(33265)


X(33265) = (name pending)

Barycentrics    12 a^2 SA - 12 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 - 3*a^2*b^2 - b^4 - 3*a^2*c^2 + 3*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33265) has Shinagawa coefficients ((E+F)2-7S2,12S2).

X(33265) lies on these lines: {2, 3}, {99, 754}, {148, 187}, {315, 14976}, {316, 32456}, {385, 20094}, {532, 8594}, {533, 8595}, {538, 8591}, {543, 19570}, {1992, 32449}, {2080, 13172}, {2482, 7809}, {2896, 7816}, {3849, 7799}, {4366, 15326}, {5162, 9890}, {5182, 19924}, {5206, 18546}, {5210, 17004}, {6645, 15338}, {7739, 32480}, {7756, 7797}, {7782, 7785}, {7783, 20088}, {7801, 11057}, {7802, 7818}, {7823, 9766}, {7830, 31168}, {7837, 8716}, {7847, 10583}, {7925, 32459}, {8596, 22329}, {9939, 32833}, {13468, 32819}, {26613, 32479}

X(33265) = reflection of X(2) in X(13586)
X(33265) = anticomplement of X(14041)
X(33265) = {X(2),X(20)}-harmonic conjugate of X(33264)


X(33266) = (name pending)

Barycentrics    16 a^2 SA - 8 SB SC - 3 (a^4 + b^4 + c^4) : :
Barycentrics    13*a^4 - 8*a^2*b^2 + b^4 - 8*a^2*c^2 + 4*b^2*c^2 + c^4 : :

As a point on the Euler line, X(33266) has Shinagawa coefficients (3(E+F)2-11S2,12S2).

X(33266) lies on these lines: {2, 3}, {187, 32833}, {193, 5026}, {5032, 12212}, {5210, 16990}, {5309, 32456}, {7618, 12150}, {7739, 7782}, {7774, 32459}, {7793, 32836}, {7799, 7949}, {7880, 14907}, {19569, 32816}


X(33267) = (name pending)

Barycentrics    16 a^2 SA - 12 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 - 4*a^2*b^2 - 2*b^4 - 4*a^2*c^2 + 3*b^2*c^2 - 2*c^4 : :

As a point on the Euler line, X(33267) has Shinagawa coefficients ((E+F)2+7S2,-14S2).

X(33267) lies on these lines: {2, 3}, {99, 7873}, {194, 6144}, {385, 7756}, {3630, 7750}, {4316, 6645}, {4324, 4366}, {6781, 7829}, {7759, 7783}, {7767, 20094}, {7781, 11057}, {7782, 7885}, {7816, 7928}, {7830, 17128}, {7839, 14712}, {7842, 7925}, {7872, 16984}, {7898, 7947}, {7910, 7931}, {7911, 32456}, {7946, 8716}, {14907, 17129}, {15515, 17005}


X(33268) = (name pending)

Barycentrics    16 a^2 SA - 12 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    6*a^4 - 4*a^2*b^2 - b^4 - 4*a^2*c^2 + 3*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33268) has Shinagawa coefficients ((E+F)2-9S2,14S2).

X(33268) lies on these lines: {2, 3}, {99, 7855}, {148, 5023}, {2482, 7860}, {3793, 20105}, {6781, 7764}, {7756, 7806}, {7802, 7821}, {7816, 7904}, {7863, 11057}, {7906, 14712}, {7912, 32459}, {9939, 32820}, {15513, 17004}


X(33269) = (name pending)

Barycentrics    8 a^2 SA + 16 SB SC + 3 (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 + 4*a^2*b^2 - b^4 + 4*a^2*c^2 + 8*b^2*c^2 - c^4 : :

As a point on the Euler line, X(33269) has Shinagawa coefficients (3(E+F)2+S2,4S2).

X(33269) lies on these lines: {2, 3}, {83, 5319}, {99, 31450}, {193, 24256}, {1975, 9606}, {2023, 20094}, {2548, 7796}, {3619, 7885}, {3620, 7900}, {3734, 9698}, {3926, 31407}, {3934, 20065}, {4309, 27020}, {4317, 26959}, {5286, 10334}, {5395, 15589}, {5475, 7849}, {7736, 17128}, {7745, 16990}, {7765, 7808}, {7766, 32834}, {7787, 32828}, {7795, 7814}, {7804, 32832}, {7816, 31457}, {7832, 31415}, {7836, 31404}, {7938, 32827}, {7939, 18840}, {9607, 11174}, {9656, 26561}, {9671, 26590}, {9710, 26687}, {9711, 20172}, {13571, 32836}, {14907, 31239}, {16986, 32006}


X(33270) = (name pending)

Barycentrics    16 a^2 SA + 24 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 - 8*a^2*b^2 + 7*b^4 - 8*a^2*c^2 - 12*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33270) has Shinagawa coefficients ((E+F)2-9S2,-4S2).

X(33270) lies on these lines: {2, 3}, {148, 32839}, {2896, 32867}, {7775, 12815}, {7821, 32832}, {7912, 32838}, {17006, 32006}

X(33270) = {X(2),X(4)}-harmonic conjugate of X(33206)
X(33270) = {X(2),X(5)}-harmonic conjugate of X(14035)
X(33270) = {X(2),X(20)}-harmonic conjugate of X(33204)
X(33270) = orthocentroidal-circle-inverse of X(33206)


X(33271) = (name pending)

Barycentrics    12 a^2 SA - 16 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    9*a^4 - 6*a^2*b^2 - 5*b^4 - 6*a^2*c^2 + 8*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(33271) has Shinagawa coefficients ((E+F)2+5S2,-14S2).

X(33271) lies on these lines: {2, 3}, {2549, 7894}, {7756, 7774}, {7802, 14023}, {7854, 32479}, {7904, 32826}, {7929, 32822}


X(33272) = (name pending)

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

As a point on the Euler line, X(33272) has Shinagawa coefficients ((E+F)2+2S2,-6S2).

X(33272) lies on these lines: {2, 3}, {148, 15589}, {193, 754}, {538, 11160}, {543, 32836}, {574, 32827}, {1570, 3849}, {1991, 6462}, {2031, 5304}, {3785, 7748}, {3620, 7761}, {3926, 7756}, {5286, 7802}, {5395, 7747}, {6392, 7750}, {7615, 32885}, {7800, 32826}, {7825, 32829}, {7830, 18546}, {7842, 32816}, {7879, 32822}, {7885, 32831}, {7904, 32834}, {7939, 32840}, {8596, 8782}, {9740, 19570}, {9766, 32006}, {10519, 23698}, {14568, 14907}, {14976, 20065}, {15515, 32839}

X(33272) = anticomplement of X(14033)


X(33273) = (name pending)

Barycentrics    16 a^2 SA + 4 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 - 4*a^2*b^2 - 4*a^2*c^2 - b^2*c^2 : :

As a point on the Euler line, X(33273) has Shinagawa coefficients ((E+F)2+7S2,-6S2).

X(33273) lies on these lines: {2, 3}, {76, 15515}, {83, 15513}, {98, 11152}, {99, 8589}, {115, 17006}, {183, 8716}, {187, 3329}, {194, 8667}, {316, 17005}, {385, 574}, {524, 5116}, {538, 1078}, {597, 2076}, {599, 12215}, {618, 14905}, {619, 14904}, {620, 7831}, {1153, 9166}, {1975, 8556}, {2023, 12191}, {2482, 5152}, {2549, 17004}, {2896, 7947}, {3098, 22486}, {3785, 7906}, {3788, 7928}, {3815, 14712}, {3972, 8588}, {4045, 16984}, {4048, 21358}, {4366, 5010}, {5013, 7793}, {5024, 7766}, {5092, 5182}, {5162, 26613}, {5206, 7786}, {5210, 11174}, {5303, 26752}, {5309, 5569}, {6645, 7280}, {7610, 32480}, {7618, 32833}, {7622, 7818}, {7749, 7847}, {7750, 7941}, {7751, 11055}, {7760, 31652}, {7761, 7925}, {7763, 7904}, {7769, 7830}, {7775, 11057}, {7777, 14907}, {7782, 7815}, {7799, 7810}, {7800, 7891}, {7802, 31455}, {7806, 21843}, {7811, 7840}, {7820, 16988}, {7823, 31401}, {7857, 7923}, {7862, 7910}, {7865, 7870}, {7880, 8290}, {7888, 7936}, {7921, 31400}, {7935, 7940}, {8289, 15483}, {8591, 11168}, {9734, 22712}, {9764, 9983}, {9766, 9939}, {10000, 11149}, {10163, 30786}, {11171, 21445}, {13468, 19570}, {15819, 21166}, {20088, 31406}

X(33273) = reflection of X(33013) in X(2)
X(33273) = {X(2),X(3)}-harmonic conjugate of X(13586)
X(33273) = {X(2),X(20)}-harmonic conjugate of X(33016)


X(33274) = (name pending)

Barycentrics    16 a^2 SA + 4 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    4*a^4 - 4*a^2*b^2 + b^4 - 4*a^2*c^2 - b^2*c^2 + c^4 : :

As a point on the Euler line, X(33274) has Shinagawa coefficients ((E+F)2-9S2,6S2).

X(33274) lies on these lines: {2, 3}, {32, 7622}, {76, 2482}, {83, 10484}, {99, 17004}, {187, 7777}, {194, 22329}, {315, 8182}, {316, 8588}, {325, 9939}, {385, 21843}, {524, 7793}, {543, 7749}, {574, 7806}, {598, 1506}, {599, 7836}, {620, 3314}, {626, 9167}, {671, 7746}, {1078, 5569}, {1153, 7816}, {1975, 7610}, {3053, 7921}, {3095, 22564}, {3096, 15810}, {3785, 7947}, {3788, 7883}, {3849, 7752}, {5013, 7920}, {7785, 11184}, {5206, 7769}, {5210, 14712}, {5215, 7817}, {5254, 32480}, {5442, 30139}, {5461, 7756}, {6054, 9863}, {6055, 11257}, {6337, 17129}, {7607, 11151}, {7618, 7783}, {7665, 20481}, {7737, 17005}, {7748, 9166}, {7750, 22110}, {7754, 11165}, {7763, 7840}, {7781, 11054}, {7790, 8589}, {7797, 15815}, {7802, 31173}, {7828, 15515}, {7830, 7940}, {7835, 16986}, {7856, 31652}, {7925, 14907}, {7934, 31274}, {7941, 32829}, {8290, 13086}, {8591, 8860}, {8716, 19570}, {8724, 10104}, {9126, 13306}, {9770, 20065}, {10168, 22486}, {11160, 32831}, {11168, 31276}, {11185, 17006}, {13571, 15534}, {15533, 32821}, {16220, 32231}, {19661, 31406}

X(33274) = homothetic center of anti-McCay and Moses-Steiner osculatory triangles
X(33274) = {X(2),X(3)}-harmonic conjugate of X(7833)
X(33274) = {X(2),X(20)}-harmonic conjugate of X(33006)


X(33275) = (name pending)

Barycentrics    16 a^2 SA - 4 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    4*a^4 - 4*a^2*b^2 - b^4 - 4*a^2*c^2 + b^2*c^2 - c^4 : :

As a point on the Euler line, X(33275) has Shinagawa coefficients ((E+F)2+7S2,-10S2).

X(33275) lies on these lines: {2, 3}, {99, 7854}, {187, 7856}, {316, 15515}, {574, 7823}, {620, 7910}, {2482, 7922}, {3053, 7920}, {3096, 32456}, {3314, 7782}, {5013, 7921}, {5023, 7797}, {5024, 20088}, {5206, 7806}, {6337, 7939}, {6390, 7929}, {6781, 7786}, {7748, 17004}, {7750, 7906}, {7752, 8589}, {7756, 7771}, {7758, 7783}, {7761, 7891}, {7764, 11057}, {7777, 7802}, {7785, 15815}, {7790, 15513}, {7812, 31652}, {7816, 16986}, {7828, 8588}, {7945, 32459}, {10991, 11152}, {15228, 30140}

X(33275) = {X(2),X(20)}-harmonic conjugate of X(33280)


X(33276) = (name pending)

Barycentrics    16 a^2 SA - 4 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 - 4*a^2*b^2 - 4*a^2*c^2 + b^2*c^2 : :

As a point on the Euler line, X(33276) has Shinagawa coefficients ((E+F)2-9S2,10S2).

X(33276) lies on these lines: {2, 3}, {76, 8588}, {83, 8589}, {99, 7780}, {187, 7760}, {194, 5023}, {385, 5206}, {574, 7878}, {620, 7885}, {1078, 32456}, {2076, 3629}, {2482, 7768}, {3053, 7839}, {3972, 15515}, {4366, 7280}, {5010, 6645}, {5116, 6329}, {5171, 10131}, {5210, 7793}, {6337, 7893}, {6781, 7769}, {7747, 17005}, {7750, 7947}, {7754, 15655}, {7755, 26613}, {7771, 17128}, {7787, 15815}, {7802, 7925}, {7830, 7931}, {7835, 7928}, {7836, 32459}, {7847, 16984}, {7888, 11057}, {7891, 7939}, {7941, 14712}, {9939, 32821}, {10159, 15810}, {12150, 31652}, {15603, 20105}

X(33276) = {X(2),X(20)}-harmonic conjugate of X(33279)


X(33277) = (name pending)

Barycentrics    8 a^2 SA + 16 SB SC - 3 (a^4 + b^4 + c^4) : :
Barycentrics    3*a^4 - 4*a^2*b^2 + 7*b^4 - 4*a^2*c^2 - 8*b^2*c^2 + 7*c^4 : :

As a point on the Euler line, X(33277) has Shinagawa coefficients (3(E+F)2-7S2,-4S2).

X(33277) lies on these lines: {2, 3}, {193, 5031}, {315, 6722}, {625, 20065}, {2023, 20081}, {3767, 7814}, {5319, 7752}, {5461, 7888}, {7746, 7848}, {7751, 14971}, {7763, 31275}, {7765, 7862}, {7790, 31450}, {7796, 14061}, {7844, 9698}, {7849, 32832}, {7851, 9606}, {7861, 31457}, {7865, 12815}, {7932, 31404}, {7938, 32838}, {7942, 31415}, {9656, 26686}, {9671, 26629}, {19570, 32825}


X(33278) = (name pending)

Barycentrics    8 a^2 SA - 16 SB SC + 3 (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 - 4*a^2*b^2 - 7*b^4 - 4*a^2*c^2 + 8*b^2*c^2 - 7*c^4 : :

As a point on the Euler line, X(33278) has Shinagawa coefficients (3(E+F)2+S2,-12S2).

X(33278) lies on these lines: {2, 3}, {148, 32836}, {315, 11648}, {316, 7739}, {2549, 7809}, {2996, 7929}, {3767, 11057}, {5309, 7842}, {7737, 7884}, {7748, 7895}, {7753, 7872}, {7797, 19569}, {7803, 14537}, {7830, 18362}, {7837, 32006}, {7865, 11185}, {7898, 19570}, {7912, 32837}, {7938, 32826}

X(33278) = reflection of X(2) in X(33251)
X(33278) = reflection of X(33187) in X(2)
X(33278) = anticomplement of X(33255)


X(33279) = (name pending)

Barycentrics    4 a^2 SA - 16 SB SC + (a^4 + b^4 + c^4) : :
Barycentrics    5*a^4 - 2*a^2*b^2 - 5*b^4 - 2*a^2*c^2 + 8*b^2*c^2 - 5*c^4 : :

As a point on the Euler line, X(33279) has Shinagawa coefficients ((E+F)2+S2,-10S2).

X(33279) lies on these lines: {2, 3}, {148, 7946}, {316, 7758}, {671, 14023}, {2549, 7858}, {3314, 32826}, {7737, 7856}, {7747, 7902}, {7748, 7774}, {7783, 32827}, {7802, 17008}, {7825, 7863}, {7842, 7854}, {7885, 32815}, {7897, 32822}, {7936, 16990}, {8586, 11008}, {20094, 32818}

X(33279) = anticomplement of X(33235)
X(33279) = {X(2),X(20)}-harmonic conjugate of X(33276)


X(33280) = (name pending)

Barycentrics    4 a^2 SA - 16 SB SC - (a^4 + b^4 + c^4) : :
Barycentrics    7*a^4 - 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 8*b^2*c^2 - 3*c^4 : :

As a point on the Euler line, X(33280) has Shinagawa coefficients ((E+F)2-3S2,10S2).

X(33280) lies on these lines: {2, 3}, {148, 12829}, {385, 32826}, {732, 11008}, {2549, 7878}, {6781, 32832}, {7737, 7760}, {7747, 7774}, {7748, 16989}, {7779, 32822}, {7780, 11185}, {7802, 16990}, {7823, 32815}, {7840, 32824}, {7891, 32827}, {7900, 32817}, {15031, 21843}, {20065, 32819}, {23334, 32825}

X(33280) = anticomplement of X(33234)
X(33280) = {X(2),X(20)}-harmonic conjugate of X(33275)


X(33281) = MIDPOINT OF X(3) AND X(11009)

Barycentrics    a*(2*a^6-4*(b+c)*a^5-2*(b^2-5*b*c+c^2)*a^4+(b+c)*(8*b^2-15*b*c+8*c^2)*a^3-2*(b^4+c^4+3*b*c*(b^2-3*b*c+c^2))*a^2-(b^2-c^2)*(b-c)*(4*b^2-7*b*c+4*c^2)*a+2*(b^2-c^2)^2*(b-c)^2) : :
X(33281) = 3*X(1)+X(11014), X(35)-3*X(10246), 3*X(5790)-5*X(31262)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29107.

X(33281) lies on these lines: {1, 3}, {145, 26487}, {355, 5141}, {952, 25639}, {1125, 12619}, {1483, 3813}, {3622, 26492}, {5790, 31262}, {5836, 22935}, {5844, 31659}, {6265, 7504}, {11230, 30147}, {11231, 30144}, {17577, 21740}

X(33281) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 11009}, {1482, 11012}
X(33281) = reflection of X(2646) in X(15178)
X(33281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3, 11567), (1385, 10225, 13624), (10246, 32612, 1385)


X(33282) = 36TH HATZIPOLAKIS-MOSES-EULER POINT

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 + 9*a^10*b^2*c^2 - 7*a^8*b^4*c^2 - 4*a^6*b^6*c^2 + 9*a^4*b^8*c^2 - 5*a^2*b^10*c^2 + b^12*c^2 + a^10*c^4 - 7*a^8*b^2*c^4 + 16*a^6*b^4*c^4 - 9*a^4*b^6*c^4 - 4*a^2*b^8*c^4 + 3*b^10*c^4 + 5*a^8*c^6 - 4*a^6*b^2*c^6 - 9*a^4*b^4*c^6 + 12*a^2*b^6*c^6 - 3*b^8*c^6 - 5*a^6*c^8 + 9*a^4*b^2*c^8 - 4*a^2*b^4*c^8 - 3*b^6*c^8 - a^4*c^10 - 5*a^2*b^2*c^10 + 3*b^4*c^10 + 3*a^2*c^12 + b^2*c^12 - c^14) : :

As a point on the Euler line, X(33282) has Shinagawa coefficients (E2+8EF+64F2, -3E2-8EF-64F2).

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29109.

X(33282) lies on these lines: {2,3}, {10627,25487}, {12901,23358}

X(33282) = reflection of X(i) in X(j) for these lines: {i,j}: {7488,15331}, {18377,1594}, {21950,7885}

X(33283) = (name pending)

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

As a point on the Euler line, X(33283) has Shinagawa coefficients (3(E+F)2-3S2,-4S2).

X(33283) lies on these lines: {2, 3}, {115, 7869}, {194, 32825}, {315, 7755}, {625, 7803}, {626, 17131}, {1007, 7864}, {2548, 7919}, {2549, 7899}, {3767, 7768}, {5254, 32821}, {5286, 7912}, {5304, 7900}, {5319, 7809}, {6392, 7897}, {6722, 7935}, {7735, 7885}, {7736, 7923}, {7737, 7942}, {7738, 7925}, {7739, 7814}, {7763, 7861}, {7773, 16989}, {7774, 7851}, {7778, 32820}, {7784, 17008}, {7787, 32827}, {7797, 32816}, {7800, 14061}, {7806, 32006}, {7815, 12815}, {7828, 7860}, {7836, 32824}, {7839, 32823}, {7853, 32832}, {7859, 31415}, {7867, 11185}, {7886, 14907}, {7910, 21843}, {7915, 18424}, {7918, 31401}, {7938, 32828}, {7945, 32815}, {13881, 16990}


X(33284) = (name pending)

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

As a point on the Euler line, X(33284) has Shinagawa coefficients (7(E+F)2-7S2,-10S2).

X(33284) lies on these lines: {2, 3}, {625, 7923}, {5207, 6329}, {6179, 7844}, {7751, 7934}, {7825, 16984}, {7849, 9166}, {7851, 7941}, {7861, 7925}, {7873, 8859}, {7918, 17005}, {7928, 14061}, {7931, 17130}, {7935, 17006}


X(33285) = (name pending)

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

As a point on the Euler line, X(33285) has Shinagawa coefficients (2(E+F)2-2S2,-3S2).

X(33285) lies on these lines: {2, 3}, {69, 7934}, {316, 1285}, {625, 7736}, {754, 7735}, {1007, 7790}, {1992, 7809}, {2996, 7881}, {3618, 7919}, {3767, 7818}, {5207, 7884}, {5225, 30104}, {5229, 30103}, {5254, 32818}, {5286, 9766}, {5461, 7865}, {5485, 32836}, {6337, 7899}, {7738, 7861}, {7739, 9770}, {7778, 32817}, {7784, 13468}, {7792, 32827}, {7795, 18546}, {7799, 9741}, {7828, 32006}, {7851, 32816}, {7913, 31415}, {8164, 26590}, {9166, 21356}, {31168, 32832}

X(33285) = reflection of X(2) in X(33240)
X(33285) = reflection of X(33191) in X(2)
X(33285) = {X(2),X(4)}-harmonic conjugate of X(14039)
X(33285) = {X(2),X(20)}-harmonic conjugate of X(11288)
X(33285) = orthocentroidal-circle-inverse of X(14039)


X(33286) = (name pending)

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

As a point on the Euler line, X(33286) has Shinagawa coefficients (9(E+F)2-9S2,-14S2).

X(33286) lies on these lines: {2, 3}, {7755, 7885}, {7831, 12815}, {7844, 7860}, {7896, 7934}


X(33287) = (name pending)

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

As a point on the Euler line, X(33287) has Shinagawa coefficients (5(E+F)2-5S2,-8S2).

X(33287) lies on these lines: {2, 3}, {3767, 7850}, {7844, 20065}, {7932, 32827}


X(33288) = (name pending)

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

As a point on the Euler line, X(33288) has Shinagawa coefficients (11(E+F)2-11S2,-18S2).

X(33288) lies on these lines: {2, 3}, {7931, 18546}, {7934, 17131}, {7939, 14568}, {12156, 31173}


X(33289) = (name pending)

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

As a point on the Euler line, X(33289) has Shinagawa coefficients (5(E+F)2-5S2,-14S2).

X(33289) lies on these lines: {2, 3}, {115, 7939}, {5207, 32455}, {6179, 7825}, {7751, 7850}, {7849, 10302}, {7872, 17005}, {7873, 9166}, {7910, 17006}, {7920, 32827}, {7934, 17130}, {7936, 18362}


X(33290) = (name pending)

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

As a point on the Euler line, X(33290) has Shinagawa coefficients (3(E+F)2-3S2,-8S2).

X(33290) lies on these lines: {2, 3}, {115, 7896}, {148, 32824}, {3767, 7860}, {7755, 7825}, {7797, 32827}, {7869, 11185}, {7912, 32825}, {7918, 31415}, {7945, 32826}, {13571, 32816}


X(33291) = (name pending)

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

As a point on the Euler line, X(33291) has Shinagawa coefficients (7(E+F)2-7S2,-18S2).

X(33291) lies on these lines: {2, 3}, {1916, 14711}, {5207, 8584}, {7817, 12156}, {7818, 17129}, {7826, 7885}, {7934, 18546}


X(33292) = (name pending)

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

As a point on the Euler line, X(33292) has Shinagawa coefficients (2(E+F)2-2S2,-5S2).

X(33292) lies on these lines: {2, 3}, {625, 7738}, {1285, 7828}, {5254, 32823}, {5319, 31173}, {6179, 32006}, {7615, 7849}, {7735, 7825}, {7736, 7861}, {7765, 9770}, {7778, 32822}, {7784, 15598}, {7851, 32827}


X(33293) = (name pending)

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

As a point on the Euler line, X(33293) has Shinagawa coefficients (9(E+F)2-9S2,-22S2).

X(33293) lies on these lines: {2, 3}, {7939, 17131}


X(33294) = CROSSSUM OF X(32) AND X(647)

Barycentrics    (b^2 - c^2)*(-a^4 + b^4 + c^4) : :
Barycentrics    Sin[B - C]*(2*Cos[A] - Csc[A]*Tan[w]) : :
Barycentrics    (cot A)(tan B - tan C) - (cot B)(tan C - tan A) - (cot C)(tan A - tan B) : :
X(33294) = 3 X[2] - 4 X[6587],X[669] - 3 X[14420],X[850] - 3 X[9979],3 X[1637] - X[2525],3 X[1637] - 2 X[30476],2 X[2501] - 3 X[9979],2 X[2525] - 3 X[30474],2 X[6562] - 3 X[9147],3 X[14424] - 5 X[31279],3 X[30474] - 4 X[30476]

X(33294) lies on these lines: {2, 2419}, {23, 385}, {193, 9007}, {297, 525}, {520, 16230}, {620, 23589}, {647, 2799}, {648, 23964}, {690, 12075}, {1637, 2525}, {1993, 32320}, {2485, 16757}, {2986, 10754}, {3268, 9209}, {5422, 30442}, {5664, 31859}, {7178, 27712}, {7471, 9514}, {9479, 23301}, {10561, 13485}, {12077, 23878}, {14424, 31279}

X(33294) = reflection of X(i) in X(j) for these lines: {i,j}: {850, 2501}, {2525, 30476}, {3265, 6587}, {3268, 9209}, {6563, 647}, {30474, 1637}
X(33294) = anticomplement of X(3265)
X(33294) = polar conjugate of X(1289)
X(33294) = anticomplement of the isogonal conjugate of X(32713)
X(33294) = anticomplement of the isotomic conjugate of X(107)
X(33294) = isotomic conjugate of the isogonal conjugate of X(2485)
X(33294) = polar conjugate of the isogonal conjugate of X(8673)
X(33294) = X(2980)-complementary conjugate of X(21253)
X(33294) = X(i)-Ceva conjugate of X(j) for these (i,j): {107, 2}, {648, 8743}, {17907, 127}
X(33294) = X(127)-cross conjugate of X(17907)
X(33294) = cevapoint of X(2485) and X(8673)
X(33294) = crosspoint of X(i) and X(j) for these (i,j): {76, 648}, {308, 6528}
X(33294) = crosssum of X(32) and X(647)
X(33294) = crossdifference of every pair of points on line {39, 184}
X(33294) = pole wrt polar circle of trilinear polar of X(1289) (line X(6)X(66))
X(33294) = pole of van Aubel line wrt Steiner circumellipse
X(33294) = X(i)-isoconjugate of X(j) for these (i,j): {48, 1289}, {66, 163}, {110, 2156}, {656, 15388}, {662, 2353}, {4575, 13854}, {14376, 32676}
X(33294) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 13219}, {107, 6327}, {112, 4329}, {162, 1370}, {163, 6527}, {393, 21294}, {823, 315}, {1096, 3448}, {2207, 21221}, {5317, 150}, {6528, 21275}, {6529, 21270}, {8747, 21293}, {23582, 17217}, {23964, 7192}, {24000, 512}, {24019, 69}, {24022, 520}, {32230, 21300}, {32674, 2897}, {32676, 20}, {32713, 8}
X(33294) = barycentric product X(i)*X(j) for these lines: {i,j}: {10, 21178}, {22, 850}, {76, 2485}, {83, 23881}, {127, 648}, {264, 8673}, {315, 523}, {321, 16757}, {338, 4611}, {514, 4150}, {525, 17907}, {661, 20641}, {693, 4463}, {1577, 1760}, {2172, 20948}, {2799, 31636}, {3261, 4456}, {3267, 8743}, {3700, 17076}, {4077, 4123}, {4086, 7210}, {6335, 18187}, {14618, 20806}
X(33294) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {4, 1289}, {22, 110}, {112, 15388}, {127, 525}, {206, 1576}, {315, 99}, {512, 2353}, {523, 66}, {525, 14376}, {661, 2156}, {850, 18018}, {1760, 662}, {2172, 163}, {2485, 6}, {2501, 13854}, {3313, 1634}, {4123, 643}, {4150, 190}, {4456, 101}, {4463, 100}, {4611, 249}, {7210, 1414}, {8673, 3}, {8743, 112}, {10316, 32661}, {11605, 935}, {11610, 2715}, {14396, 3284}, {15451, 27372}, {16757, 81}, {17076, 4573}, {17907, 648}, {18187, 905}, {20641, 799}, {20806, 4558}, {20968, 14574}, {21034, 32739}, {21122, 2206}, {21178, 86}, {23881, 141}, {31636, 2966}
X(33294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {850, 9979, 2501}, {1637, 2525, 30476}, {2525, 30476, 30474}, {3265, 6587, 2}


X(33295) = X(1)X(4093)∩X(2)X(6)

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

X(33295) lies on these lines: {1, 4093}, {2, 6}, {10, 17200}, {21, 8844}, {31, 75}, {58, 274}, {76, 1724}, {83, 29433}, {85, 1451}, {99, 2382}, {110, 9073}, {172, 16827}, {238, 350}, {239, 1914}, {261, 1178}, {286, 2299}, {314, 983}, {315, 1714}, {319, 15523}, {595, 17143}, {659, 3004}, {666, 2311}, {741, 3510}, {748, 30963}, {757, 873}, {765, 4600}, {1078, 3216}, {1428, 1447}, {1434, 7195}, {1444, 5324}, {1468, 31997}, {1509, 17175}, {1621, 4068}, {1909, 5247}, {1929, 17930}, {1931, 2109}, {1961, 2663}, {2280, 3759}, {2651, 17139}, {2669, 3286}, {3769, 30758}, {3875, 8616}, {3879, 29653}, {3915, 17144}, {3954, 30168}, {4037, 6651}, {4357, 29654}, {4361, 21793}, {4426, 17033}, {4441, 17127}, {4653, 16497}, {4974, 5009}, {5291, 18047}, {5564, 32945}, {6626, 16705}, {6629, 17205}, {6652, 27918}, {7760, 16552}, {8040, 17322}, {10030, 14024}, {10458, 17017}, {14953, 24378}, {16065, 33088}, {16514, 18205}, {16583, 16735}, {16707, 26234}, {17201, 32004}, {17377, 33093}, {17685, 23903}, {17735, 17759}, {17762, 27368}, {20179, 21764}, {20553, 33139}, {27660, 28660}

X(33295) = isotomic conjugate of the isogonal conjugate of X(5009)
X(33295) = isotomic conjugate of the polar conjugate of X(31905)
X(33295) = X(i)-Ceva conjugate of X(j) for these (i,j): {1509, 4366}, {17930, 7192}
X(33295) = X(i)-cross conjugate of X(j) for these (i,j): {239, 30940}, {659, 3570}, {4366, 1509}, {4974, 239}, {5009, 31905}, {8300, 6654}
X(33295) = cevapoint of X(i) and X(j) for these (i,j): {81, 8849}, {238, 239}, {385, 2236}, {18206, 18792}
X(33295) = crosssum of X(i) and X(j) for these (i,j): {37, 21897}, {2238, 2295}
X(33295) = trilinear pole of line {812, 4366}
X(33295) = crossdifference of every pair of points on line {512, 1500}
X(33295) = X(i)-isoconjugate of X(j) for these (i,j): {10, 1911}, {37, 292}, {42, 291}, {65, 7077}, {213, 335}, {295, 1824}, {313, 14598}, {321, 1922}, {334, 1918}, {512, 660}, {594, 18268}, {661, 813}, {669, 4583}, {694, 2295}, {733, 16587}, {741, 756}, {798, 4562}, {872, 18827}, {875, 3952}, {876, 4557}, {882, 4579}, {1018, 3572}, {1215, 1967}, {1237, 1927}, {1400, 4876}, {1402, 4518}, {1441, 18265}, {1581, 20964}, {1826, 2196}, {2171, 2311}, {2205, 18895}, {3122, 5378}, {3252, 18785}, {3747, 30663}, {3963, 9468}, {4079, 4584}, {9506, 20693}, {14970, 21752}, {18897, 27801}, {20715, 30648}
X(33295) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 30940}, {21, 10030}, {58, 1921}, {69, 31905}, {76, 5009}, {81, 350}, {86, 239}, {99, 812}, {238, 274}, {242, 17206}, {261, 16609}, {284, 18033}, {286, 20769}, {310, 1914}, {314, 1429}, {333, 1447}, {348, 14024}, {385, 32010}, {552, 3985}, {659, 799}, {662, 3766}, {670, 8632}, {740, 1509}, {757, 3948}, {873, 2238}, {874, 1019}, {1014, 3975}, {1178, 3978}, {1333, 18891}, {1412, 4087}, {1428, 28660}, {1434, 3685}, {2210, 6385}, {3570, 7192}, {3573, 7199}, {3716, 4573}, {3733, 27853}, {4010, 4610}, {4037, 6628}, {4107, 4594}, {4124, 4620}, {4148, 4616}, {4164, 7260}, {4366, 18827}, {4375, 4589}, {4435, 4625}, {4448, 4615}, {4584, 27855}, {4600, 27918}, {4601, 27846}, {4603, 14296}, {4623, 21832}, {4633, 4830}, {4974, 32014}, {6331, 22384}, {6654, 30941}, {8033, 18786}, {14616, 27950}, {16704, 27922}, {17103, 17493}, {17930, 27929}
X(33295) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {21, 4876}, {58, 292}, {60, 2311}, {81, 291}, {86, 335}, {99, 4562}, {110, 813}, {238, 37}, {239, 10}, {242, 1826}, {274, 334}, {284, 7077}, {310, 18895}, {333, 4518}, {350, 321}, {385, 1215}, {419, 1840}, {593, 741}, {659, 661}, {662, 660}, {740, 594}, {799, 4583}, {812, 523}, {849, 18268}, {874, 4033}, {1019, 876}, {1178, 694}, {1281, 4071}, {1284, 2171}, {1333, 1911}, {1428, 1400}, {1429, 65}, {1434, 7233}, {1437, 2196}, {1447, 226}, {1509, 18827}, {1580, 2295}, {1691, 20964}, {1790, 295}, {1874, 8736}, {1914, 42}, {1921, 313}, {1966, 3963}, {2201, 1824}, {2206, 1922}, {2210, 213}, {2236, 16587}, {2238, 756}, {3253, 27809}, {3286, 3252}, {3570, 3952}, {3573, 1018}, {3684, 210}, {3685, 2321}, {3716, 3700}, {3733, 3572}, {3736, 3862}, {3747, 1500}, {3766, 1577}, {3797, 3773}, {3948, 1089}, {3975, 3701}, {3978, 1237}, {3985, 6057}, {4010, 4024}, {4037, 6535}, {4039, 21021}, {4087, 30713}, {4107, 2533}, {4124, 21044}, {4366, 740}, {4368, 4037}, {4375, 4010}, {4432, 3943}, {4435, 4041}, {4448, 4120}, {4455, 4079}, {4465, 3994}, {4486, 4122}, {4495, 4377}, {4567, 5378}, {4610, 4589}, {4623, 4639}, {4760, 4062}, {4800, 4931}, {4810, 4838}, {4830, 4841}, {4974, 1213}, {5009, 6}, {6651, 6541}, {6652, 4368}, {6654, 13576}, {7192, 4444}, {7193, 71}, {8298, 20693}, {8299, 3930}, {8300, 2238}, {8632, 512}, {10030, 1441}, {12215, 4019}, {14024, 281}, {14433, 14431}, {14599, 1918}, {15507, 21801}, {16609, 12}, {17103, 30669}, {17206, 337}, {17755, 3932}, {17941, 18047}, {18033, 349}, {18206, 22116}, {18891, 27801}, {18892, 2205}, {18904, 7237}, {19557, 20715}, {20142, 3842}, {20663, 21830}, {20769, 72}, {21832, 4705}, {22384, 647}, {24459, 4064}, {27846, 3125}, {27853, 27808}, {27912, 21093}, {27916, 20716}, {27918, 3120}, {27922, 4080}, {27929, 18004}, {27943, 22321}, {27950, 758}, {30940, 75}, {31905, 4}, {32010, 1916}
X(33295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {58, 274, 17103}, {86, 333, 30966}, {86, 17731, 30941}, {385, 2238, 3570}, {385, 20142, 2238}, {16704, 30941, 17731}, {21764, 24592, 20179}


X(33296) = X(1)X(75)∩X(2)X(21024)

Barycentrics    (a + b)*(a + c)*(a*b + a*c - b*c) : :
X(33296) = 3 X[16712] - 2 X[16887]

X(33296) lies on these lines: {1, 75}, {2, 21024}, {6, 194}, {8, 16705}, {21, 8844}, {37, 16827}, {39, 17034}, {42, 310}, {43, 6376}, {58, 99}, {65, 664}, {69, 4201}, {76, 386}, {81, 330}, {145, 18600}, {183, 4255}, {190, 213}, {192, 2176}, {239, 257}, {320, 24214}, {325, 1834}, {350, 1193}, {385, 18755}, {387, 3926}, {519, 16712}, {538, 17499}, {648, 2332}, {668, 3293}, {869, 7033}, {870, 5331}, {904, 7260}, {940, 24621}, {978, 30963}, {980, 14829}, {986, 17206}, {1078, 4256}, {1268, 16828}, {1403, 3212}, {1509, 4658}, {1575, 16744}, {1655, 2238}, {2271, 7754}, {2275, 17027}, {2276, 17033}, {2295, 17759}, {2303, 16523}, {2309, 23485}, {3009, 32928}, {3017, 7799}, {3214, 25280}, {3216, 18140}, {3241, 16711}, {3244, 17205}, {3294, 32026}, {3672, 20036}, {3679, 17210}, {3723, 25130}, {3759, 21384}, {3760, 5313}, {3761, 5312}, {3770, 4272}, {3780, 21226}, {3870, 16750}, {3879, 24215}, {3896, 16703}, {3928, 9311}, {3946, 30038}, {3995, 27643}, {4184, 17150}, {4225, 20247}, {4251, 7760}, {4253, 7757}, {4257, 7782}, {4258, 14614}, {4262, 6179}, {4361, 27164}, {4398, 17753}, {4449, 16737}, {4511, 21422}, {4561, 18035}, {4595, 16742}, {4852, 16696}, {4970, 7304}, {5021, 31859}, {5088, 18732}, {5208, 20358}, {5224, 9534}, {5235, 16816}, {5283, 17277}, {5292, 7763}, {5333, 29570}, {6542, 30965}, {7786, 29455}, {7864, 19698}, {10458, 21352}, {11110, 16825}, {11112, 17378}, {11321, 20159}, {13588, 21010}, {16050, 16974}, {16054, 24378}, {16706, 29960}, {16710, 31999}, {16746, 21877}, {16748, 17018}, {16752, 17316}, {16777, 25508}, {16781, 20162}, {16826, 25507}, {16969, 17318}, {16975, 29767}, {16992, 19765}, {17011, 30599}, {17152, 20040}, {17233, 27248}, {17234, 17670}, {17300, 17565}, {17307, 25499}, {17350, 32107}, {17352, 17540}, {17669, 23903}, {17673, 24366}, {18147, 30022}, {20168, 21785}, {20170, 21769}, {21070, 30106}, {23447, 24519}, {23682, 33073}, {24790, 27191}, {24897, 29559}, {27195, 29750}, {28620, 32014}, {31036, 32911}

X(33296) = reflection of X(17499) and X(20970)
X(33296) = isogonal conjugate of X(23493)
X(33296) = isotomic conjugate of isogonal conjugate of X(38832)
X(33296) = anticomplement of X(21024)
X(33296) = X(1258)-anticomplementary conjugate of X(1330)
X(33296) = X(i)-Ceva conjugate of X(j) for these (i,j): {81, 86}, {99, 16695}, {7304, 27644}, {17103, 6626}
X(33296) = cevapoint of X(i) and X(j) for these (i,j): {1, 194}, {43, 192}, {4083, 16742}, {4992, 21138}, {17217, 23824}
X(33296) = crosspoint of X(81) and X(27644)
X(33296) = crosssum of X(37) and X(16606)
X(33296) = trilinear pole of line {3835, 17217}
X(33296) = crossdifference of every pair of points on line {798, 3221}
X(33296) = crosspoint, wrt excentral or anticomplementary triangle, of X(1) and X(194)
X(33296) = X(i)-cross conjugate of X(j) for these (i,j): {43, 27644}, {192, 31008}, {4083, 4595}, {4970, 192}, {8640, 190}, {16722, 274}, {23824, 17217}, {25300, 668}, {31008, 86}
X(33296) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23493}, {2, 21759}, {4, 22381}, {6, 16606}, {10, 7121}, {37, 2162}, {42, 87}, {58, 7148}, {65, 2053}, {81, 6378}, {213, 330}, {512, 932}, {669, 18830}, {798, 4598}, {1334, 7153}, {1400, 2319}, {1402, 7155}, {1824, 23086}, {1826, 15373}, {1918, 6384}, {2205, 6383}, {3121, 5383}
X(33296) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 31008}, {10, 7304}, {21, 30545}, {43, 274}, {58, 6382}, {75, 27644}, {81, 6376}, {86, 192}, {99, 3835}, {190, 17217}, {286, 22370}, {310, 2176}, {314, 1423}, {333, 3212}, {662, 20906}, {664, 27527}, {668, 18197}, {670, 20979}, {799, 4083}, {811, 25098}, {873, 20691}, {893, 27891}, {1014, 4110}, {1016, 23824}, {1403, 28660}, {1434, 27538}, {1509, 3971}, {1978, 16695}, {2209, 6385}, {3123, 4601}, {4147, 4573}, {4561, 17921}, {4576, 18107}, {4595, 7192}, {4600, 21138}, {4602, 8640}, {4610, 21051}, {4623, 21834}, {4632, 4992}, {4634, 14408}, {4970, 32014}, {6331, 22090}, {7035, 16742}, {7260, 24533}, {16722, 32011}, {17752, 32010}
X(33296) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {1, 16606}, {6, 23493}, {21, 2319}, {31, 21759}, {37, 7148}, {42, 6378}, {43, 37}, {48, 22381}, {58, 2162}, {81, 87}, {86, 330}, {99, 4598}, {192, 10}, {274, 6384}, {284, 2053}, {310, 6383}, {314, 27424}, {333, 7155}, {662, 932}, {799, 18830}, {1014, 7153}, {1333, 7121}, {1403, 1400}, {1423, 65}, {1437, 15373}, {1790, 23086}, {2176, 42}, {2209, 213}, {3123, 3125}, {3208, 210}, {3212, 226}, {3835, 523}, {3875, 27432}, {3971, 594}, {4083, 661}, {4110, 3701}, {4147, 3700}, {4595, 3952}, {4600, 5383}, {4734, 5257}, {4941, 21951}, {4970, 1213}, {4992, 4988}, {6376, 321}, {6377, 3122}, {6382, 313}, {7304, 86}, {8640, 798}, {14408, 4730}, {14823, 21345}, {16695, 649}, {16722, 3840}, {16742, 244}, {17144, 27438}, {17217, 514}, {17752, 1215}, {17921, 7649}, {18197, 513}, {20284, 3778}, {20691, 756}, {20760, 71}, {20906, 1577}, {20971, 21827}, {20979, 512}, {21051, 4024}, {21138, 3120}, {21834, 4705}, {22090, 647}, {22370, 72}, {23092, 1459}, {23824, 1086}, {23886, 21051}, {25098, 656}, {25142, 21834}, {27527, 522}, {27538, 2321}, {27644, 1}, {27891, 1920}, {30545, 1441}, {30584, 4140}, {31008, 75}, {32010, 27447}
X(33296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 274, 86}, {1, 3875, 17144}, {8, 16705, 30966}, {145, 18600, 30941}, {213, 25264, 190}, {274, 17143, 10471}, {3736, 30940, 86}, {4352, 20018, 69}, {17752, 20691, 4595}


X(33297) = X(1)X(17210)∩X(2)X(20970)

Barycentrics    (a + b)*(a + c)*(a*b - b^2 + a*c - b*c - c^2) : :
X(33297) = 3 X[16712] - 4 X[16887]

X(33297) lies on these lines: {1, 17210}, {2, 20970}, {4, 69}, {8, 274}, {10, 86}, {58, 17731}, {75, 3874}, {81, 3661}, {99, 103}, {141, 17034}, {145, 16705}, {150, 2891}, {190, 21070}, {213, 31027}, {239, 21240}, {257, 8682}, {310, 2388}, {320, 20888}, {332, 947}, {333, 1174}, {519, 16712}, {524, 17499}, {668, 17751}, {758, 17762}, {1010, 1509}, {1078, 14829}, {1434, 10106}, {1444, 10623}, {1500, 6542}, {1575, 18172}, {1654, 16589}, {1909, 10471}, {2141, 17295}, {2895, 3948}, {3416, 30940}, {3501, 17294}, {3621, 18600}, {3625, 17205}, {3678, 20947}, {3679, 17175}, {3686, 29968}, {3730, 17233}, {3759, 30107}, {4006, 18184}, {4044, 33066}, {4361, 24190}, {4416, 21071}, {4417, 7752}, {4445, 18166}, {4515, 16728}, {4553, 22292}, {4576, 32032}, {4653, 6626}, {4669, 17180}, {4677, 17179}, {4851, 27164}, {4886, 24603}, {4921, 29577}, {5235, 17244}, {5333, 29576}, {5739, 30830}, {5839, 27299}, {6376, 17360}, {7058, 14013}, {7357, 21285}, {8025, 29593}, {8822, 29040}, {9534, 30962}, {10453, 31008}, {16696, 17372}, {16704, 17230}, {16711, 31145}, {16726, 21868}, {16738, 17373}, {17275, 25508}, {17297, 17758}, {17343, 27269}, {17362, 20255}, {17363, 27644}, {20290, 32031}, {20913, 32863}, {21904, 27324}, {24549, 32853}, {24690, 25264}, {24995, 33081}

X(33297) = anticomplement of X(20970)
X(33297) = reflection of X(17499) and X(21024)
X(33297) = isotomic conjugate of X(15320)
X(33297) = anticomplement of the isogonal of X(32014)
X(33297) = isotomic conjugate of the isogonal conjugate of X(4184)
X(33297) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {274, 2891}, {662, 14779}, {1126, 1655}, {1171, 192}, {1255, 1654}, {1268, 2895}, {1796, 18666}, {4567, 24074}, {4596, 514}, {4608, 21221}, {4629, 17494}, {4632, 513}, {6578, 4560}, {32014, 8}, {32018, 1330}
X(33297) = X(21045)-cross conjugate of X(25259)
X(33297) = X(i)-isoconjugate of X(j) for these (i,j): {31, 15320}, {213, 14377}, {810, 26705}, {1924, 31624}, {3125, 15378}
X(33297) = cevapoint of X(i) and X(j) for these (i,j): {69, 17135}, {1734, 18184}, {3681, 17233}, {21045, 25259}
X(33297) = crosspoint of X(670) and X(4600)
X(33297) = crosssum of X(i) and X(j) for these (i,j): {669, 3122}, {8663, 20975}
X(33297) = trilinear pole of line {6586, 16751}
X(33297) = barycentric product X(i)*X(j) for these lines: {i,j}: {76, 4184}, {86, 17233}, {99, 25259}, {116, 4600}, {274, 3681}, {310, 3730}, {668, 16751}, {670, 6586}, {799, 1734}, {873, 4006}, {1016, 17198}, {4567, 20901}, {4590, 21045}, {4601, 17463}, {6385, 15624}, {7035, 18184}
X(33297) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {2, 15320}, {86, 14377}, {116, 3120}, {648, 26705}, {670, 31624}, {1734, 661}, {3681, 37}, {3730, 42}, {4006, 756}, {4184, 6}, {4570, 15378}, {6586, 512}, {15624, 213}, {16751, 513}, {17198, 1086}, {17233, 10}, {17463, 3125}, {17671, 3914}, {17746, 1962}, {17916, 1824}, {18184, 244}, {20901, 16732}, {20974, 3122}, {21045, 115}, {22388, 3049}, {25259, 523}
X(33297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 30941, 274}, {69, 10449, 76}, {86, 14007, 32014}, {86, 32004, 4658}, {1043, 17206, 99}, {17135, 17137, 17143}


X(33298) = X(1)X(17095)∩X(2)X(220)

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

X(33298) lies on these lines: {1, 17095}, {2, 220}, {3, 150}, {5, 17753}, {7, 12}, {8, 348}, {10, 85}, {40, 4872}, {46, 4911}, {57, 7247}, {63, 7079}, {65, 7179}, {69, 7080}, {75, 225}, {77, 319}, {86, 3193}, {100, 21285}, {116, 3730}, {144, 25000}, {145, 25592}, {223, 4886}, {226, 24603}, {241, 3661}, {269, 17270}, {279, 3617}, {325, 21281}, {329, 28827}, {333, 1396}, {355, 5088}, {388, 1434}, {484, 4056}, {499, 24203}, {517, 17181}, {644, 28734}, {651, 17346}, {986, 24211}, {1025, 16552}, {1078, 4998}, {1088, 25006}, {1111, 18395}, {1146, 3177}, {1150, 6649}, {1212, 26531}, {1213, 26125}, {1231, 3263}, {1323, 3626}, {1329, 30946}, {1358, 17090}, {1418, 17239}, {1442, 17377}, {1445, 17289}, {1447, 24914}, {1452, 7282}, {1565, 5690}, {1654, 6180}, {1698, 32007}, {1737, 3673}, {2099, 17084}, {2284, 17077}, {2975, 6516}, {3061, 24318}, {3085, 14828}, {3207, 20096}, {3212, 3665}, {3244, 25723}, {3336, 7272}, {3476, 17081}, {3501, 17046}, {3616, 32003}, {3619, 8732}, {3632, 25716}, {3668, 4967}, {3672, 5740}, {3674, 4848}, {3679, 9312}, {3691, 6168}, {3775, 4334}, {3911, 29596}, {3912, 31225}, {3927, 16091}, {4357, 8582}, {4361, 17086}, {4363, 17950}, {4389, 24433}, {4417, 17137}, {4429, 10030}, {4554, 17143}, {4690, 6610}, {4751, 21617}, {4847, 31627}, {5195, 12702}, {5252, 7176}, {5543, 5550}, {5657, 17170}, {5723, 16816}, {6554, 31640}, {6646, 26659}, {6735, 16284}, {7090, 31548}, {7181, 10944}, {7185, 24798}, {7190, 17322}, {7196, 31330}, {7201, 27691}, {7210, 8270}, {7377, 20367}, {8545, 17256}, {10708, 24047}, {11680, 20244}, {11681, 20347}, {14121, 31547}, {14829, 28795}, {17062, 17754}, {17079, 31994}, {17118, 23897}, {17158, 26015}, {17227, 30379}, {17277, 28739}, {17347, 28968}, {17352, 28780}, {17555, 18026}, {18134, 26942}, {19877, 32098}, {20110, 24553}, {21872, 27129}, {23058, 30625}, {25005, 26563}, {25964, 26059}, {26001, 30854}, {26013, 30988}, {26258, 30616}, {26526, 26690}, {26543, 27334}, {26653, 27006}, {27135, 28737}, {27170, 27283}, {30545, 32773}

X(33298) = X(3681)-cross conjugate of X(17233)
X(33298) = cevapoint of X(116) and X(1734)
X(33298) = crosspoint of X(4572) and X(4998)
X(33298) = barycentric product X(i)*X(j) for these lines: {i,j}: {7, 17233}, {85, 3681}, {116, 4998}, {349, 4184}, {664, 25259}, {1734, 4554}, {3730, 6063}, {4564, 20901}, {4572, 6586}, {4620, 21045}, {7182, 17916}, {8817, 17671}, {15624, 20567}
X(33298) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {7, 14377}, {59, 15378}, {116, 11}, {226, 15320}, {653, 26705}, {1734, 650}, {3681, 9}, {3730, 55}, {4006, 210}, {4184, 284}, {4572, 31624}, {6586, 663}, {15624, 41}, {16751, 3737}, {17198, 17197}, {17233, 8}, {17463, 2170}, {17671, 497}, {17746, 3683}, {17916, 33}, {18184, 18191}, {20901, 4858}, {20974, 3271}, {21045, 21044}, {21133, 21132}, {22084, 7117}, {25259, 522}
X(33298) = X(i)-isoconjugate of X(j) for these (i,j): {41, 14377}, {1946, 26705}, {2170, 15378}, {2194, 15320}
X(33298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 348, 664}, {10, 9436, 85}, {116, 3730, 17671}, {1323, 3626, 25719}, {24914, 30617, 1447}, {26942, 27339, 18134}, {31640, 32024, 6554}


X(33299) = X(1)X(1390)∩X(2)X(17048)

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

X(33299) lies on these lines: {1, 1390}, {2, 17048}, {3, 5282}, {5, 21029}, {6, 976}, {8, 2170}, {9, 21}, {10, 17451}, {37, 992}, {38, 39}, {43, 22230}, {63, 21495}, {72, 672}, {75, 18055}, {100, 3496}, {101, 17744}, {141, 3665}, {191, 24047}, {200, 2082}, {210, 1212}, {218, 3940}, {220, 7124}, {257, 26752}, {312, 28659}, {346, 19582}, {386, 21840}, {392, 3991}, {404, 3509}, {427, 15523}, {518, 1475}, {519, 4006}, {594, 1953}, {596, 22035}, {599, 3942}, {604, 5227}, {661, 29029}, {728, 15829}, {756, 869}, {758, 16549}, {762, 1573}, {899, 16583}, {942, 25068}, {960, 1334}, {965, 16356}, {978, 26242}, {986, 17756}, {997, 9310}, {1018, 3878}, {1125, 3970}, {1146, 21031}, {1215, 26035}, {1229, 21246}, {1329, 21044}, {1574, 3125}, {1575, 3721}, {1698, 21921}, {1759, 25440}, {1925, 1978}, {1930, 4568}, {1959, 3661}, {2171, 2345}, {2241, 3722}, {2269, 3694}, {2276, 2292}, {2280, 3811}, {2294, 17303}, {2321, 3702}, {2329, 4511}, {2347, 3965}, {2650, 17750}, {3057, 4515}, {3119, 6554}, {3142, 21024}, {3208, 3877}, {3216, 16600}, {3219, 20769}, {3263, 29960}, {3290, 27627}, {3294, 10176}, {3436, 24247}, {3452, 27390}, {3501, 3869}, {3555, 17474}, {3678, 16552}, {3681, 21384}, {3684, 4420}, {3687, 20684}, {3696, 20593}, {3726, 16604}, {3727, 20691}, {3730, 5692}, {3735, 4642}, {3780, 20693}, {3868, 17754}, {3885, 4050}, {3934, 30850}, {3938, 16502}, {3952, 26770}, {3959, 4695}, {4053, 17369}, {4109, 5741}, {4134, 17746}, {4253, 5904}, {4358, 21071}, {4414, 31448}, {4513, 5289}, {4557, 16689}, {4662, 4875}, {4692, 21067}, {4853, 7323}, {4919, 5330}, {4968, 21101}, {5021, 32912}, {5030, 6763}, {5044, 16601}, {5266, 21764}, {5276, 5293}, {5280, 30115}, {5690, 21013}, {5750, 22021}, {6646, 33021}, {7146, 29611}, {7201, 7229}, {7237, 17872}, {8568, 24391}, {9534, 22197}, {16788, 22836}, {16927, 17260}, {17141, 24631}, {17143, 18061}, {17281, 21801}, {17355, 21078}, {17439, 30144}, {17755, 27109}, {17760, 20911}, {19237, 27065}, {20335, 20880}, {20347, 25244}, {21017, 21687}, {21061, 25078}, {21073, 21616}, {21232, 27096}, {21233, 27514}, {21272, 26757}, {21285, 31080}, {21331, 21951}, {21872, 31165}, {24266, 24612}, {25242, 30946}, {26234, 29991}, {27408, 27420}, {27523, 27538}, {29690, 31466}, {29966, 30758}, {30742, 31240}

X(33299) = reflection of X(20247) and X(17048)
X(33299) = complement of X(20247)
X(33299) = anticomplement of X(17048)
X(33299) = X(i)-Ceva conjugate of X(j) for these (i,j): {141, 38}, {7257, 4041}
X(33299) = X(3688)-cross conjugate of X(38)
X(33299) = crosspoint of X(i) and X(j) for these (i,j): {9, 312}, {141, 3703}, {765, 27805}
X(33299) = crosssum of X(i) and X(j) for these (i,j): {57, 604}, {244, 20981}
X(33299) = crossdifference of every pair of points on line {4017, 18108}
X(33299) = X(i)-isoconjugate of X(j) for these (i,j): {7, 251}, {56, 83}, {57, 82}, {58, 18097}, {109, 10566}, {222, 32085}, {278, 1176}, {308, 1397}, {331, 10547}, {604, 3112}, {608, 1799}, {651, 18108}, {827, 7178}, {1014, 18098}, {1118, 28724}, {1262, 18101}, {1412, 18082}, {3676, 4628}, {4017, 4599}, {4573, 18105}, {4577, 7180}, {18111, 29055}
X(33299) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 3703}, {8, 38}, {9, 141}, {21, 15523}, {33, 3933}, {39, 312}, {41, 8024}, {55, 1930}, {75, 3688}, {78, 427}, {200, 3665}, {210, 16887}, {212, 1235}, {219, 20883}, {314, 21035}, {318, 3917}, {333, 3954}, {341, 1401}, {345, 17442}, {522, 4553}, {643, 826}, {644, 16892}, {645, 8061}, {646, 21123}, {650, 4568}, {1334, 16703}, {1634, 4086}, {1812, 21016}, {1843, 3718}, {1964, 3596}, {2318, 16747}, {2321, 16696}, {2530, 3699}, {3005, 7257}, {3051, 28659}, {3680, 4884}, {3694, 17171}, {3701, 17187}, {3719, 27376}, {4020, 7017}, {4041, 4576}, {4571, 21108}, {21814, 28660}
X(33299) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {8, 3112}, {9, 83}, {33, 32085}, {37, 18097}, {38, 7}, {39, 57}, {41, 251}, {55, 82}, {78, 1799}, {141, 85}, {210, 18082}, {212, 1176}, {312, 308}, {427, 273}, {643, 4577}, {645, 4593}, {650, 10566}, {663, 18108}, {826, 4077}, {1212, 18087}, {1334, 18098}, {1401, 269}, {1634, 1414}, {1843, 34}, {1923, 1397}, {1930, 6063}, {1964, 56}, {2084, 7180}, {2289, 28724}, {2310, 18101}, {2530, 3676}, {3005, 4017}, {3051, 604}, {3287, 18111}, {3313, 7210}, {3596, 18833}, {3665, 1088}, {3688, 1}, {3691, 18089}, {3700, 18070}, {3703, 75}, {3917, 77}, {3933, 7182}, {3954, 226}, {4020, 222}, {4093, 1284}, {4553, 664}, {4568, 4554}, {4576, 4625}, {5546, 4599}, {7069, 17500}, {7257, 689}, {8024, 20567}, {8061, 7178}, {8611, 4580}, {15523, 1441}, {16587, 4032}, {16696, 1434}, {16720, 7196}, {16892, 24002}, {17187, 1014}, {17442, 278}, {17457, 7198}, {18715, 17088}, {20775, 603}, {20883, 331}, {21033, 27067}, {21035, 65}, {21123, 3669}, {21814, 1400}, {27369, 1395}
X(33299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20247, 17048}, {8, 3061, 2170}, {9, 78, 41}, {9, 27396, 21811}, {39, 3954, 38}, {72, 25066, 672}, {210, 1212, 3691}, {960, 3693, 1334}, {997, 17742, 9310}, {1575, 3721, 24443}, {3061, 4095, 20594}, {3678, 24036, 16552}, {3681, 26690, 21384}, {3876, 25082, 9}


X(33300) = (name pending)

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

X(33300) lies on these lines: {2, 3}, {1916, 11185}, {7790, 10352}, {10347, 15031}, {19120, 32528}


X(33301) = (name pending)

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

X(33301) lies on these lines: {2, 3}, {4159, 5989}, {7790, 10329}


X(33302) = (name pending)

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

X(33302) lies on these lines: {2, 3}, {11, 3220}, {242, 2968}, {513, 676}, {2834, 8758}


X(33303) = (name pending)

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

X(33303) lies on these lines: {2, 3}, {3669, 17410}


X(33304) = (name pending)

Barycentrics    (a^2 - b^2) (a - b + c)^4 (a^2 + b^2 - c^2) - (a + b - c)^4 (-a^2 + c^2) (a^2 - b^2 + c^2) : :
Barycentrics    2*a^8 + 11*a^6*b^2 - 4*a^5*b^3 - 5*a^4*b^4 - 7*a^2*b^6 + 4*a*b^7 - b^8 - 24*a^6*b*c + 4*a^5*b^2*c + 4*a^4*b^3*c + 8*a^3*b^4*c + 16*a^2*b^5*c - 12*a*b^6*c + 4*b^7*c + 11*a^6*c^2 + 4*a^5*b*c^2 + 2*a^4*b^2*c^2 - 8*a^3*b^3*c^2 - a^2*b^4*c^2 + 12*a*b^5*c^2 - 4*b^6*c^2 - 4*a^5*c^3 + 4*a^4*b*c^3 - 8*a^3*b^2*c^3 - 16*a^2*b^3*c^3 - 4*a*b^4*c^3 - 4*b^5*c^3 - 5*a^4*c^4 + 8*a^3*b*c^4 - a^2*b^2*c^4 - 4*a*b^3*c^4 + 10*b^4*c^4 + 16*a^2*b*c^5 + 12*a*b^2*c^5 - 4*b^3*c^5 - 7*a^2*c^6 - 12*a*b*c^6 - 4*b^2*c^6 + 4*a*c^7 + 4*b*c^7 - c^8 : :

X(33304) lies on these lines: {2, 3}


X(33305) = (name pending)

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

X(33305) lies on these lines: {2, 3}, {200, 3704}, {516, 25968}, {522, 650}, {1211, 2328}, {1260, 27540}, {1626, 23304}, {1754, 13567}, {1936, 26932}, {2968, 3100}, {3743, 13405}, {6703, 17194}, {13329, 26005}, {17056, 17188}, {27394, 28826}


X(33306) = (name pending)

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

X(33306) lies on these lines: {2, 3}, {3239, 3900}


X(33307) = (name pending)

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

X(33307) lies on these lines: {2, 3}, {4130, 4163}


X(33308) = (name pending)

Barycentrics    ((a^2 - b^2) (a^2 + b^2 - c^2))/(a - b + c)^4 - ((-a^2 + c^2) (a^2 - b^2 + c^2))/(a + b - c)^4 : :
Barycentrics    (a - b - c)^4*(2*a^8 + 11*a^6*b^2 + 4*a^5*b^3 - 5*a^4*b^4 - 7*a^2*b^6 - 4*a*b^7 - b^8 - 24*a^6*b*c - 4*a^5*b^2*c + 4*a^4*b^3*c - 8*a^3*b^4*c + 16*a^2*b^5*c + 12*a*b^6*c + 4*b^7*c + 11*a^6*c^2 - 4*a^5*b*c^2 + 2*a^4*b^2*c^2 + 8*a^3*b^3*c^2 - a^2*b^4*c^2 - 12*a*b^5*c^2 - 4*b^6*c^2 + 4*a^5*c^3 + 4*a^4*b*c^3 + 8*a^3*b^2*c^3 - 16*a^2*b^3*c^3 + 4*a*b^4*c^3 - 4*b^5*c^3 - 5*a^4*c^4 - 8*a^3*b*c^4 - a^2*b^2*c^4 + 4*a*b^3*c^4 + 10*b^4*c^4 + 16*a^2*b*c^5 - 12*a*b^2*c^5 - 4*b^3*c^5 - 7*a^2*c^6 + 12*a*b*c^6 - 4*b^2*c^6 - 4*a*c^7 + 4*b*c^7 - c^8) : :

X(33308) lies on these lines: {2, 3}


X(33309) = (name pending)

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

X(33309) lies on these lines: {2, 3}, {36, 25531}, {190, 30117}, {238, 519}, {540, 17297}, {1220, 5259}, {3241, 16466}, {3488, 26685}, {3579, 25965}, {4422, 16086}, {5080, 24542}, {5251, 32942}, {15325, 26139}, {15934, 17350}, {16485, 30568}, {25055, 25496}


X(33310) = (name pending)

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

X(33310) lies on these lines: {2, 3}, {3573, 6632}


X(33311) = (name pending)

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

X(33311) lies on these lines: {2, 3}, {11, 659}, {764, 1647}


X(33312) = (name pending)

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

X(33312) lies on these lines: {2, 3}, {6550, 7336}


X(33313) = (name pending)

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

X(33313) lies on these lines: {2, 3}, {349, 16607}, {824, 1577}, {14963, 21253}, {21207, 21234}


X(33314) = (name pending)

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

X(33314) lies on these lines: {2, 3}, {76, 23293}, {311, 6697}, {316, 9218}, {340, 11416}, {826, 850}, {22089, 31279}


X(33315) = (name pending)

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

X(33315) lies on these lines: {2,3}


X(33316) = (name pending)

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

X(33316) lies on these lines: {2, 3}, {23285, 30870}


X(33317) = (name pending)

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

X(33317) lies on these lines: {2, 3}


X(33318) = (name pending)

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

X(33318) lies on these lines: {2, 3}


X(33319) = (name pending)

Barycentrics    b^10 (a^2 - b^2) (a^2 + b^2 - c^2) - c^10 (-a^2 + c^2) (a^2 - b^2 + c^2) : :
Barycentrics    a^4 b^10 - b^14 - a^2 b^10 c^2 + b^12 c^2 + a^4 c^10 - a^2 b^2 c^10 + b^2 c^12 - c^14 : :

X(33319) lies on these lines: {2, 3}


X(33320) = (name pending)

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

X(33320) lies on these lines: {2, 3}, {1924, 1980}


X(33321) = (name pending)

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

X(33321) lies on these lines: {2, 3}, {9006, 9426}


X(33322) = (name pending)

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

X(33322) lies on these lines: {2, 3}


X(33323) = (name pending)

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

X(33323) lies on these lines: {2, 3}


X(33324) = (name pending)

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

X(33324) lies on these lines: {2, 3}, {115, 6697}, {2549, 30794}


X(33325) = (name pending)

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

X(33325) lies on these lines: {2, 3}, {60, 3337}, {81, 4860}, {110, 2717}, {229, 4267}, {244, 5009}, {659, 3733}, {1610, 17150}, {1631, 33108}, {1730, 5012}, {1754, 26881}, {1929, 17940}, {3913, 33093}, {4276, 29657}, {4658, 17017}, {5144, 26015}, {6186, 33135}, {8301, 32842}, {8666, 32914}, {17174, 25533}, {17798, 33139}, {23868, 33112}


X(33326) = (name pending)

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

X(33326) lies on these lines: {2, 3}


X(33327) = (name pending)

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

X(33327) lies on these lines: {2, 3}


X(33328) = (name pending)

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

X(33328) lies on these lines: {2, 3}


X(33329) = (name pending)

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

X(33329) lies on these lines: {2, 3}, {35, 14873}, {115, 3011}, {118, 3258}, {125, 516}, {523, 661}, {1155, 8287}, {1211, 32930}, {1290, 15168}, {1544, 2777}, {2651, 21221}, {2690, 5134}, {3678, 3690}, {3936, 17777}, {5099, 5513}, {5972, 18653}, {6627, 20666}, {6684, 30436}, {6739, 28160}, {8013, 21670}, {8818, 17718}, {16177, 20622}, {17763, 23947}, {20117, 22076}, {20337, 29632}


X(33330) = COMPLEMENT OF X(2698)

Barycentrics    a^2*(a^6*b^2 - a^4*b^4 + a^6*c^2 - 2*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6)*(a^4*b^4 - 2*a^2*b^6 + b^8 - 2*b^6*c^2 + a^4*c^4 + 4*b^4*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + c^8) : :
X(33330) = X[14510] - 3 X[14651],3 X[14639] - X[31513]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29114.

X(33330) lies on the nine-point circle and these lines: {2, 2698}, {3, 22103}, {4, 805}, {5, 2679}, {114, 512}, {115, 511}, {125, 21531}, {127, 5031}, {136, 297}, {137, 11675}, {626, 31848}, {1567, 2782}, {2080, 8623}, {3258, 5650}, {5099, 24206}, {5446, 16979}, {6033, 9467}, {12833, 13137}, {14510, 14651}, {14639, 31513}

X(33330) = complement of X(2698)
X(33330) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 805}, {6071, 6072}, {12833, 13137}
X(33330) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 22103}, {2679, 5}, {16979, 5446}
X(33330) = complement of the isogonal of X(2782)
X(33330) = orthic-isogonal conjugate of X(2782)
X(33330) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2782}, {2782, 10}, {16068, 18904}
X(33330) = X(4)-Ceva conjugate of X(2782)
X(33330) = center of hyperbola {{A,B,C,X(4),X(805)}}


X(33331) = COMPLEMENT OF X(2724)

Barycentrics    (a^4*b^2 - 2*a^3*b^3 + 2*a*b^5 - b^6 + a^4*c^2 + 2*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 + 4*b^3*c^3 - b^2*c^4 + 2*a*c^5 - c^6)*(2*a^6 - 2*a^5*b + a^4*b^2 - 2*a^3*b^3 + b^6 - 2*a^5*c + 2*a^3*b^2*c + 2*a^2*b^3*c - 2*b^5*c + a^4*c^2 + 2*a^3*b*c^2 - 4*a^2*b^2*c^2 - b^4*c^2 - 2*a^3*c^3 + 2*a^2*b*c^3 + 4*b^3*c^3 - b^2*c^4 - 2*b*c^5 + c^6) : :
X(33331) = 5 X[3091] - X[14732]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29114.

X(33331) lies on the nine-point circle and these lines: {2, 2724}, {4, 927}, {5, 1566}, {11, 241}, {116, 516}, {118, 514}, {123, 20544}, {125, 857}, {1517, 2808}, {3091, 14732}, {3259, 9779}, {5519, 18343}, {10739, 14942}

X(33331) = complement of X(2724)
X(33331) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 927}, {6074, 14505}
X(33331) = reflection of X(1566) in X(5)
X(33331) = complement of the isogonal of X(2808)
X(33331) = orthic isogonal conjugate of X(2808)
X(33331) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2808}, {2808, 10}, {23694, 518}
X(33331) = X(4)-Ceva conjugate of X(2808)


X(33332) = COMPLEMENT OF X(13564)

Barycentrics    a^8 b^2-2 a^6 b^4+2 a^2 b^8-b^10+a^8 c^2-4 a^6 b^2 c^2-a^4 b^4 c^2+a^2 b^6 c^2+3 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+a^2 b^2 c^6-2 b^4 c^6+2 a^2 c^8+3 b^2 c^8-c^10 : :
Barycentrics    S^2 (7 R^2 - 2 SW) -R^2 SB SC - 2 SB SC SW : :

As a point on the Euler line, X(33332) has Shinagawa coefficients [e+8f,9e+8f].

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29115.

X(33332) lies on these lines: {2,3}, {51,13561}, {125,10095}, {389,10264}, {511,6153}, {542,1493}, {1173,9140}, {1209,13391}, {1503,10274}, {3448,14627}, {3574,5663}, {5944,13419}, {5946,20299}, {6000,32351}, {6689,29012}, {6748,9380}, {7703,9781}, {10263,21243}, {10280,23301}, {10540,15806}, {11550,32046}, {13754,20424}, {13851,15807}, {14676,32134}, {15026,19130}, {16105,20304}, {17702,22804}, {22330,25328}, {23315,32767}, {23319,25147}, {31664,31665}

X(33332) = complement of X(13564)
X(33332) = reflection of X(5) in X(5576)
X(33332) = anticomplement of X(34004)

X(33333) = COMPLEMENT OF X(15907)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8 - 4*a^10*c^2 + 10*a^8*b^2*c^2 - 8*a^6*b^4*c^2 + 3*a^4*b^6*c^2 - 2*a^2*b^8*c^2 + b^10*c^2 + 6*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 - 4*a^6*c^6 + 3*a^4*b^2*c^6 + 2*a^2*b^4*c^6 + 6*b^6*c^6 + a^4*c^8 - 2*a^2*b^2*c^8 - 4*b^4*c^8 + b^2*c^10)*(a^12*b^4 - 6*a^10*b^6 + 15*a^8*b^8 - 20*a^6*b^10 + 15*a^4*b^12 - 6*a^2*b^14 + b^16 - 2*a^10*b^4*c^2 + 4*a^8*b^6*c^2 + 4*a^6*b^8*c^2 - 16*a^4*b^10*c^2 + 14*a^2*b^12*c^2 - 4*b^14*c^2 + a^12*c^4 - 2*a^10*b^2*c^4 + 6*a^8*b^4*c^4 - 8*a^6*b^6*c^4 + 10*a^4*b^8*c^4 - 16*a^2*b^10*c^4 + 9*b^12*c^4 - 6*a^10*c^6 + 4*a^8*b^2*c^6 - 8*a^6*b^4*c^6 + 8*a^2*b^8*c^6 - 16*b^10*c^6 + 15*a^8*c^8 + 4*a^6*b^2*c^8 + 10*a^4*b^4*c^8 + 8*a^2*b^6*c^8 + 20*b^8*c^8 - 20*a^6*c^10 - 16*a^4*b^2*c^10 - 16*a^2*b^4*c^10 - 16*b^6*c^10 + 15*a^4*c^12 + 14*a^2*b^2*c^12 + 9*b^4*c^12 - 6*a^2*c^14 - 4*b^2*c^14 + c^16) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29114.

X(33333) lies on the nine-point circle and these lines: {2, 15907}, {125, 16336}, {128, 1510}, {136, 14106}, {137, 1154}, {3258, 32142}, {11583, 11792}

X(33333) = reflection of X(35591) in X(5)
X(33333) = complement of X(15907)
X(33333) = complement of the isogonal of X(25150)
X(33333) = nine-point circle antipode of X(35591)
X(33333) = X(477)-of-orthic-triangle
X(33333) = orthic isogonal conjugate of X(25150)
X(33333) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 25150}, {25150, 10}
X(33333) = X(4)-Ceva conjugate of X(25150)

X(33334) = (name pending)

Barycentrics    a^8 b^2-b^10+a^8 c^2+8 a^6 b^2 c^2+3 a^4 b^4 c^2-a^2 b^6 c^2+b^8 c^2+3 a^4 b^2 c^4+10 a^2 b^4 c^4-a^2 b^2 c^6+b^2 c^8-c^10 : :
Barycentrics    (R^2-SW)S^4 + (9 R^2 SB SC-SB SC SW+SW^3)S^2 + SB SC SW^3 : :

As a point on the Euler line, X(33334) has Shinagawa coefficients [R^2 S^2-S^2 SW+SW^3,9 R^2 S^2-S^2 SW+SW^3].

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29115.

X(33334) lies on these lines: {2,3}


X(33335) = X(2)X(3)∩X(5806)X(10265)

Barycentrics    a^8 b^2-2 a^7 b^3-2 a^6 b^4+6 a^5 b^5-6 a^3 b^7+2 a^2 b^8+2 a b^9-b^10-4 a^8 b c+2 a^7 b^2 c+5 a^6 b^3 c-a^5 b^4 c+4 a^4 b^5 c-4 a^3 b^6 c-7 a^2 b^7 c+3 a b^8 c+2 b^9 c+a^8 c^2+2 a^7 b c^2+8 a^6 b^2 c^2+5 a^5 b^3 c^2-2 a^4 b^4 c^2+2 a^3 b^5 c^2-10 a^2 b^6 c^2-9 a b^7 c^2+3 b^8 c^2-2 a^7 c^3+5 a^6 b c^3+5 a^5 b^2 c^3-4 a^4 b^3 c^3+8 a^3 b^4 c^3+7 a^2 b^5 c^3-11 a b^6 c^3-8 b^7 c^3-2 a^6 c^4-a^5 b c^4-2 a^4 b^2 c^4+8 a^3 b^3 c^4+16 a^2 b^4 c^4+15 a b^5 c^4-2 b^6 c^4+6 a^5 c^5+4 a^4 b c^5+2 a^3 b^2 c^5+7 a^2 b^3 c^5+15 a b^4 c^5+12 b^5 c^5-4 a^3 b c^6-10 a^2 b^2 c^6-11 a b^3 c^6-2 b^4 c^6-6 a^3 c^7-7 a^2 b c^7-9 a b^2 c^7-8 b^3 c^7+2 a^2 c^8+3 a b c^8+3 b^2 c^8+2 a c^9+2 b c^9-c^10 : :

As a point on the Euler line, X(33335) has Shinagawa coefficients [r(2r+5 R), 2 r^2 + 13 r R + 16 R^2].

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29115.

X(33335) lies on these lines: {2,3}, {5806,10265}, {20116,20330}, {31664,31665}


X(33336) = X(2)X(3)∩X(6)X(19571)

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

As a point on the Euler line, X(33336) has Shinagawa coefficients ((E+F)4-2(E+F)(E+3F)S2+S4, 4(E+F)2S2-4S4).

X(33336) lies on these lines: {2,3}, {6,19571}, {76,16985}, {3978,4159}, {7864,10329}


X(33337) =  COMPLEMENT OF X(9897)

Barycentrics    4*a^4-3*(b+c)*a^3-3*(b-c)^2*a^2+(b+c)*(3*b^2-5*b*c+3*c^2)*a-(b^2-c^2)^2 : :
X(33337) = 3*X(1)-X(149), X(8)-3*X(15015), 3*X(10)-4*X(3035), 5*X(10)-4*X(3036), 3*X(10)-2*X(15863), 2*X(11)-3*X(551), X(100)+3*X(10031), X(149)+3*X(6224), 2*X(149)-3*X(21630), 3*X(214)-2*X(3035), 5*X(214)-2*X(3036), 3*X(214)-X(15863), 3*X(1317)+X(6154), 5*X(1317)+X(12732), 3*X(1317)-X(25416), 5*X(3035)-3*X(3036), 6*X(3036)-5*X(15863), 3*X(3244)+2*X(6154), X(3244)+2*X(10609), 5*X(3244)+2*X(12732), 3*X(3244)-2*X(25416), X(6154)-3*X(10609), 5*X(6154)-3*X(12732), 2*X(6224)+X(21630), X(7972)-3*X(10031), 3*X(10165)-2*X(12619), 5*X(10609)-X(12732), 3*X(10609)+X(25416), 3*X(12732)+5*X(25416)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29121.

X(33337) lies on these lines: {1, 149}, {2, 9897}, {8, 15015}, {10, 140}, {11, 551}, {20, 13253}, {36, 100}, {65, 1317}, {80, 1125}, {104, 5267}, {145, 3336}, {226, 18976}, {515, 6265}, {516, 10698}, {528, 5542}, {758, 17660}, {944, 6326}, {946, 11567}, {950, 12740}, {993, 3655}, {997, 5531}, {1145, 3625}, {1320, 5557}, {1483, 5885}, {1484, 15178}, {1768, 5731}, {2550, 6264}, {2771, 3878}, {2800, 4297}, {2932, 8715}, {3241, 12653}, {3576, 12247}, {3616, 20085}, {3623, 9802}, {3626, 12531}, {3636, 16173}, {3754, 17636}, {3814, 11698}, {3884, 17638}, {4084, 4311}, {4301, 5840}, {4304, 12758}, {4314, 15558}, {4669, 6174}, {4973, 5855}, {5493, 24466}, {5727, 10199}, {5836, 32900}, {5854, 9945}, {5883, 6797}, {5886, 12747}, {6667, 19883}, {6684, 19914}, {6702, 19862}, {7982, 13199}, {9803, 18231}, {10057, 13411}, {10106, 12739}, {10197, 13384}, {10738, 13464}, {11571, 21578}, {12019, 15808}, {12053, 12743}, {12331, 25440}, {12573, 14151}, {12611, 31673}, {12737, 13607}, {12751, 28236}, {13205, 25439}, {13605, 31525}, {14792, 17100}, {17439, 21090}, {25558, 30424}

X(33337) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 6224}, {20, 13253}, {100, 7972}, {145, 5541}, {944, 6326}, {1317, 10609}, {6154, 25416}, {7982, 13199}, {10698, 12119}, {12653, 20095}
X(33337) = reflection of X(i) in X(j) for these (i,j): (10, 214), (80, 1125), (946, 19907), (1484, 15178), (3244, 1317), (3625, 1145), (4084, 11570), (4301, 25485), (4669, 6174), (5493, 24466), (10265, 1385), (10738, 13464), (12531, 3626), (12737, 13607), (13605, 31525), (15863, 3035), (17636, 3754), (17638, 3884), (19914, 6684), (21630, 1), (21635, 6265), (30424, 25558), (31673, 12611)
X(33337) = complement of X(9897)
X(33337) = (anti-Aquila)-anticomplement of-X(11)
X(33337) = (3rd Euler)-anticomplement of-X(6246)
X(33337) = (Wasat)-anticomplement of-X(6246)
X(33337) = (2nd circumperp)-complement of-X(12247)
X(33337) = (hexyl)-complement of-X(12247)
X(33337) = (5th mixtilinear)-complement of-X(12653)
X(33337) = X(6224)-of-anti-Aquila-triangle
X(33337) = X(7722)-of-Wasat-triangle
X(33337) = X(11807)-of-excenters-reflections-triangle
X(33337) = X(12308)-of-2nd Zaniah-triangle
X(33337) = X(21630)-of-5th mixtilinear-triangle
X(33337) = X(21650)-of-2nd circumperp-triangle
X(33337) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (214, 15863, 3035), (3035, 15863, 10)

leftri

Half-squares and half-diamonds triangles: X(33338)-X(33503)

rightri

This preamble and centers X(33338)-X(33503) were contributed by César Eliud Lozada, June 27, 2019.

In a triangle ABC, build the triangles Ta = AB'C', Tb = BC'A' and Tc = CA'B', all isosceles with the same vertical angle θ in A, B, C, respectively. Barycentrics coordinates of A' are

    A' = (a^2*sin(θ) + S)/a : b*sin(C-θ) : c*sin(B-θ)

and cyclically for B' and C'.

There are two triads of such triangles, according as Ta, Tb, Tc have all the same or opposite orientation as ABC (this fact can be translated by using ±θ). Let A'B' C' and A"B"C" be the respective resulting triangles. Then

  1. A'B'C' and A"B"C" are both perspective to ABC with perspectors Q = a*csc(A - θ) : : (barycentrics). These perspectors lie on the Kiepert hyperbola of ABC and their isogonal conjugates satisfy
        OQ-1 = OK*cos(θ)*cos(ω)/cos(θ + ω), where O=X(3), K=X(6) and ω is the Brocard angle of ABC.
  2. A'B'C' and A"B"C" are perspective with perspector Q* = cos(A)*cos(θ)+cos(B)*cos(C) : :. Q* lies on the Euler line of ABC and OQ* = OH/(1+2*cos(θ)), where H=X(4).
  3. ABC is orthologic to both A'B'C' and A"B"C". The orthologic centers A'B'C'→ABC and A"B"C"→ABC are both Q and the reciprocal orthologic centers lie also on the Kiepert hyperbola of ABC.

Two particular cases are considered here: θ = ±π/2 and θ = ±π/3. For the first case, Ta is a half-square (and similarly for Tb, Tc) and, for the second case, these three triangles are equilateral and we can regard Ta as a half-diamond. These names are introduced here for the triangles A'B'C' and A"B"C". Their A-vertex barycentrics coordinates are

  1st half-squares triangle, with A' = -(a^2-S)/a : b*cos(C) : c*cos(B) = -(a^2+S) : SC : SB

  2nd half-squares triangle, with A" = -(a^2+S)/a : b*cos(C) : c*cos(B) = -(a^2-S) : SC : SB

  1st half-diamonds triangle, with A' = -(sqrt(3)*a^2-2*S)/(2*a) : b*cos(C-π/6) : c*cos(B-π/6) = -(sqrt(3)*a^2-2*S) : sqrt(3)*SC+S : sqrt(3)*SB+S

  2nd half-diamonds triangle, with A" = -(sqrt(3)*a^2+2*S)/(2*a) : b*cos(C+π/6) : c*cos(B+π/6) = -(sqrt(3)*a^2+2*S) : sqrt(3)*SC-S : sqrt(3)*SB-S

Moreover, when θ = π/3, the centers Ao, Bo, Co of the equilateral triangles Ta, Tb and Tc are vertices of an equilateral triangle. These triangles are here named the 1st and 2nd diamonds-central triangles. They have center X(2) and A-vertices

  1st half-diamonds-central triangle: A'o = -(a^2+2*sqrt(3)*S) : SC-sqrt(3)*S : SB-sqrt(3)*S

  2nd half-diamonds-central triangle: A"o = -(a^2-2*sqrt(3)*S) : SC+sqrt(3)*S : SB+sqrt(3)*S

Also, for any value of θ, the 1st or 2nd Fermat points of Ta, Tb, Tc are the vertices of other equilateral triangles.

A complete list of triangles and centers related with the six triangles above defined can be seen here.


X(33338) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND ANTI-ARTZT

Barycentrics    (19*a^4+14*(b^2+c^2)*a^2-(5*b^2-c^2)*(b^2-5*c^2))*S+(a^2+b^2+c^2)*(4*a^4+5*(b^2+c^2)*a^2-5*b^4+14*b^2*c^2-5*c^4) : :

X(33338) lies on these lines: {3068,13874}, {3363,33339}, {5860,12159}, {12158,19054}, {13789,13832}


X(33339) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND ANTI-ARTZT

Barycentrics    -(19*a^4+14*(b^2+c^2)*a^2-(5*b^2-c^2)*(b^2-5*c^2))*S+(c^2+a^2+b^2)*(4*a^4-5*b^4+14*b^2*c^2-5*c^4+5*(b^2+c^2)*a^2) : :

X(33339) lies on these lines: {3069,13927}, {3363,33338}, {5861,12158}, {12159,19053}, {13669,13831}


X(33340) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 1st ANTI-BROCARD

Barycentrics    2*S^4-SA*SW*S^2+SW*(S^2+SA*(3*SA-2*SW))*S-SB*SC*SW^2 : :
X(33340) = X(22501)-3*X(22562)

X(33340) lies on these lines: {2,7599}, {3,8293}, {4,99}, {30,13791}, {69,6231}, {98,638}, {147,487}, {148,32488}, {315,9991}, {325,9867}, {486,1916}, {488,13873}, {490,33370}, {491,33431}, {492,33434}, {542,32811}, {620,11291}, {637,32458}, {642,8290}, {2023,7388}, {3314,6229}, {3564,9868}, {5860,14645}, {5976,6811}, {5988,31583}, {5989,6290}, {7840,22501}, {8305,13934}, {9758,9772}, {9995,13653}, {13881,33348}, {32421,33342}

X(33340) = reflection of X(i) in X(j) for these (i,j): (9867, 325), (33341, 8781)
X(33340) = anticomplement of X(13926)
X(33340) = inverse of X(32500) in the orthoptic circle of Steiner inellipse
X(33340) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (99, 114, 33341), (1007, 13172, 33341)


X(33341) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 1st ANTI-BROCARD

Barycentrics    2*S^4-SA*SW*S^2-SW*(S^2+SA*(3*SA-2*SW))*S-SB*SC*SW^2 : :
X(33341) = X(22502)-3*X(22563)

X(33341) lies on these lines: {2,7598}, {3,8294}, {4,99}, {30,13671}, {69,6230}, {98,637}, {147,488}, {148,32489}, {315,9992}, {325,9868}, {485,1916}, {487,13926}, {489,33371}, {491,33435}, {492,33430}, {542,32810}, {620,11292}, {638,32458}, {641,8290}, {2023,7389}, {3314,6228}, {3564,9867}, {5861,14645}, {5976,6813}, {5988,31582}, {5989,6289}, {7840,22502}, {8304,13882}, {8997,9994}, {9757,9772}, {13881,33349}, {32419,33343}

X(33341) = reflection of X(i) in X(j) for these (i,j): (9868, 325), (33340, 8781)
X(33341) = anticomplement of X(13873)
X(33341) = inverse of X(32501) in the orthoptic circle of Steiner inellipse
X(33341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (99, 114, 33340), (1007, 13172, 33340)


X(33342) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND ANTI-MCCAY

Barycentrics    9*(SA-SW)*S^2-(3*SA-SW)^2*S+(9*SB*SC+SW^2)*SW : :

X(33342) lies on these lines: {69,2482}, {99,5860}, {524,9891}, {542,12256}, {671,3069}, {1992,9892}, {6782,33442}, {6783,33440}, {7735,19058}, {8598,13797}, {9485,13316}, {9773,13801}, {9862,26616}, {9893,33432}, {10488,10813}, {10812,11317}, {11152,13789}, {13757,33433}, {32421,33340}

X(33342) = reflection of X(i) in X(j) for these (i,j): (671, 13968), (13797, 8598)
X(33342) = {X(2482), X(8593)}-harmonic conjugate of X(33343)


X(33343) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND ANTI-MCCAY

Barycentrics    9*(SA-SW)*S^2+(3*SA-SW)^2*S+(9*SB*SC+SW^2)*SW : :

X(33343) lies on these lines: {69,2482}, {99,5861}, {524,9893}, {542,12257}, {671,3068}, {1992,9894}, {6782,33443}, {6783,33441}, {7735,19057}, {8598,13677}, {9485,13317}, {9773,13681}, {9862,26615}, {9891,33433}, {10488,10812}, {10813,11317}, {11152,13669}, {13637,33432}, {32419,33341}

X(33343) = reflection of X(i) in X(j) for these (i,j): (671, 13908), (13677, 8598)
X(33343) = {X(2482), X(8593)}-harmonic conjugate of X(33342)


X(33344) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND ARTZT

Barycentrics    4*S^4+(SB+SC)*SW*S^2+3*SW*(S^2+SB*SC)*S+SB*SC*SW^2 : :
X(33344) = 2*X(6289)+X(6462) = X(12257)-4*X(13882)

X(33344) lies on these lines: {4,9757}, {5,6337}, {262,5490}, {485,7612}, {488,9752}, {3068,13873}, {3545,13801}, {5590,33435}, {5860,9768}, {5870,6811}, {6289,6462}, {6460,22646}, {7709,22724}, {10839,33457}, {12510,33364}, {13681,32421}, {31412,33370}


X(33345) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND ARTZT

Barycentrics    4*S^4+(SB+SC)*SW*S^2-3*SW*(S^2+SB*SC)*S+SB*SC*SW^2 : :

X(33345) lies on these lines: {4,9758}, {5,6337}, {262,5491}, {486,7612}, {487,9752}, {3069,13926}, {3545,13681}, {5591,33434}, {5861,9767}, {5871,6813}, {6290,6463}, {6459,22617}, {7709,22725}, {10840,33456}, {12509,33365}, {13801,32419}


X(33346) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 1st BROCARD-REFLECTED

Barycentrics    S^4+(SA^2-2*SB*SC-4*SW^2)*S^2-SW*(2*S^2+SA^2+SW^2)*S+2*SB*SC*SW^2 : :

X(33346) lies on these lines: {371,33452}, {485,33348}, {641,33370}, {2459,33364}, {3934,33347}, {5590,12256}, {5870,21737}, {6278,33430}, {11825,22716}, {22623,33434}


X(33347) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 1st BROCARD-REFLECTED

Barycentrics    S^4+(SA^2-2*SB*SC-4*SW^2)*S^2+SW*(2*S^2+SA^2+SW^2)*S+2*SB*SC*SW^2 : :

X(33347) lies on these lines: {372,33453}, {486,33349}, {642,33371}, {2460,33365}, {3934,33346}, {5591,12257}, {6281,33431}, {11824,22718}, {22594,33435}


X(33348) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 1st BROCARD

Barycentrics    S^4+(SA^2+2*SW^2)*S^2+(SA^2-2*SB*SC+SW^2)*SW*S-2*SB*SC*SW^2 : :

X(33348) lies on these lines: {371,33454}, {485,33346}, {626,33349}, {641,33372}, {1352,5870}, {3094,7388}, {6228,33430}, {10008,12221}, {13881,33340}


X(33349) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 1st BROCARD

Barycentrics    S^4+(SA^2+2*SW^2)*S^2-(SA^2-2*SB*SC+SW^2)*SW*S-2*SB*SC*SW^2 : :

X(33349) lies on these lines: {372,33455}, {486,33347}, {626,33348}, {642,33373}, {1352,5871}, {3094,7389}, {6229,33431}, {10008,12222}, {13881,33341}


X(33350) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND INNER-FERMAT

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

X(33350) lies on the cubic K801 and these lines: {2,3366}, {18,624}, {182,2045}, {298,639}, {302,10576}, {371,6305}, {485,492}, {488,22639}, {490,33442}, {638,18581}, {641,33368}, {3365,6307}, {3391,33441}, {6564,33358}, {22627,33436}

X(33350) = anticomplement of X(33394)
X(33350) = {X(18), X(624)}-harmonic conjugate of X(33353)


X(33351) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND OUTER-FERMAT

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

X(33351) lies on the cubic K801 and these lines: {2,3364}, {17,623}, {182,2045}, {299,640}, {303,10577}, {372,6300}, {486,491}, {487,22609}, {489,33441}, {637,18582}, {642,33369}, {3367,33442}, {3389,6302}, {6565,33359}, {22600,33439}

X(33351) = anticomplement of X(33395)
X(33351) = {X(17), X(623)}-harmonic conjugate of X(33352)


X(33352) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND OUTER-FERMAT

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

X(33352) lies on the cubic K801 and these lines: {2,3365}, {17,623}, {182,2046}, {299,639}, {303,10576}, {371,6304}, {485,492}, {488,22638}, {490,33440}, {638,18582}, {641,33366}, {3366,33443}, {3390,6306}, {6564,33360}, {22629,33438}

X(33352) = anticomplement of X(33393)
X(33352) = {X(17), X(623)}-harmonic conjugate of X(33351)


X(33353) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND INNER-FERMAT

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

X(33353) lies on the cubic K801 and these lines: {2,3367}, {18,624}, {182,2046}, {298,640}, {302,10577}, {372,6301}, {486,491}, {487,22610}, {489,33443}, {637,18581}, {642,33367}, {3364,6303}, {3392,33440}, {6565,33361}, {22598,33437}

X(33353) = anticomplement of X(33392)
X(33353) = {X(18), X(624)}-harmonic conjugate of X(33350)


X(33354) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 1st HALF-DIAMONDS-CENTRAL

Barycentrics    (-21+31*sqrt(3))*S^2-(sqrt(3)*(7*SA-19*SW)-9*SA+15*SW)*S+(31*sqrt(3)-43)*SB*SC : :

X(33354) lies on these lines: {485,33438}, {6564,33368}, {33440,33444}


X(33355) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 2nd HALF-DIAMONDS-CENTRAL

Barycentrics    (-21+31*sqrt(3))*S^2+(sqrt(3)*(7*SA-19*SW)-9*SA+15*SW)*S+(31*sqrt(3)-43)*SB*SC : :

X(33355) lies on these lines: {486,33437}, {6565,33369}, {33443,33447}


X(33356) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 1st HALF-DIAMONDS-CENTRAL

Barycentrics    (21+31*sqrt(3))*S^2+(sqrt(3)*(7*SA-19*SW)+9*SA-15*SW)*S+(31*sqrt(3)+43)*SB*SC : :

X(33356) lies on these lines: {486,33439}, {6565,33367}, {33441,33445}


X(33357) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 2nd HALF-DIAMONDS-CENTRAL

Barycentrics    (21+31*sqrt(3))*S^2-(sqrt(3)*(7*SA-19*SW)+9*SA-15*SW)*S+(31*sqrt(3)+43)*SB*SC : :

X(33357) lies on these lines: {485,33436}, {6564,33366}, {33442,33446}


X(33358) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 1st HALF-DIAMONDS

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

X(33358) lies on these lines: {303,33449}, {485,33442}, {490,33366}, {492,33438}, {621,33394}, {630,33361}, {641,33440}, {2044,22797}, {6564,33350}, {11300,33472}, {33436,33448}


X(33359) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 2nd HALF-DIAMONDS

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

X(33359) lies on these lines: {302,33450}, {486,33441}, {489,33367}, {491,33437}, {622,33395}, {629,33360}, {642,33443}, {2044,22796}, {6565,33351}, {11299,33471}, {33439,33451}


X(33360) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 2nd HALF-DIAMONDS

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

X(33360) lies on these lines: {302,33451}, {485,33440}, {490,33368}, {492,33436}, {622,33393}, {629,33359}, {641,33442}, {2043,22796}, {6564,33352}, {11299,33473}, {33438,33450}


X(33361) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 1st HALF-DIAMONDS

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

X(33361) lies on these lines: {303,33448}, {486,33443}, {489,33369}, {491,33439}, {621,33392}, {630,33358}, {642,33441}, {2043,22797}, {6565,33353}, {11300,33470}, {33437,33449}


X(33362) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND MCCAY

Barycentrics    30*S^4+3*(SA^2-7*SB*SC-SW^2)*S^2+3*((3*SA+2*SW)*S^2-SB*SC*SW)*S+SB*SC*SW^2 : :

X(33362) lies on these lines: {}


X(33363) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND MCCAY

Barycentrics    30*S^4+3*(SA^2-7*SB*SC-SW^2)*S^2-3*((3*SA+2*SW)*S^2-SB*SC*SW)*S+SB*SC*SW^2 : :

X(33363) lies on the line {13087,33433}


X(33364) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND MEDIAL

Barycentrics    (a^2+S)*(-a^2+b^2+c^2+S) : :
X(33364) = X(488)+2*X(15293)

X(33364) lies on these lines: {2,490}, {3,5590}, {4,641}, {39,3069}, {99,5490}, {140,26362}, {141,3523}, {371,5860}, {376,639}, {486,26619}, {488,3068}, {492,6337}, {615,7738}, {631,642}, {637,2482}, {638,32785}, {640,3525}, {1151,1270}, {1321,3535}, {1587,11315}, {1588,11165}, {1589,6509}, {1599,6503}, {2459,33346}, {3071,3593}, {3146,23311}, {3311,26340}, {3524,13821}, {3564,26516}, {5200,13051}, {5420,7376}, {5745,14121}, {5861,9540}, {6292,11291}, {6396,7375}, {6449,26289}, {7374,12305}, {7388,13934}, {7583,26288}, {8400,11314}, {10518,11824}, {11294,32805}, {12257,33430}, {12510,33344}, {13886,32421}, {23249,32491}, {32488,32812}

X(33364) = complementary conjugate of X(23311)
X(33364) = isotomic conjugate of the polar conjugate of X(19042)
X(33364) = complement of X(1131)
X(33364) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 490, 31412), (4, 641, 26361)


X(33365) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND MEDIAL

Barycentrics    (a^2-S)*(-a^2+b^2+c^2-S) : :
X(33365) = X(487)+2*X(15294)

X(33365) lies on these lines: {2,489}, {3,5591}, {4,642}, {39,3068}, {99,5491}, {140,26361}, {141,3523}, {372,5861}, {376,640}, {485,26620}, {487,3069}, {491,6337}, {590,7738}, {631,641}, {638,2482}, {639,3525}, {1152,1271}, {1322,3536}, {1587,11165}, {1588,11316}, {1590,6509}, {1600,6503}, {2460,33347}, {3070,3595}, {3146,23312}, {3312,26339}, {3524,13701}, {3564,26521}, {5418,7375}, {5745,7090}, {5860,13935}, {6200,7376}, {6292,11292}, {6450,26288}, {7000,12306}, {7389,9600}, {7584,26289}, {8407,11313}, {9541,11314}, {10517,11825}, {11293,31412}, {12256,33431}, {12509,33345}, {13939,32419}, {23259,32490}, {32489,32813}

X(33365) = complementary conjugate of X(23312)
X(33365) = isotomic conjugate of the polar conjugate of X(19041)
X(33365) = complement of X(1132)
X(33365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 642, 26362), (141, 3523, 33364)


X(33366) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND INNER-NAPOLEON

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

X(33366) lies on these lines: {2,33425}, {371,33438}, {485,33368}, {490,33358}, {636,33369}, {641,33352}, {2041,5617}, {6305,33442}, {6564,33357}

X(33366) = anticomplement of X(33425)


X(33367) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND OUTER-NAPOLEON

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

X(33367) lies on these lines: {2,33424}, {372,33437}, {486,33369}, {489,33359}, {635,33368}, {642,33353}, {2041,5613}, {6300,33441}, {6565,33356}

X(33367) = anticomplement of X(33424)


X(33368) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND OUTER-NAPOLEON

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

X(33368) lies on these lines: {2,33426}, {371,33436}, {485,33366}, {490,33360}, {635,33367}, {2042,5613}, {6304,33440}, {6564,33354}

X(33368) = anticomplement of X(33426)


X(33369) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND INNER-NAPOLEON

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

X(33369) lies on these lines: {2,33427}, {372,33439}, {486,33367}, {489,33361}, {636,33366}, {642,33351}, {2042,5617}, {6301,33443}, {6565,33355}

X(33369) = anticomplement of X(33427)


X(33370) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 1st NEUBERG

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

X(33370) lies on these lines: {2,8982}, {4,2459}, {98,9739}, {371,21445}, {485,33372}, {488,7763}, {490,33340}, {511,7793}, {641,33346}, {1152,9756}, {1505,19056}, {3365,33389}, {3390,33388}, {5860,12257}, {5870,13935}, {6222,9733}, {6312,33452}, {6316,11825}, {8667,12305}, {11824,13828}, {12124,33432}, {12221,26441}, {13757,14830}, {14229,33457}, {31412,33344}

X(33370) = circumtangential isogonal conjugate of X(9738)


X(33371) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 1st NEUBERG

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

X(33371) lies on these lines: {2,14234}, {4,2460}, {98,9738}, {372,21445}, {486,33373}, {487,7763}, {489,33341}, {511,7793}, {642,33347}, {1151,9756}, {1504,19055}, {3364,33389}, {3389,33388}, {5861,12256}, {5871,9540}, {6312,11824}, {6316,33453}, {6399,9732}, {8667,12306}, {8982,12222}, {11825,13708}, {12123,33433}, {13637,14830}, {14244,33456}

X(33371) = circumtangential isogonal conjugate of X(9739)


X(33372) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-SQUARES AND 2nd NEUBERG

Barycentrics    2*S^4-(SA^2+SB*SC-SW^2)*S^2+((SA+2*SW)*S^2+SB*SC*SW)*S+SB*SC*SW^2 : :

X(33372) lies on these lines: {2,9739}, {371,33430}, {485,33370}, {492,3095}, {641,33348}, {3068,12256}, {5870,8721}, {6311,33454}, {7836,24206}


X(33373) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-SQUARES AND 2nd NEUBERG

Barycentrics    2*S^4-(SA^2+SB*SC-SW^2)*S^2-((SA+2*SW)*S^2+SB*SC*SW)*S+SB*SC*SW^2 : :

X(33373) lies on these lines: {2,9738}, {372,33431}, {486,33371}, {491,3095}, {642,33349}, {1588,9675}, {3069,8911}, {5871,8721}, {6315,33455}, {7836,24206}


X(33374) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND ANTI-ARTZT

Barycentrics    -(33*S^2-3*SA^2+39*SB*SC+19*SW^2)*S+sqrt(3)*(30*S^2+(3*SA-2*SW)*(3*SA-SW))*SW : :

X(33374) lies on these lines: {3363,16647}, {8176,12154}, {9762,11152}, {22487,33458}


X(33375) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND ANTI-ARTZT

Barycentrics    (33*S^2-3*SA^2+39*SB*SC+19*SW^2)*S+sqrt(3)*(30*S^2+(3*SA-2*SW)*(3*SA-SW))*SW : :

X(33375) lies on these lines: {3363,16646}, {8176,12155}, {9760,11152}, {22488,33459}


X(33376) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND ANTI-MCCAY

Barycentrics    -(15*S^2-3*SA^2-6*SB*SC-4*SW^2)*S+sqrt(3)*((9*SA-9*SW)*S^2+SW*(9*SB*SC+SW^2)) : :

X(33376) lies on these lines: {2,6777}, {99,33458}, {141,8593}, {299,2482}, {396,671}, {524,22569}, {533,5982}, {619,22998}, {5464,11152}, {9117,22567}, {9485,22933}, {10488,10808}, {11300,33462}, {11317,16651}, {14830,14904}


X(33377) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND ANTI-MCCAY

Barycentrics    (15*S^2-3*SA^2-6*SB*SC-4*SW^2)*S+sqrt(3)*((9*SA-9*SW)*S^2+SW*(9*SB*SC+SW^2)) : :

X(33377) lies on these lines: {2,6778}, {99,33459}, {141,8593}, {298,2482}, {395,671}, {524,22567}, {532,5983}, {618,22997}, {5463,11152}, {9115,22569}, {9485,22888}, {10488,10809}, {11299,33463}, {11317,16650}, {14830,14905}


X(33378) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND ARTZT

Barycentrics    10*S^4-(SA-7*SW)*SW*S^2-3*sqrt(3)*(3*S^2+SB*SC)*SW*S+4*SB*SC*SW^2 : :

X(33378) lies on these lines: {5,16653}, {1656,33379}, {9750,22797}, {9772,32465}, {15561,33460}, {22665,33458}


X(33379) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND ARTZT

Barycentrics    10*S^4-(SA-7*SW)*SW*S^2+3*sqrt(3)*(3*S^2+SB*SC)*SW*S+4*SB*SC*SW^2 : :

X(33379) lies on these lines: {5,16652}, {1656,33378}, {9749,22796}, {9772,32466}, {15561,33461}, {22666,33459}


X(33380) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND 1st BROCARD-REFLECTED

Barycentrics    S^4-(SA^2-3*SB*SC-8*SW^2)*S^2-sqrt(3)*(4*S^2+SW^2-2*SB*SC+SA^2)*SW*S-3*SB*SC*SW^2 : :

X(33380) lies on these lines: {2,9988}, {630,33388}, {3934,22687}, {6672,33382}, {7815,33381}, {14881,22689}, {22683,33462}


X(33381) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND 1st BROCARD-REFLECTED

Barycentrics    S^4-(SA^2-3*SB*SC-8*SW^2)*S^2+sqrt(3)*(4*S^2+SW^2-2*SB*SC+SA^2)*SW*S-3*SB*SC*SW^2 : :

X(33381) lies on these lines: {2,9989}, {3934,22689}, {6671,33383}, {7815,33380}, {14881,22687}, {22685,33463}


X(33382) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND 1st BROCARD

Barycentrics    3*S^4+(SA^2+SB*SC+2*SW^2)*S^2-3*SB*SC*SW^2+sqrt(3)*(2*S^2-SW^2-SA^2)*SW*S : :

X(33382) lies on these lines: {619,22866}, {623,23019}, {626,3643}, {630,33390}, {635,1352}, {2896,5980}, {3094,23024}, {3642,14880}, {3788,33383}, {6672,33380}, {22736,25559}


X(33383) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND 1st BROCARD

Barycentrics    3*S^4+(SA^2+SB*SC+2*SW^2)*S^2-3*SB*SC*SW^2-sqrt(3)*(2*S^2-SW^2-SA^2)*SW*S : :

X(33383) lies on these lines: {618,22911}, {624,23025}, {626,3642}, {629,33391}, {636,1352}, {2896,5981}, {3094,23018}, {3643,14880}, {3788,33382}, {6671,33381}, {22737,25560}


X(33384) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND MCCAY

Barycentrics    48*S^4+(3*SA^2-30*SB*SC-7*SW^2)*S^2-3*sqrt(3)*(3*SA*S^2+SW*SB*SC)*S+2*SB*SC*SW^2 : :

X(33384) lies on these lines: {619,22736}, {5464,7607}, {22866,33460}


X(33385) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND MCCAY

Barycentrics    48*S^4+(3*SA^2-30*SB*SC-7*SW^2)*S^2+3*sqrt(3)*(3*SA*S^2+SW*SB*SC)*S+2*SB*SC*SW^2 : :

X(33385) lies on these lines: {618,22737}, {5463,7607}, {22911,33461}


X(33386) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND INNER-NAPOLEON

Barycentrics    9*a^4-13*(b^2+c^2)*a^2+4*(b^2-c^2)^2+2*sqrt(3)*(a^2+2*b^2+2*c^2)*S : :

X(33386) lies on these lines: {2,5238}, {3,22797}, {5,22843}, {13,630}, {14,11310}, {17,11302}, {18,619}, {62,33458}, {140,5617}, {303,33465}, {395,22845}, {621,6674}, {627,16242}, {628,3411}, {635,33416}, {636,5463}, {3106,7786}, {3763,33387}, {6669,10188}, {6673,11289}, {6695,16962}, {9885,22489}, {11307,31268}, {11311,33417}, {15561,25559}

X(33386) = complement of X(33412)
X(33386) = {X(628), X(6672)}-harmonic conjugate of X(3411)


X(33387) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND OUTER-NAPOLEON

Barycentrics    9*a^4-13*(b^2+c^2)*a^2+4*(b^2-c^2)^2-2*sqrt(3)*(a^2+2*b^2+2*c^2)*S : :

X(33387) lies on these lines: {2,5237}, {3,22796}, {5,22890}, {13,11309}, {14,629}, {17,618}, {18,11301}, {61,33459}, {140,5613}, {302,33464}, {622,6673}, {627,3412}, {628,16241}, {635,5464}, {636,33417}, {3107,7786}, {3763,33386}, {6670,10187}, {6674,11290}, {6694,16963}, {9886,22490}, {11308,31268}, {11312,33416}, {15561,25560}

X(33387) = complement of X(33413)
X(33387) = {X(627), X(6671)}-harmonic conjugate of X(3412)


X(33388) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND 1st NEUBERG

Barycentrics    -2*S*a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)+3*a^8-6*(b^2+c^2)*a^6+(7*b^4+4*b^2*c^2+7*c^4)*a^4-4*(b^4-c^4)*(b^2-c^2)*a^2-2*(b^2-c^2)^2*b^2*c^2 : :
X(33388) = X(9749)-3*X(21156)

X(33388) lies on these lines: {2,9749}, {3,22687}, {15,98}, {182,10007}, {511,6582}, {530,8182}, {542,13083}, {619,5617}, {621,5982}, {630,33380}, {1352,32552}, {2782,6295}, {2794,6771}, {3166,6770}, {3389,33371}, {3390,33370}, {5980,6194}, {5981,8291}, {6108,9753}, {6672,33390}, {7684,22513}, {9750,16241}, {11145,25233}, {13349,33462}, {14639,22846}, {22869,33466}, {33420,33478}

X(33388) = reflection of X(33389) in X(12042)
X(33388) = circumtangential isogonal conjugate of X(14538)


X(33389) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND 1st NEUBERG

Barycentrics    2*S*a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)+3*a^8-6*(b^2+c^2)*a^6+(7*b^4+4*b^2*c^2+7*c^4)*a^4-4*(b^4-c^4)*(b^2-c^2)*a^2-2*(b^2-c^2)^2*b^2*c^2 : :
X(33389) = X(9750)-3*X(21157)

X(33389) lies on these lines: {2,9750}, {3,22689}, {16,98}, {182,10007}, {511,6295}, {531,8182}, {542,13084}, {618,5613}, {622,5983}, {629,33381}, {1352,32553}, {2782,6582}, {2794,6774}, {3364,33371}, {3365,33370}, {5980,8292}, {5981,6194}, {6109,9753}, {6671,33391}, {7685,22512}, {9749,16242}, {11146,25234}, {13350,33463}, {14639,22891}, {22914,33467}, {33421,33479}

X(33389) = reflection of X(33388) in X(12042)
X(33389) = circumtangential isogonal conjugate of X(14539)


X(33390) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND 2nd NEUBERG

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

X(33390) lies on these lines: {2,7685}, {61,16940}, {619,5611}, {630,33382}, {6298,24206}, {6299,10796}, {22871,33468}


X(33391) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND 2nd NEUBERG

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

X(33391) lies on these lines: {2,7684}, {62,16941}, {618,5615}, {629,33383}, {6298,10796}, {6299,24206}, {6671,33389}, {22916,33469}


X(33392) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND INNER-VECTEN

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

X(33392) lies on these lines: {2,3367}, {62,303}, {397,33448}, {615,642}, {621,33361}, {624,3365}, {640,6302}, {3071,6303}, {6119,33424}, {6300,13951}, {15765,22797}, {22882,33449}, {24206,33393}

X(33392) = complement of X(33353)
X(33392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (62, 303, 33394), (630, 6672, 33394)


X(33393) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND OUTER-VECTEN

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

X(33393) lies on these lines: {2,3365}, {61,302}, {398,33451}, {590,641}, {622,33360}, {623,3389}, {639,6307}, {3070,6306}, {6118,33425}, {6305,8976}, {8531,28427}, {15765,22796}, {22928,33450}, {24206,33392}

X(33393) = complement of X(33352)
X(33393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (61, 302, 33395), (629, 6671, 33395)


X(33394) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND OUTER-VECTEN

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

X(33394) lies on these lines: {2,3366}, {62,303}, {397,33449}, {590,641}, {621,33358}, {624,3364}, {639,6306}, {3070,6307}, {6118,33426}, {6304,8976}, {18585,22797}, {22883,33448}, {24206,33395}

X(33394) = complement of X(33350)
X(33394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (62, 303, 33392), (630, 6672, 33392)


X(33395) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND INNER-VECTEN

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

X(33395) lies on these lines: {2,3364}, {61,302}, {398,33450}, {615,642}, {622,33359}, {623,3390}, {640,6303}, {3071,6302}, {6119,33427}, {6301,13951}, {18585,22796}, {22927,33451}, {24206,33394}

X(33395) = complement of X(33351)
X(33395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (61, 302, 33393), (629, 6671, 33393)


X(33396) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS AND WASAT

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

X(33396) lies on these lines: {1,30382}, {2,1277}, {3,142}, {10,624}, {14,226}, {618,11813}, {1276,5195}, {2905,15788}, {3086,30281}, {4295,30280}, {5011,5243}, {10652,12047}, {11705,17761}, {13407,16038}, {17167,17406}

X(33396) = midpoint of X(1276) and X(5195)
X(33396) = reflection of X(33397) in X(5074)
X(33396) = complement of X(1277)
X(33396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (142, 33397, 33428), (31590, 31591, 33429), (33397, 33429, 142)


X(33397) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS AND WASAT

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

X(33397) lies on these lines: {1,30383}, {2,1276}, {3,142}, {10,623}, {13,226}, {619,11813}, {1277,5195}, {2905,15789}, {3086,30280}, {4295,30281}, {5011,5242}, {10651,12047}, {11706,17761}, {17167,17405}

X(33397) = midpoint of X(1277) and X(5195)
X(33397) = reflection of X(33396) in X(5074)
X(33397) = complement of X(1276)
X(33397) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (946, 33428, 33429), (31590, 31591, 33428), (33396, 33428, 142)


X(33398) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND ANTI-ARTZT

Barycentrics    (a^2+b^2+c^2)*(5*a^4-23*(b^2+c^2)*a^2+14*b^4-32*b^2*c^2+14*c^4)-2*sqrt(3)*S*(7*a^4+47*(b^2+c^2)*a^2-16*(2*b^2-c^2)*(b^2-2*c^2)) : :

X(33398) lies on these lines: {3363,11153}, {5460,8593}, {11152,22692}, {12154,16644}, {12155,33474}


X(33399) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND ANTI-ARTZT

Barycentrics    (a^2+b^2+c^2)*(5*a^4-23*(b^2+c^2)*a^2+14*b^4-32*b^2*c^2+14*c^4)+2*sqrt(3)*S*(7*a^4+47*(b^2+c^2)*a^2-16*(2*b^2-c^2)*(b^2-2*c^2)) : :

X(33399) lies on these lines: {3363,11154}, {5459,8593}, {11152,22691}, {12154,33475}, {12155,16645}


X(33400) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND 1st ANTI-BROCARD

Barycentrics    sqrt(3)*(S^4-(SA-13*SW)*SW*S^2+(8*SA-5*SW)*SA*SW^2)*S+(7*S^4+(3*SB*SC-13*SW^2)*S^2-SB*SC*SW^2)*SW : :

X(33400) lies on these lines: {5,5978}, {624,9866}, {5460,7840}, {5979,6774}, {9865,22692}, {11290,33484}


X(33401) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND 1st ANTI-BROCARD

Barycentrics    -sqrt(3)*(S^4-(SA-13*SW)*SW*S^2+(8*SA-5*SW)*SA*SW^2)*S+(7*S^4+(3*SB*SC-13*SW^2)*S^2-SB*SC*SW^2)*SW : :

X(33401) lies on these lines: {5,5979}, {623,9866}, {5459,7840}, {5978,6771}, {9865,22691}, {11289,33485}


X(33402) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND ANTI-MCCAY

Barycentrics    378*S^4-3*(9*SB*SC+11*SW^2)*S^2+3*sqrt(3)*((27*SA-58*SW)*S^2-(SA^2-25*SB*SC-3*SW^2)*SW)*S+(9*SB*SC+SW^2)*SW^2 : :

X(33402) lies on these lines: {5460,9855}, {8594,33474}, {8595,33476}, {22564,22692}


X(33403) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND ANTI-MCCAY

Barycentrics    378*S^4-3*(9*SB*SC+11*SW^2)*S^2-3*sqrt(3)*((27*SA-58*SW)*S^2-(SA^2-25*SB*SC-3*SW^2)*SW)*S+(9*SB*SC+SW^2)*SW^2 : :

X(33403) lies on these lines: {5459,9855}, {8594,33477}, {8595,33475}, {22564,22691}


X(33404) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND ANTICOMPLEMENTARY

Barycentrics    15*a^4-28*(b^2+c^2)*a^2+13*(b^2-c^2)^2-6*sqrt(3)*(-a^2+b^2+c^2)*S : :

X(33404) lies on these lines: {2,3411}, {5,616}, {69,33405}, {298,16239}, {302,628}, {617,631}, {618,33412}, {621,3530}, {627,5067}, {633,33418}, {634,5070}, {5460,8591}, {8782,22692}, {9698,11489}, {11307,33474}

X(33404) = anticomplement of X(10188)


X(33405) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND ANTICOMPLEMENTARY

Barycentrics    15*a^4-28*(b^2+c^2)*a^2+13*(b^2-c^2)^2+6*sqrt(3)*(-a^2+b^2+c^2)*S : :

X(33405) lies on these lines: {2,3412}, {5,617}, {69,33404}, {299,16239}, {303,627}, {616,631}, {619,33413}, {622,3530}, {628,5067}, {633,5070}, {634,33419}, {5459,8591}, {8782,22691}, {9698,11488}, {11308,33475}

X(33405) = anticomplement of X(10187)


X(33406) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND ARTZT

Barycentrics    2*S^4-(SA-7*SW)*SW*S^2+sqrt(3)*(3*S^2+SB*SC)*SW*S+4*SB*SC*SW^2 : :

X(33406) lies on these lines: {5,9749}, {18,6115}, {1080,9751}, {1656,33407}, {3090,33410}, {5055,9760}, {5460,6054}, {6774,9750}, {9762,33474}, {9772,22692}, {25196,33484}


X(33407) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND ARTZT

Barycentrics    2*S^4-(SA-7*SW)*SW*S^2-sqrt(3)*(3*S^2+SB*SC)*SW*S+4*SB*SC*SW^2 : :

X(33407) lies on these lines: {5,9750}, {17,6114}, {383,9751}, {1656,33406}, {3090,33411}, {5055,9762}, {5459,6054}, {6771,9749}, {9760,33475}, {9772,22691}, {25192,33485}


X(33408) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND 1st BROCARD-REFLECTED

Barycentrics    3*S^4-(3*SA^2-9*SB*SC-16*SW^2)*S^2+sqrt(3)*(4*S^2+SW^2-2*SB*SC+SA^2)*SW*S-SB*SC*SW^2 : :

X(33408) lies on these lines: {99,22692}, {3934,22683}, {6694,33410}, {7815,33409}, {20416,33411}, {22687,33478}


X(33409) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND 1st BROCARD-REFLECTED

Barycentrics    3*S^4-(3*SA^2-9*SB*SC-16*SW^2)*S^2-sqrt(3)*(4*S^2+SW^2-2*SB*SC+SA^2)*SW*S-SB*SC*SW^2 : :

X(33409) lies on these lines: {99,22691}, {3934,22685}, {6695,33411}, {7815,33408}, {20415,33410}, {22689,33479}


X(33410) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND 1st BROCARD

Barycentrics    -sqrt(3)*(3*S^2+SA^2+SB*SC+SW^2)*S+(5*S^2+SB*SC)*SW : :

X(33410) lies on these lines: {5,3642}, {76,22692}, {599,636}, {618,33418}, {624,1352}, {626,22736}, {629,11312}, {633,33412}, {3090,33406}, {3628,3788}, {3643,6774}, {3934,33478}, {6694,33408}, {20415,33409}


X(33411) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND 1st BROCARD

Barycentrics    sqrt(3)*(3*S^2+SA^2+SB*SC+SW^2)*S+(5*S^2+SB*SC)*SW : :

X(33411) lies on these lines: {5,3643}, {76,22691}, {599,635}, {619,33419}, {623,1352}, {626,22737}, {630,11311}, {634,33413}, {3090,33407}, {3628,3788}, {3642,6771}, {3934,33479}, {6695,33409}, {20416,33408}


X(33412) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND INNER-FERMAT

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

X(33412) lies on these lines: {2,5238}, {4,6774}, {5,6770}, {14,628}, {18,616}, {20,33418}, {62,5460}, {194,22690}, {618,33404}, {624,22114}, {633,33410}, {634,5858}, {3090,16626}, {3104,18581}, {3544,3618}, {6248,33478}, {6694,33414}, {7775,33476}, {11304,33474}, {14651,16627}, {22113,22891}

X(33412) = anticomplement of X(33386)
X(33412) = {X(3544), X(3618)}-harmonic conjugate of X(33413)


X(33413) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND OUTER-FERMAT

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

X(33413) lies on these lines: {2,5237}, {4,6771}, {5,6773}, {13,627}, {17,617}, {20,33419}, {61,5459}, {194,22688}, {619,33405}, {623,22113}, {633,5859}, {634,33411}, {3090,16627}, {3105,18582}, {3544,3618}, {6248,33479}, {6695,33415}, {7775,33477}, {11303,33475}, {14651,16626}, {22114,22846}

X(33413) = anticomplement of X(33387)
X(33413) = {X(3544), X(3618)}-harmonic conjugate of X(33412)


X(33414) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND OUTER-FERMAT

Barycentrics    5*a^4-17*(b^2+c^2)*a^2+12*(b^2-c^2)^2-2*sqrt(3)*S*(3*a^2+2*b^2+2*c^2) : :

X(33414) lies on these lines: {2,5351}, {5,21156}, {13,629}, {17,5859}, {18,6669}, {62,22489}, {617,22891}, {619,10188}, {623,22845}, {1656,6774}, {3105,16966}, {5067,33418}, {6694,33412}, {11289,31709}, {11309,16808}


X(33415) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND INNER-FERMAT

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

X(33415) lies on these lines: {2,5352}, {5,21157}, {14,630}, {17,6670}, {18,5858}, {61,22490}, {616,22846}, {618,10187}, {624,22844}, {1656,6771}, {3104,16967}, {3628,16626}, {5067,33419}, {6695,33413}, {11290,31710}, {11306,33477}, {11310,16809}


X(33416) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND 15th FERMAT-DAO

Barycentrics    15*S^2-sqrt(3)*(SB+SC)*S-3*SB*SC : :

X(33416) lies on these lines: {2,13}, {3,16809}, {5,10646}, {6,3411}, {14,5054}, {15,18}, {17,10188}, {61,3525}, {62,632}, {202,5326}, {395,11539}, {396,10124}, {549,5321}, {619,21359}, {629,22894}, {630,22855}, {631,10645}, {635,33386}, {1506,19780}, {1656,11481}, {3090,5351}, {3366,32789}, {3367,32790}, {3391,6396}, {3392,6200}, {3523,5365}, {3533,11488}, {3548,11516}, {3628,5237}, {5070,16965}, {5238,5334}, {5352,14869}, {5460,25166}, {5972,10657}, {6143,10633}, {6640,10635}, {6670,23004}, {6673,22900}, {6674,31703}, {6689,10677}, {6771,22850}, {6774,6777}, {7006,7294}, {7505,11476}, {7542,11515}, {7911,11289}, {7918,11290}, {10018,10641}, {10125,11267}, {10187,15720}, {10643,16238}, {10654,15702}, {10658,15061}, {10676,23329}, {11312,33387}, {11485,15694}, {11542,16239}, {12100,12817}, {15709,16268}, {16644,16963}, {20299,30403}, {22493,33474}, {22577,33476}, {22607,33445}, {22636,33444}, {22695,33478}, {25182,33481}, {25199,33482}, {25200,33484}, {25201,33486}, {25202,33488}, {25228,33491}

X(33416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 16, 16966), (2, 16242, 13), (16242, 16966, 16)


X(33417) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND 16th FERMAT-DAO

Barycentrics    15*S^2+sqrt(3)*(SB+SC)*S-3*SB*SC : :

X(33417) lies on these lines: {2,14}, {3,16808}, {5,10645}, {6,3411}, {13,5054}, {16,17}, {18,10187}, {61,632}, {62,3525}, {203,5326}, {395,10124}, {396,11539}, {549,5318}, {618,21360}, {629,22901}, {630,22850}, {631,10646}, {636,33387}, {1506,19781}, {1656,11480}, {3090,5352}, {3366,6396}, {3367,6200}, {3391,32789}, {3392,32790}, {3523,5366}, {3533,11489}, {3548,11515}, {3628,5238}, {5070,16964}, {5237,5335}, {5351,14869}, {5459,25156}, {5972,10658}, {6143,10632}, {6640,10634}, {6669,23005}, {6673,31704}, {6674,22856}, {6689,10678}, {6771,6778}, {6774,22894}, {7005,7294}, {7505,11475}, {7542,11516}, {7911,11290}, {7918,11289}, {10018,10642}, {10125,11268}, {10188,15720}, {10644,16238}, {10653,15702}, {10657,15061}, {10675,23329}, {11311,33386}, {11486,15694}, {11543,16239}, {12100,12816}, {15709,16267}, {16645,16962}, {20299,30402}, {22494,33475}, {22578,33477}, {22608,33447}, {22637,33446}, {22696,33479}, {25177,33480}, {25203,33483}, {25204,33485}, {25205,33487}, {25206,33489}, {25227,33490}

X(33417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (15, 16967, 14), (6780, 22490, 14), (16241, 16967, 15)


X(33418) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND MCCAY

Barycentrics    sqrt(3)*(7*S^2-SB*SC)*S+(3*SA-7*SW)*S^2+2*SW*SB*SC : :

X(33418) lies on these lines: {3,5460}, {18,631}, {20,33412}, {140,13083}, {618,33410}, {629,3526}, {632,20582}, {633,33404}, {3104,22692}, {5067,33414}, {6683,33478}, {7746,16773}, {11310,15069}, {13084,20398}, {14813,33486}, {14814,33488}, {15709,22493}, {16242,22891}, {16964,31684}


X(33419) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND MCCAY

Barycentrics    -sqrt(3)*(7*S^2-SB*SC)*S+(3*SA-7*SW)*S^2+2*SW*SB*SC : :

X(33419) lies on these lines: {3,5459}, {17,631}, {20,33413}, {140,13084}, {619,33411}, {630,3526}, {632,20582}, {634,33405}, {3105,22691}, {5067,33415}, {6683,33479}, {7746,16772}, {11309,15069}, {13083,20398}, {14813,33489}, {14814,33487}, {15709,22494}, {16241,22846}, {16965,31683}


X(33420) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND 1st NEUBERG

Barycentrics    10*S^4+(3*SA^2-4*SB*SC-3*SW^2)*S^2+sqrt(3)*((SA-2*SW)*S^2+SW*SB*SC)*S+6*SB*SC*SW^2 : :

X(33420) lies on these lines: {4,22891}, {62,98}, {182,33421}, {511,22869}, {629,5617}, {5460,14830}, {5864,8667}, {5873,22916}, {6194,14540}, {6582,33482}, {6694,33422}, {33388,33478}

X(33420) = circumtangential isogonal conjugate of X(14541)


X(33421) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND 1st NEUBERG

Barycentrics    10*S^4+(3*SA^2-4*SB*SC-3*SW^2)*S^2-sqrt(3)*((SA-2*SW)*S^2+SW*SB*SC)*S+6*SB*SC*SW^2 : :

X(33421) lies on these lines: {4,22846}, {61,98}, {182,33420}, {511,22914}, {630,5613}, {5459,14830}, {5865,8667}, {5872,22871}, {6194,14541}, {6295,33483}, {6695,33423}, {33389,33479}

X(33421) = circumtangential isogonal conjugate of X(14540)


X(33422) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND 2nd NEUBERG

Barycentrics    4*S^4-(3*SA^2-2*SB*SC-15*SW^2)*S^2+sqrt(3)*((SA+4*SW)*S^2-SW*SB*SC)*S+6*SB*SC*SW^2 : :

X(33422) lies on these lines: {2,14540}, {6298,33484}, {6694,33420}, {22871,24206}


X(33423) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND 2nd NEUBERG

Barycentrics    4*S^4-(3*SA^2-2*SB*SC-15*SW^2)*S^2-sqrt(3)*((SA+4*SW)*S^2-SW*SB*SC)*S+6*SB*SC*SW^2 : :

X(33423) lies on these lines: {2,14541}, {6299,33485}, {6695,33421}, {22916,24206}


X(33424) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND INNER-VECTEN

Barycentrics    (2*(6*a^2+b^2+c^2)*S-7*(b^2+c^2)*a^2+7*b^4-14*b^2*c^2+7*c^4)*sqrt(3)+6*(4*a^2+b^2+c^2)*S+2*a^4-17*(b^2+c^2)*a^2+15*(b^2-c^2)^2 : :

X(33424) lies on these lines: {2,33367}, {640,22882}, {642,33427}, {6119,33392}, {6302,33445}, {6303,32490}, {6694,33426}, {6774,14814}

X(33424) = complement of X(33367)


X(33425) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND OUTER-VECTEN

Barycentrics    (-2*(6*a^2+b^2+c^2)*S-7*(b^2+c^2)*a^2+7*b^4-14*b^2*c^2+7*c^4)*sqrt(3)-6*(4*a^2+b^2+c^2)*S+2*a^4-17*(b^2+c^2)*a^2+15*(b^2-c^2)^2 : :

X(33425) lies on these lines: {2,33366}, {639,22928}, {641,33426}, {6118,33393}, {6306,32491}, {6307,33446}, {6695,33427}, {6771,14814}

X(33425) = complement of X(33366)


X(33426) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND OUTER-VECTEN

Barycentrics    (2*(6*a^2+b^2+c^2)*S+7*(b^2+c^2)*a^2-7*b^4+14*b^2*c^2-7*c^4)*sqrt(3)-3*(8*a^2+2*b^2+2*c^2)*S+2*a^4-17*(b^2+c^2)*a^2+15*(b^2-c^2)^2 : :

X(33426) lies on these lines: {2,33368}, {639,22883}, {641,33425}, {6118,33394}, {6306,33444}, {6307,32491}, {6694,33424}, {6774,14813}

X(33426) = complement of X(33368)


X(33427) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND INNER-VECTEN

Barycentrics    (-2*(6*a^2+b^2+c^2)*S+7*(b^2+c^2)*a^2-7*b^4+14*b^2*c^2-7*c^4)*sqrt(3)+3*(8*a^2+2*b^2+2*c^2)*S+2*a^4-17*(b^2+c^2)*a^2+15*(b^2-c^2)^2 : :

X(33427) lies on these lines: {2,33369}, {640,22927}, {642,33424}, {6119,33395}, {6302,32490}, {6303,33447}, {6695,33425}, {6771,14813}

X(33427) = complement of X(33369)


X(33428) = PERSPECTOR OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL AND WASAT

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

X(33428) lies on these lines: {2,6191}, {3,142}, {10,635}, {17,226}, {86,15789}, {11740,17761}, {13407,30383}, {15772,17167}

X(33428) = complement of X(6191)
X(33428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (142, 33397, 33396), (31590, 31591, 33397), (33397, 33429, 946)


X(33429) = PERSPECTOR OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL AND WASAT

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

X(33429) lies on these lines: {2,6192}, {3,142}, {10,636}, {18,226}, {86,15788}, {11739,17761}, {13407,30382}, {15771,17167}

X(33429) = complement of X(6192)
X(33429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (946, 33428, 33397), (31590, 31591, 33396), (33396, 33428, 946)


X(33430) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(9868)

X(33430) lies on these lines: {2,98}, {4,32495}, {99,488}, {115,1587}, {371,33372}, {490,2782}, {492,33341}, {543,26288}, {2794,5870}, {3068,13873}, {3564,9868}, {5477,19056}, {5860,13172}, {6228,33348}, {6278,33346}, {6561,33434}, {6564,22502}, {8980,13640}, {9862,9986}, {10723,33457}, {12221,23698}, {12243,13794}, {12257,33364}, {13773,13967}, {14651,31412}, {32421,33432}

X(33430) = reflection of X(i) in X(j) for these (i,j): (147, 6231), (33431, 98)
X(33430) = anticomplement of X(6230)
X(33430) = {X(147), X(6776)}-harmonic conjugate of X(33431)


X(33431) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(9867)

X(33431) lies on these lines: {2,98}, {4,32492}, {99,487}, {115,1588}, {372,33373}, {489,2782}, {491,33340}, {543,26289}, {2794,5871}, {3069,13926}, {3564,9867}, {5477,19055}, {5861,13172}, {6229,33349}, {6281,33347}, {6560,33435}, {6565,22501}, {8980,13653}, {9862,9987}, {10723,33456}, {12222,23698}, {12243,13674}, {12256,33365}, {13760,13967}, {32419,33433}

X(33431) = reflection of X(i) in X(j) for these (i,j): (147, 6230), (33430, 98)
X(33431) = anticomplement of X(6231)
X(33431) = {X(147), X(6776)}-harmonic conjugate of X(33430)


X(33432) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9893)

X(33432) lies on these lines: {2,99}, {542,5870}, {3068,13874}, {6564,22563}, {9893,33342}, {12124,33370}, {12221,14645}, {12243,12256}, {13088,33362}, {13637,33343}, {13642,13908}, {18800,19058}, {32421,33430}

X(33432) = reflection of X(i) in X(j) for these (i,j): (8591, 9892), (33433, 671)
X(33432) = anticomplement of X(9894)
X(33432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7620, 8591, 33433), (9890, 11185, 33433)


X(33433) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9891)

X(33433) lies on these lines: {2,99}, {542,5871}, {3069,13927}, {6565,22562}, {9891,33343}, {12123,33371}, {12222,14645}, {12243,12257}, {13087,33363}, {13757,33342}, {13761,13968}, {18800,19057}, {32419,33431}

X(33433) = reflection of X(i) in X(j) for these (i,j): (8591, 9894), (33432, 671)
X(33433) = anticomplement of X(9892)
X(33433) = {X(9890), X(11185)}-harmonic conjugate of X(33432)


X(33434) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 1st BROCARD-REFLECTED

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

The reciprocal orthologic center of these triangles is X(22623)

X(33434) lies on these lines: {2,51}, {6,10852}, {39,19063}, {371,21445}, {372,22521}, {492,33340}, {1351,10839}, {3068,22724}, {3102,6459}, {5052,19064}, {5591,33345}, {5870,22700}, {6561,33430}, {6564,22622}, {9675,19055}, {22720,22722}

X(33434) = reflection of X(i) in X(j) for these (i,j): (6194, 22726), (7709, 3102), (33435, 262)
X(33434) = anticomplement of X(22727)


X(33435) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 1st BROCARD-REFLECTED

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

The reciprocal orthologic center of these triangles is X(22594)

X(33435) lies on these lines: {2,51}, {6,10851}, {39,19064}, {371,22521}, {372,21445}, {491,33341}, {1351,10840}, {3069,22725}, {3103,6460}, {5052,19063}, {5590,33344}, {5871,22699}, {6560,33431}, {6565,22593}, {22594,33347}, {22721,22723}

X(33435) = reflection of X(i) in X(j) for these (i,j): (6194, 22727), (7709, 3103), (33434, 262)
X(33435) = anticomplement of X(22726)


X(33436) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(22627)

X(33436) lies on these lines: {2,18}, {371,33368}, {485,33357}, {492,33360}, {3068,22880}, {5870,22854}, {5965,33439}, {6561,33438}, {6564,22626}, {12256,22531}, {22627,33350}, {22876,22878}, {33358,33448}

X(33436) = reflection of X(i) in X(j) for these (i,j): (628, 22882), (33437, 18)
X(33436) = anticomplement of X(22883)


X(33437) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(22598)

X(33437) lies on these lines: {2,18}, {372,33367}, {486,33355}, {491,33359}, {3069,22881}, {5871,22853}, {5965,33438}, {6560,33439}, {6565,22597}, {12257,22531}, {22598,33353}, {22877,22879}, {33361,33449}

X(33437) = reflection of X(i) in X(j) for these (i,j): (628, 22883), (33436, 18)
X(33437) = anticomplement of X(22882)


X(33438) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(22629)

X(33438) lies on these lines: {2,17}, {371,33366}, {485,33354}, {492,33358}, {3068,22925}, {5870,22899}, {5965,33437}, {6561,33436}, {6564,22628}, {12256,22532}, {22629,33352}, {22921,22923}, {33360,33450}

X(33438) = reflection of X(i) in X(j) for these (i,j): (627, 22927), (33439, 17)
X(33438) = anticomplement of X(22928)


X(33439) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(22600)

X(33439) lies on these lines: {2,17}, {372,33369}, {486,33356}, {491,33361}, {3069,22926}, {5871,22898}, {5965,33436}, {6560,33437}, {6565,22599}, {12257,22532}, {22600,33351}, {22922,22924}, {33359,33451}

X(33439) = reflection of X(i) in X(j) for these (i,j): (627, 22928), (33438, 17)
X(33439) = anticomplement of X(22927)


X(33440) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 11th FERMAT-DAO

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

The reciprocal orthologic center of these triangles is X(22634)

X(33440) lies on these lines: {2,13}, {4,22634}, {99,492}, {298,22601}, {302,6565}, {371,6305}, {485,33360}, {490,33352}, {542,33443}, {641,33358}, {2043,5617}, {2044,9739}, {3068,13876}, {3392,33353}, {5870,6268}, {6304,33368}, {6307,32553}, {6564,22630}, {6770,12256}, {6783,33342}, {11129,32808}, {13103,18586}, {13646,13917}, {13701,30471}, {33354,33444}

X(33440) = reflection of X(i) in X(j) for these (i,j): (616, 6302), (33441, 13)
X(33440) = anticomplement of X(6306)
X(33440) = inverse of X(6302) in the inner-Napoleon circle
X(33440) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 616, 33441), (618, 6302, 2), (5980, 14904, 33441)


X(33441) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 11th FERMAT-DAO

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

The reciprocal orthologic center of these triangles is X(22605)

X(33441) lies on these lines: {2,13}, {4,22605}, {99,491}, {298,22630}, {302,6564}, {372,6301}, {486,33359}, {489,33351}, {542,33442}, {642,33361}, {2043,9738}, {2044,5617}, {3069,13929}, {3391,33350}, {5472,9675}, {5871,6270}, {6300,33367}, {6303,32553}, {6565,22601}, {6770,12257}, {6783,33343}, {11129,32809}, {13103,18587}, {13765,13982}, {13821,30471}, {33356,33445}

X(33441) = reflection of X(i) in X(j) for these (i,j): (616, 6306), (33440, 13)
X(33441) = anticomplement of X(6302)
X(33441) = inverse of X(6306) in the inner-Napoleon circle
X(33441) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 616, 33440), (618, 5463, 33440), (5980, 14904, 33440)


X(33442) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 12th FERMAT-DAO

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

The reciprocal orthologic center of these triangles is X(22635)

X(33442) lies on these lines: {2,14}, {4,22635}, {99,492}, {299,22603}, {303,6565}, {371,6304}, {485,33358}, {490,33350}, {542,33441}, {641,33360}, {2043,9739}, {2044,5613}, {3068,13875}, {3367,33351}, {5870,6269}, {6305,33366}, {6306,32552}, {6564,22632}, {6773,12256}, {6782,33342}, {11128,32808}, {13102,18587}, {13645,13916}, {13701,30472}, {33357,33446}

X(33442) = reflection of X(i) in X(j) for these (i,j): (617, 6303), (33443, 14)
X(33442) = anticomplement of X(6307)
X(33442) = inverse of X(6303) in the outer-Napoleon circle
X(33442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 617, 33443), (15, 6299, 33443), (5981, 14905, 33443)


X(33443) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 12th FERMAT-DAO

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

The reciprocal orthologic center of these triangles is X(22606)

X(33443) lies on these lines: {2,14}, {4,22606}, {99,491}, {299,22632}, {303,6564}, {372,6300}, {486,33361}, {489,33353}, {542,33440}, {642,33359}, {2043,5613}, {2044,9738}, {3069,13928}, {3366,33352}, {5471,9675}, {5871,6271}, {6301,33369}, {6302,32552}, {6565,22603}, {6773,12257}, {6782,33343}, {11128,32809}, {13102,18586}, {13764,13981}, {13821,30472}, {33355,33447}

X(33443) = reflection of X(i) in X(j) for these (i,j): (617, 6307), (33442, 14)
X(33443) = anticomplement of X(6303)
X(33443) = inverse of X(6307) in the outer-Napoleon circle
X(33443) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 617, 33442), (15, 6299, 33442), (5981, 14905, 33442)


X(33444) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 1st HALF-SQUARES

Barycentrics    (2*(2*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)+2*(-2*a^2+b^2+c^2)*S-2*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2 : :
X(33444) = 4*X(6118)-X(33448) = 2*X(6118)+X(33450) = X(33448)+2*X(33450)

The reciprocal orthologic center of these triangles is X(33440)

X(33444) lies on these lines: {2,372}, {3,22634}, {16,31699}, {30,33471}, {62,22631}, {395,13876}, {530,33486}, {639,6307}, {3564,33447}, {6250,18586}, {6306,33426}, {11301,33473}, {13882,16645}, {16966,22638}, {18581,22640}, {22633,22891}, {22636,33416}, {33354,33440}

X(33444) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22634}, {485, 6305}, {33446, 33450}
X(33444) = reflection of X(33448) in X(33446)
X(33444) = complement of X(6304)
X(33444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 641, 33446), (2, 6305, 6118), (6118, 33450, 33448)


X(33445) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 2nd HALF-SQUARES

Barycentrics    (2*(2*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)+2*(2*a^2-b^2-c^2)*S-2*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2 : :
X(33445) = X(33449)+2*X(33451)

The reciprocal orthologic center of these triangles is X(33441)

X(33445) lies on these lines: {2,371}, {3,22605}, {16,31697}, {30,33473}, {62,22602}, {395,13929}, {530,33488}, {640,6303}, {3564,33446}, {6251,18587}, {6302,33424}, {11301,33471}, {13934,16645}, {16966,22609}, {18581,22611}, {22604,22891}, {22607,33416}, {33356,33441}

X(33445) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22605}, {486, 6301}, {33447, 33451}
X(33445) = reflection of X(33449) in X(33447)
X(33445) = complement of X(6300)
X(33445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 642, 33447), (2, 6301, 6119), (486, 642, 33451)


X(33446) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 1st HALF-SQUARES

Barycentrics    (2*(2*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)+2*(2*a^2-b^2-c^2)*S+2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2 : :
X(33446) = 2*X(6118)+X(33448) = 4*X(6118)-X(33450) = 2*X(33448)+X(33450)

The reciprocal orthologic center of these triangles is X(33442)

X(33446) lies on these lines: {2,372}, {3,22635}, {15,31700}, {30,33470}, {61,22633}, {396,13875}, {531,33487}, {639,6306}, {3564,33445}, {6250,18587}, {6307,33425}, {11302,33472}, {13882,16644}, {16967,22639}, {18582,22641}, {22631,22846}, {22637,33417}, {33357,33442}

X(33446) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22635}, {485, 6304}, {33444, 33448}
X(33446) = reflection of X(33450) in X(33444)
X(33446) = complement of X(6305)
X(33446) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 641, 33444), (2, 6304, 6118), (485, 641, 33448)


X(33447) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 2nd HALF-SQUARES

Barycentrics    (2*(2*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)+(-4*a^2+2*b^2+2*c^2)*S+2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2 : :
X(33447) = 2*X(33449)+X(33451)

The reciprocal orthologic center of these triangles is X(33443)

X(33447) lies on these lines: {2,371}, {3,22606}, {15,31698}, {30,33472}, {61,22604}, {396,13928}, {531,33489}, {640,6302}, {3564,33444}, {6251,18586}, {6303,33427}, {11302,33470}, {13934,16644}, {16967,22610}, {18582,22612}, {22602,22846}, {22608,33417}, {33355,33443}

X(33447) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22606}, {486, 6300}, {33445, 33449}
X(33447) = reflection of X(33451) in X(33445)
X(33447) = complement of X(6301)
X(33447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 642, 33445), (2, 6300, 6119), (6119, 33449, 33451)


X(33448) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 1st HALF-SQUARES

Barycentrics    (2*(2*a^2-b^2-c^2)*S+2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*sqrt(3)+2*(2*a^2+b^2+c^2)*S-2*a^4+5*(b^2+c^2)*a^2-3*(b^2-c^2)^2 : :
X(33448) = X(488)-3*X(6304) = 4*X(6118)-3*X(33444) = 2*X(6118)-3*X(33446) = 3*X(33444)-2*X(33450) = 3*X(33446)-X(33450)

The reciprocal orthologic center of these triangles is X(33436)

X(33448) lies on these lines: {2,372}, {303,33361}, {395,22880}, {397,33392}, {533,33470}, {3564,33451}, {22600,22641}, {22625,22797}, {22883,33394}, {33358,33436}

X(33448) = midpoint of X(485) and X(22629)
X(33448) = reflection of X(33444) in X(33446)
X(33448) = complement of X(22627)
X(33448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (488, 641, 33450), (6118, 33450, 33444), (33446, 33450, 6118)


X(33449) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 2nd HALF-SQUARES

Barycentrics    (2*(2*a^2-b^2-c^2)*S-2*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)+(-4*a^2-2*b^2-2*c^2)*S-2*a^4+5*(b^2+c^2)*a^2-3*(b^2-c^2)^2 : :
X(33449) = X(487)-3*X(6300) = 3*X(33445)-2*X(33451) = 3*X(33447)-X(33451)

The reciprocal orthologic center of these triangles is X(33437)

X(33449) lies on these lines: {2,371}, {303,33358}, {395,22881}, {397,33394}, {533,33472}, {3564,33450}, {22596,22797}, {22612,22629}, {22882,33392}, {33361,33437}

X(33449) = midpoint of X(486) and X(22600)
X(33449) = reflection of X(33445) in X(33447)
X(33449) = complement of X(22598)
X(33449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (486, 642, 33447), (487, 642, 33451), (33447, 33451, 6119)


X(33450) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 1st HALF-SQUARES

Barycentrics    (2*(2*a^2-b^2-c^2)*S+2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*sqrt(3)+(-4*a^2-2*b^2-2*c^2)*S+2*a^4-5*(b^2+c^2)*a^2+3*(b^2-c^2)^2 : :
X(33450) = X(488)-3*X(6305) = 2*X(6118)-3*X(33444) = 4*X(6118)-3*X(33446) = 3*X(33444)-X(33448) = 3*X(33446)-2*X(33448)

The reciprocal orthologic center of these triangles is X(33438)

X(33450) lies on these lines: {2,372}, {302,33359}, {396,22925}, {398,33395}, {532,33471}, {3564,33449}, {22598,22640}, {22625,22796}, {22928,33393}, {33360,33438}

X(33450) = midpoint of X(485) and X(22627)
X(33450) = reflection of X(i) in X(j) for these (i,j): (33446, 33444), (33448, 6118)
X(33450) = complement of X(22629)
X(33450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (485, 641, 33444), (488, 641, 33448), (33444, 33448, 6118)


X(33451) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 2nd HALF-SQUARES

Barycentrics    (2*(2*a^2-b^2-c^2)*S-2*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)+2*(2*a^2+b^2+c^2)*S+2*a^4-5*(b^2+c^2)*a^2+3*(b^2-c^2)^2 : :
X(33451) = X(487)-3*X(6301) = 3*X(33445)-X(33449) = 3*X(33447)-2*X(33449)

The reciprocal orthologic center of these triangles is X(33439)

X(33451) lies on these lines: {2,371}, {302,33360}, {396,22926}, {398,33393}, {532,33473}, {3564,33448}, {22596,22796}, {22611,22627}, {22927,33395}, {33359,33439}

X(33451) = midpoint of X(486) and X(22598)
X(33451) = reflection of X(33447) in X(33445)
X(33451) = complement of X(22600)
X(33451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (487, 642, 33449), (6119, 33449, 33447), (33445, 33449, 6119)


X(33452) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 1st NEUBERG

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

The reciprocal orthologic center of these triangles is X(6312)

X(33452) lies on these lines: {2,39}, {371,33346}, {511,5870}, {698,3071}, {732,33455}, {1587,6273}, {3068,13877}, {6312,33370}, {6423,7754}, {6561,33454}, {6564,22642}, {8992,13647}, {12251,12256}

X(33452) = reflection of X(i) in X(j) for these (i,j): (194, 6318), (33453, 76)
X(33452) = anticomplement of X(6314)


X(33453) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 1st NEUBERG

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

The reciprocal orthologic center of these triangles is X(6316)

X(33453) lies on these lines: {2,39}, {372,33347}, {511,5871}, {698,3070}, {732,33454}, {1588,6272}, {3069,13930}, {6316,33371}, {6424,7754}, {6560,33455}, {6565,22613}, {12251,12257}, {13766,13983}

X(33453) = reflection of X(i) in X(j) for these (i,j): (194, 6314), (33452, 76)
X(33453) = anticomplement of X(6318)


X(33454) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(6311)

X(33454) lies on these lines: {2,32}, {371,33348}, {732,33453}, {3068,13878}, {5870,6274}, {6311,33372}, {6561,33452}, {6564,22643}, {8993,13648}, {12252,12256}

X(33454) = reflection of X(i) in X(j) for these (i,j): (2896, 6317), (33455, 83)
X(33454) = anticomplement of X(6313)
X(33454) = {X(315), X(18769)}-harmonic conjugate of X(33455)


X(33455) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(6315)

X(33455) lies on these lines: {2,32}, {372,33349}, {732,33452}, {3069,13931}, {5871,6275}, {6315,33373}, {6560,33453}, {6565,22614}, {12252,12257}, {13767,13984}

X(33455) = reflection of X(i) in X(j) for these (i,j): (2896, 6313), (33454, 83)
X(33455) = anticomplement of X(6317)
X(33455) = {X(315), X(18769)}-harmonic conjugate of X(33454)


X(33456) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 1st TRI-SQUARES-CENTRAL

Barycentrics    (5*a^2-b^2-c^2)*S+5*a^4-(b^2+c^2)*a^2-4*(b^2-c^2)^2 : :
X(33456) = 5*X(2)-4*X(13701) = X(488)-4*X(23251) = 5*X(488)-8*X(23311) = 4*X(1327)-X(13678) = 5*X(1327)-2*X(13701) = 3*X(1327)-X(13712) = 3*X(3543)+2*X(13690) = 3*X(3545)-2*X(13692) = 3*X(3839)-4*X(13687) = 3*X(10304)-2*X(13666) = X(12222)+2*X(22644) = X(13674)+2*X(13713) = 5*X(13678)-8*X(13701) = 3*X(13678)-4*X(13712) = 6*X(13701)-5*X(13712) = 5*X(23251)-2*X(23311)

The reciprocal orthologic center of these triangles is X(13711)

X(33456) lies on these lines: {2,1327}, {30,12257}, {485,26617}, {488,23251}, {519,13679}, {1991,13798}, {1992,3830}, {3069,13932}, {3543,5871}, {3545,13692}, {3839,13687}, {5860,23334}, {6565,22616}, {7714,13668}, {10304,13666}, {10385,13699}, {10723,33431}, {10840,33345}, {11001,13637}, {12222,22644}, {13639,15640}, {13757,22806}, {13769,13988}, {13831,32788}, {14241,26615}, {14244,33371}, {23253,26288}, {23269,26619}, {32811,32815}

X(33456) = reflection of X(i) in X(j) for these (i,j): (2, 1327), (13678, 2), (26617, 485)
X(33456) = anticomplement of X(13712)
X(33456) = {X(1992), X(3830)}-harmonic conjugate of X(33457)


X(33457) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    -(5*a^2-b^2-c^2)*S+5*a^4-(b^2+c^2)*a^2-4*(b^2-c^2)^2 : :
X(33457) = 5*X(2)-4*X(13821) = X(487)-4*X(23261) = 5*X(487)-8*X(23312) = 4*X(1328)-X(13798) = 5*X(1328)-2*X(13821) = 3*X(1328)-X(13835) = 3*X(3543)+2*X(13811) = 3*X(3545)-2*X(13812) = 3*X(3839)-4*X(13807) = 3*X(10304)-2*X(13786) = X(12221)+2*X(22615) = X(13794)+2*X(13836) = 5*X(13798)-8*X(13821) = 3*X(13798)-4*X(13835) = 6*X(13821)-5*X(13835) = 5*X(23261)-2*X(23312)

The reciprocal orthologic center of these triangles is X(13834)

X(33457) lies on these lines: {2,1328}, {30,12256}, {486,26618}, {487,23261}, {519,13799}, {591,13678}, {1992,3830}, {3068,13850}, {3543,5870}, {3545,13812}, {3839,13807}, {5861,23334}, {6564,22645}, {7714,13788}, {10304,13786}, {10385,13819}, {10723,33430}, {10839,33344}, {11001,13757}, {12221,22615}, {13637,22807}, {13759,15640}, {13832,32787}, {13833,13848}, {14226,26616}, {14229,33370}, {23263,26289}, {23275,26620}, {32810,32815}

X(33457) = reflection of X(i) in X(j) for these (i,j): (2, 1328), (13798, 2), (26618, 486)
X(33457) = anticomplement of X(13835)
X(33457) = {X(1992), X(3830)}-harmonic conjugate of X(33456)


X(33458) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO ANTI-ARTZT

Barycentrics    (2*a^2-b^2-c^2)*sqrt(3)+4*S : :
X(33458) = 5*X(2)-X(5862) = 3*X(2)+X(5863) = 5*X(2)-3*X(9761) = X(2)-3*X(9763) = 4*X(2)-3*X(33474) = 2*X(2)-3*X(33475) = X(3830)-3*X(22492) = 4*X(11812)-3*X(13084) = 2*X(12100)-3*X(13083) = 5*X(19709)-3*X(22491)

The reciprocal orthologic center of these triangles is X(22487)

X(33458) lies on these lines: {2,6}, {5,533}, {61,21360}, {62,33386}, {99,33376}, {397,628}, {530,8703}, {531,3845}, {532,549}, {543,32552}, {617,5318}, {634,16772}, {1353,6774}, {3642,11542}, {3830,22492}, {5464,22900}, {5480,5613}, {6778,22568}, {7768,8259}, {9117,14537}, {11118,11139}, {11812,13084}, {12100,13083}, {14711,25183}, {19709,22491}, {22487,33374}, {22665,33378}, {32521,33483}

X(33458) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 5859}, {5858, 5863}, {6778, 22568}
X(33458) = reflection of X(i) in X(j) for these (i,j): (33459, 2), (33474, 33475), (33475, 9763)
X(33458) = complement of X(5858)
X(33458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5862, 9761), (299, 396, 141), (5858, 5859, 5863)


X(33459) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO ANTI-ARTZT

Barycentrics    (2*a^2-b^2-c^2)*sqrt(3)-4*S : :
X(33459) = 3*X(2)+X(5862) = 5*X(2)-X(5863) = X(2)-3*X(9761) = 5*X(2)-3*X(9763) = 2*X(2)-3*X(33474) = 4*X(2)-3*X(33475) = X(3830)-3*X(22491) = 4*X(11812)-3*X(13083) = 2*X(12100)-3*X(13084) = 5*X(19709)-3*X(22492)

The reciprocal orthologic center of these triangles is X(22488)

X(33459) lies on these lines: {2,6}, {5,532}, {61,33387}, {62,21359}, {99,33377}, {398,627}, {530,3845}, {531,8703}, {533,549}, {543,32553}, {616,5321}, {633,16773}, {1353,6771}, {3643,11543}, {3830,22491}, {5463,22856}, {5480,5617}, {6777,22570}, {7768,8260}, {9115,14537}, {11812,13083}, {12100,13084}, {14711,25187}, {19709,22492}, {22488,33375}, {22666,33379}, {32521,33482}

X(33459) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 5858}, {5859, 5862}, {6777, 22570}
X(33459) = reflection of X(i) in X(j) for these (i,j): (33458, 2), (33474, 9761), (33475, 33474)
X(33459) = complement of X(5859)
X(33459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5862, 5859), (5858, 5859, 5862), (5858, 9761, 2)


X(33460) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO ANTI-MCCAY

Barycentrics    (a^2+b^2+c^2)*(2*a^4-2*(b^2+c^2)*a^2-b^4+4*b^2*c^2-c^4)*sqrt(3)+2*S*(2*a^4-2*(b^2+c^2)*a^2+5*b^4-8*b^2*c^2+5*c^4) : :
X(33460) = 4*X(5461)-3*X(33476) = 2*X(5461)-3*X(33477) = X(8591)-3*X(9886) = 2*X(33461)-3*X(33476) = X(33461)-3*X(33477)

The reciprocal orthologic center of these triangles is X(22567)

X(33460) lies on these lines: {2,99}, {530,22566}, {533,25559}, {542,5872}, {5459,5969}, {5460,33484}, {5470,11305}, {5858,6778}, {8176,16808}, {9117,22567}, {14645,22580}, {15561,33378}, {22866,33384}

X(33460) = midpoint of X(i) and X(j) for these lines: {i,j}: {671, 22570}, {5858, 6778}
X(33460) = reflection of X(i) in X(j) for these (i,j): (33461, 5461), (33476, 33477)
X(33460) = complement of X(22568)
X(33460) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5461, 33461, 33476), (7617, 8591, 33461), (33461, 33477, 5461)


X(33461) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO ANTI-MCCAY

Barycentrics    (a^2+b^2+c^2)*(2*a^4-2*(b^2+c^2)*a^2-b^4+4*b^2*c^2-c^4)*sqrt(3)-2*S*(2*a^4-2*(b^2+c^2)*a^2+5*b^4-8*b^2*c^2+5*c^4) : :
X(33461) = 2*X(5461)-3*X(33476) = 4*X(5461)-3*X(33477) = X(8591)-3*X(9885) = X(33460)-3*X(33476) = 2*X(33460)-3*X(33477)

The reciprocal orthologic center of these triangles is X(22569)

X(33461) lies on these lines: {2,99}, {531,22566}, {532,25560}, {542,5873}, {5459,33485}, {5460,5969}, {5469,11306}, {5859,6777}, {8176,16809}, {9115,22569}, {14645,22579}, {15561,33379}, {22911,33385}

X(33461) = midpoint of X(i) and X(j) for these lines: {i,j}: {671, 22568}, {5859, 6777}
X(33461) = reflection of X(i) in X(j) for these (i,j): (33460, 5461), (33477, 33476)
X(33461) = complement of X(22570)
X(33461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5461, 33460, 33477), (7617, 8591, 33460), (33460, 33476, 5461)


X(33462) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 1st BROCARD-REFLECTED

Barycentrics    -6*S*a^2*((b^2+c^2)*a^2-b^4-c^4)*sqrt(3)+3*(b^2+c^2)*a^6-2*(2*b^2-b*c+2*c^2)*(2*b^2+b*c+2*c^2)*a^4+(b^2+c^2)*(5*b^4-16*b^2*c^2+5*c^4)*a^2+4*(b^2-c^2)^2*b^2*c^2 : :
X(33462) = 3*X(3107)-X(32519) = X(6194)-3*X(22715) = 2*X(33463)-3*X(33478) = X(33463)-3*X(33479)

The reciprocal orthologic center of these triangles is X(22683)

X(33462) lies on these lines: {2,51}, {39,22701}, {303,5982}, {2782,32907}, {3105,7697}, {3107,32519}, {3972,21401}, {11300,33376}, {13349,33388}, {22509,23025}, {22681,22797}, {22683,33380}

X(33462) = midpoint of X(i) and X(j) for these lines: {i,j}: {262, 22686}, {3105, 7697}
X(33462) = reflection of X(33478) in X(33479)
X(33462) = complement of X(22684)
X(33462) = {X(6194), X(11261)}-harmonic conjugate of X(33463)


X(33463) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 1st BROCARD-REFLECTED

Barycentrics    6*S*a^2*((b^2+c^2)*a^2-b^4-c^4)*sqrt(3)+3*(b^2+c^2)*a^6-2*(2*b^2-b*c+2*c^2)*(2*b^2+b*c+2*c^2)*a^4+(b^2+c^2)*(5*b^4-16*b^2*c^2+5*c^4)*a^2+4*(b^2-c^2)^2*b^2*c^2 : :
X(33463) = 3*X(3106)-X(32519) = X(6194)-3*X(22714) = X(33462)-3*X(33478) = 2*X(33462)-3*X(33479)

The reciprocal orthologic center of these triangles is X(22685)

X(33463) lies on these lines: {2,51}, {39,22702}, {302,5983}, {2782,32909}, {3104,7697}, {3106,32519}, {3972,21402}, {11299,33377}, {13350,33389}, {22507,23019}, {22681,22796}, {22685,33381}

X(33463) = midpoint of X(i) and X(j) for these lines: {i,j}: {262, 22684}, {3104, 7697}
X(33463) = reflection of X(33479) in X(33478)
X(33463) = complement of X(22686)
X(33463) = {X(6194), X(11261)}-harmonic conjugate of X(33462)


X(33464) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO INNER-FERMAT

Barycentrics    2*S*(4*a^2-c^2-b^2)*sqrt(3)-5*(b^2+c^2)*a^2+5*b^4-10*b^2*c^2+5*c^4 : :
X(33464) = 3*X(2)-5*X(18) = 9*X(2)-5*X(628) = 6*X(2)-5*X(630) = 9*X(2)-10*X(6674) = 3*X(2)+5*X(22114) = 3*X(18)-X(628) = 3*X(18)-2*X(6674) = 5*X(18)-X(22845) = X(382)-5*X(16628) = 6*X(546)-5*X(22794) = 4*X(546)-5*X(22831) = 2*X(628)-3*X(630) = X(628)+3*X(22114) = 5*X(628)-3*X(22845) = 3*X(630)-4*X(6674) = X(630)+2*X(22114) = 5*X(630)-2*X(22845) = 2*X(6674)+3*X(22114) = 10*X(6674)-3*X(22845) = 2*X(22794)-3*X(22831)

The reciprocal orthologic center of these triangles is X(22844)

X(33464) lies on these lines: {2,18}, {5,3629}, {14,22844}, {302,33387}, {382,5615}, {396,12815}, {398,618}, {531,16773}, {546,5478}, {621,3411}, {623,6329}, {636,3631}, {3528,22843}, {3529,22531}, {3530,13350}, {3632,22651}, {3636,11740}, {3851,16627}, {5459,20583}, {5872,7685}, {10301,22481}, {11008,18581}, {11308,16961}, {20057,22867}, {20850,22656}, {22853,26339}, {22854,26340}

X(33464) = midpoint of X(18) and X(22114)
X(33464) = reflection of X(i) in X(j) for these (i,j): (628, 6674), (630, 18)
X(33464) = complement of X(22845)
X(33464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 628, 6674), (18, 22845, 2), (628, 6674, 630)


X(33465) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO OUTER-FERMAT

Barycentrics    -2*S*(4*a^2-c^2-b^2)*sqrt(3)-5*(b^2+c^2)*a^2+5*b^4-10*b^2*c^2+5*c^4 : :
X(33465) = 3*X(2)-5*X(17) = 9*X(2)-5*X(627) = 6*X(2)-5*X(629) = 9*X(2)-10*X(6673) = 3*X(2)+5*X(22113) = 3*X(17)-X(627) = 3*X(17)-2*X(6673) = 5*X(17)-X(22844) = X(382)-5*X(16629) = 6*X(546)-5*X(22795) = 4*X(546)-5*X(22832) = 2*X(627)-3*X(629) = X(627)+3*X(22113) = 5*X(627)-3*X(22844) = 3*X(629)-4*X(6673) = X(629)+2*X(22113) = 5*X(629)-2*X(22844) = 2*X(6673)+3*X(22113) = 10*X(6673)-3*X(22844) = 2*X(22795)-3*X(22832)

The reciprocal orthologic center of these triangles is X(22845)

X(33465) lies on these lines: {2,17}, {5,3629}, {13,22845}, {303,33386}, {382,5611}, {395,12815}, {397,619}, {530,16772}, {546,5479}, {622,3412}, {624,6329}, {635,3631}, {3529,22532}, {3632,22652}, {3851,16626}, {5873,7684}, {10301,22482}, {20850,22657}, {22898,26339}, {22899,26340}

X(33465) = midpoint of X(17) and X(22113)
X(33465) = reflection of X(i) in X(j) for these (i,j): (627, 6673), (629, 17)
X(33465) = complement of X(22844)
X(33465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17, 627, 6673), (17, 22844, 2), (627, 6673, 629)


X(33466) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 1st NEUBERG

Barycentrics    (a^2+b^2+c^2)*((b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)+2*((b^2+c^2)*a^2+2*b^2*c^2)*S : :
X(33466) = X(194)-3*X(6581) = 4*X(3934)-3*X(33482) = 2*X(3934)-3*X(33483) = 3*X(6294)-5*X(7786)

The reciprocal orthologic center of these triangles is X(22869)

X(33466) lies on these lines: {2,39}, {15,7751}, {511,5873}, {622,7759}, {698,11542}, {732,33469}, {5980,7780}, {6114,7764}, {14881,22797}, {22513,22915}, {22869,33388}

X(33466) = midpoint of X(76) and X(22913)
X(33466) = reflection of X(i) in X(j) for these (i,j): (33467, 3934), (33482, 33483)
X(33466) = complement of X(22868)
X(33466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (194, 8149, 33467), (3934, 33467, 33482), (33467, 33483, 3934)


X(33467) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 1st NEUBERG

Barycentrics    -(a^2+b^2+c^2)*((b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)+2*((b^2+c^2)*a^2+2*b^2*c^2)*S : :
X(33467) = X(194)-3*X(6294) = 2*X(3934)-3*X(33482) = 4*X(3934)-3*X(33483) = 3*X(6581)-5*X(7786)

The reciprocal orthologic center of these triangles is X(22914)

X(33467) lies on these lines: {2,39}, {16,7751}, {511,5872}, {621,7759}, {698,11543}, {732,33468}, {5981,7780}, {6115,7764}, {14881,22796}, {22512,22870}, {22914,33389}

X(33467) = midpoint of X(76) and X(22868)
X(33467) = reflection of X(i) in X(j) for these (i,j): (33466, 3934), (33483, 33482)
X(33467) = complement of X(22913)
X(33467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (194, 8149, 33466), (3934, 33466, 33483), (33466, 33482, 3934)


X(33468) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 2nd NEUBERG

Barycentrics    (a^2+b^2+c^2)*(2*a^4-b^4-c^4)*sqrt(3)+2*S*(2*a^4+4*(b^2+c^2)*a^2+b^4+4*b^2*c^2+c^4) : :
X(33468) = X(2896)-3*X(6296) = 3*X(6297)-5*X(31268) = 4*X(6704)-3*X(33484) = 2*X(6704)-3*X(33485)

The reciprocal orthologic center of these triangles is X(22871)

X(33468) lies on these lines: {2,32}, {732,33467}, {22708,22913}, {22797,22803}, {22871,33390}

X(33468) = midpoint of X(83) and X(22915)
X(33468) = reflection of X(i) in X(j) for these (i,j): (33469, 6704), (33484, 33485)
X(33468) = complement of X(22870)
X(33468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2896, 8150, 33469), (6704, 33469, 33484), (33469, 33485, 6704)


X(33469) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 2nd NEUBERG

Barycentrics    -(a^2+b^2+c^2)*(2*a^4-b^4-c^4)*sqrt(3)+2*S*(2*a^4+4*(b^2+c^2)*a^2+b^4+4*b^2*c^2+c^4) : :
X(33469) = X(2896)-3*X(6297) = 3*X(6296)-5*X(31268) = 2*X(6704)-3*X(33484) = 4*X(6704)-3*X(33485)

The reciprocal orthologic center of these triangles is X(22916)

X(33469) lies on these lines: {2,32}, {732,33466}, {22707,22868}, {22796,22803}, {22916,33391}

X(33469) = midpoint of X(83) and X(22870)
X(33469) = reflection of X(i) in X(j) for these (i,j): (33468, 6704), (33485, 33484)
X(33469) = complement of X(22915)
X(33469) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2896, 8150, 33468), (6704, 33468, 33485), (33468, 33484, 6704)


X(33470) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    2*(2*a^2+2*b^2+2*c^2-(b^2+c^2)*sqrt(3))*(5*sqrt(3)+6)*S+26*a^4-7*(b^2+c^2)*a^2+18*((b^2+c^2)*a^2-(b^2-c^2)^2)*sqrt(3)-19*(b^2-c^2)^2 : :
X(33470) = X(13678)-3*X(13706) = 2*X(33471)-3*X(33486) = X(33471)-3*X(33487)

The reciprocal orthologic center of these triangles is X(22873)

X(33470) lies on these lines: {2,1327}, {30,33446}, {533,33448}, {11300,33361}, {11302,33447}, {13687,18587}, {22797,22806}, {23026,32419}

X(33470) = midpoint of X(1327) and X(22917)
X(33470) = reflection of X(33486) in X(33487)
X(33470) = complement of X(22872)
X(33470) = {X(2), X(13701)}-harmonic conjugate of X(33471)


X(33471) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    2*((b^2+c^2)*sqrt(3)+2*a^2+2*b^2+2*c^2)*(-6+5*sqrt(3))*S+(18*(b^2+c^2)*a^2-18*b^4+36*b^2*c^2-18*c^4)*sqrt(3)-26*a^4+7*(b^2+c^2)*a^2+19*(b^2-c^2)^2 : :
X(33471) = X(13678)-3*X(13704) = X(33470)-3*X(33486) = 2*X(33470)-3*X(33487)

The reciprocal orthologic center of these triangles is X(22918)

X(33471) lies on these lines: {2,1327}, {30,33444}, {532,33450}, {11299,33359}, {13687,18586}, {22796,22806}, {23020,32419}

X(33471) = midpoint of X(1327) and X(22872)
X(33471) = reflection of X(33487) in X(33486)
X(33471) = complement of X(22917)
X(33471) = {X(2), X(13701)}-harmonic conjugate of X(33470)


X(33472) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    2*((b^2+c^2)*sqrt(3)+2*a^2+2*b^2+2*c^2)*(-6+5*sqrt(3))*S+26*a^4-7*(b^2+c^2)*a^2+(-18*(b^2+c^2)*a^2+18*b^4-36*b^2*c^2+18*c^4)*sqrt(3)-19*(b^2-c^2)^2 : :
X(33472) = X(13798)-3*X(13826) = 2*X(33473)-3*X(33488) = X(33473)-3*X(33489)

The reciprocal orthologic center of these triangles is X(22875)

X(33472) lies on these lines: {2,1328}, {30,33447}, {533,33449}, {11300,33358}, {11302,33446}, {13807,18586}, {22797,22807}, {23027,32421}

X(33472) = midpoint of X(1328) and X(22919)
X(33472) = reflection of X(33488) in X(33489)
X(33472) = complement of X(22874)
X(33472) = {X(2), X(13821)}-harmonic conjugate of X(33473)


X(33473) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    2*((-b^2-c^2)*sqrt(3)+2*a^2+2*b^2+2*c^2)*(6+5*sqrt(3))*S+(-18*(b^2+c^2)*a^2+18*b^4-36*b^2*c^2+18*c^4)*sqrt(3)-26*a^4+7*(b^2+c^2)*a^2+19*(b^2-c^2)^2 : :
X(33473) = X(13798)-3*X(13824) = X(33472)-3*X(33488) = 2*X(33472)-3*X(33489)

The reciprocal orthologic center of these triangles is X(22920)

X(33473) lies on these lines: {2,1328}, {30,33445}, {532,33451}, {11299,33360}, {11301,33444}, {13807,18587}, {22796,22807}, {23021,32421}

X(33473) = midpoint of X(1328) and X(22874)
X(33473) = reflection of X(33489) in X(33488)
X(33473) = complement of X(22919)
X(33473) = {X(2), X(13821)}-harmonic conjugate of X(33472)


X(33474) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO ANTI-ARTZT

Barycentrics    4*sqrt(3)*S+b^2+c^2-2*a^2 : :
X(33474) = 5*X(2)+X(5858) = 7*X(2)-X(5859) = 11*X(2)+X(5862) = 13*X(2)-X(5863) = 4*X(2)-X(33458) = 2*X(2)+X(33459) = 3*X(5055)-X(22492)

The reciprocal orthologic center of these triangles is X(12155)

X(33474) lies on these lines: {2,6}, {3,22491}, {5,530}, {14,9886}, {16,31693}, {18,9885}, {30,9736}, {62,22489}, {140,13083}, {531,549}, {532,15699}, {533,11539}, {543,618}, {619,1153}, {623,3849}, {3642,5569}, {3643,7617}, {5055,22492}, {5242,17243}, {5463,20112}, {5969,22692}, {6114,9830}, {6670,16509}, {7603,9115}, {7622,11543}, {8260,33249}, {8594,33402}, {9166,14904}, {9762,33406}, {10617,26613}, {11295,18581}, {11303,16773}, {11304,33412}, {11307,33404}, {12155,33398}, {15810,22848}, {16241,22496}, {16966,22495}, {22490,22891}, {22493,33416}

X(33474) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 9761}, {3, 22491}, {14, 9886}, {33459, 33475}
X(33474) = reflection of X(i) in X(j) for these (i,j): (13083, 140), (33458, 33475), (33459, 9761), (33475, 2), (33476, 6670)
X(33474) = complement of X(9763)
X(33474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 33459, 33458), (591, 1991, 5862), (7610, 20582, 33475)


X(33475) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO ANTI-ARTZT

Barycentrics    -4*sqrt(3)*S+b^2+c^2-2*a^2 : :
X(33475) = 7*X(2)-X(5858) = 5*X(2)+X(5859) = 13*X(2)-X(5862) = 11*X(2)+X(5863) = 2*X(2)+X(33458) = 4*X(2)-X(33459) = 3*X(5055)-X(22491)

The reciprocal orthologic center of these triangles is X(12154)

X(33475) lies on these lines: {2,6}, {3,22492}, {5,531}, {13,9885}, {15,31694}, {17,9886}, {30,9735}, {61,22490}, {140,13084}, {530,549}, {532,11539}, {533,15699}, {543,619}, {618,1153}, {624,3849}, {3642,7617}, {3643,5569}, {5055,22491}, {5243,17243}, {5464,20112}, {5969,22691}, {6115,9830}, {6669,16509}, {7603,9117}, {7622,11542}, {8259,33249}, {8595,33403}, {9166,14905}, {9760,33407}, {10616,26613}, {11296,18582}, {11303,33413}, {11304,16772}, {11308,33405}, {12154,33399}, {15810,22892}, {16242,22495}, {16967,22496}, {22489,22846}, {22494,33417}

X(33475) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 9763}, {3, 22492}, {13, 9885}, {33458, 33474}
X(33475) = reflection of X(i) in X(j) for these (i,j): (13084, 140), (33458, 9763), (33459, 33474), (33474, 2), (33477, 6669)
X(33475) = complement of X(9761)
X(33475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (141, 15597, 33474), (591, 1991, 5863), (7610, 20582, 33474)


X(33476) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO ANTI-MCCAY

Barycentrics    2*S*(2*a^4-2*(b^2+c^2)*a^2+5*b^4-8*b^2*c^2+5*c^4)*sqrt(3)-(a^2+b^2+c^2)*(2*a^4-2*(b^2+c^2)*a^2-b^4+4*b^2*c^2-c^4) : :
X(33476) = 3*X(5055)-X(9760) = 4*X(5461)-X(33460) = 2*X(5461)+X(33461) = X(9761)-3*X(22490) = X(33460)+2*X(33461)

The reciprocal orthologic center of these triangles is X(8595)

X(33476) lies on these lines: {2,99}, {3,22575}, {5,531}, {14,8176}, {16,31695}, {18,9761}, {62,22571}, {395,22573}, {524,624}, {530,6774}, {538,22692}, {3849,6109}, {5055,9760}, {5459,9830}, {5464,16966}, {5569,11295}, {6670,16509}, {7775,33412}, {8595,33402}, {9762,11632}, {11305,33414}, {11623,22492}, {12154,16644}, {13084,20398}, {14762,22893}, {18581,22579}, {22572,22891}, {22577,33416}, {31709,32479}

X(33476) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22575}, {14, 9763}, {671, 9885}, {9762, 11632}, {33461, 33477}
X(33476) = reflection of X(i) in X(j) for these (i,j): (33460, 33477), (33474, 6670), (33477, 5461)
X(33476) = complement of X(9886)
X(33476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 9885, 7619), (5461, 33461, 33460), (7615, 7844, 33477)


X(33477) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO ANTI-MCCAY

Barycentrics    -2*S*(2*a^4-2*(b^2+c^2)*a^2+5*b^4-8*b^2*c^2+5*c^4)*sqrt(3)-(a^2+b^2+c^2)*(2*a^4-2*(b^2+c^2)*a^2-b^4+4*b^2*c^2-c^4) : :
X(33477) = 3*X(5055)-X(9762) = 2*X(5461)+X(33460) = 4*X(5461)-X(33461) = X(9763)-3*X(22489) = 2*X(33460)+X(33461)

The reciprocal orthologic center of these triangles is X(8594)

X(33477) lies on these lines: {2,99}, {3,22576}, {5,530}, {13,8176}, {15,31696}, {17,9763}, {61,22572}, {396,22574}, {524,623}, {531,6771}, {538,22691}, {3849,6108}, {5055,9762}, {5460,9830}, {5463,16967}, {5569,11296}, {6669,16509}, {7775,33413}, {8594,33403}, {9760,11632}, {11306,33415}, {11623,22491}, {12155,16645}, {13083,20398}, {14762,22847}, {18582,22580}, {22571,22846}, {22578,33417}, {31710,32479}

X(33477) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22576}, {13, 9761}, {671, 9886}, {9760, 11632}, {33460, 33476}
X(33477) = reflection of X(i) in X(j) for these (i,j): (33461, 33476), (33475, 6669), (33476, 5461)
X(33477) = complement of X(9885)
X(33477) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 7617, 33476), (5461, 33460, 33461), (7615, 7844, 33476)


X(33478) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 1st BROCARD-REFLECTED

Barycentrics    3*(b^2+c^2)*a^6-2*((2*b^2+2*c^2)^2-b^2*c^2)*a^4+(b^2+c^2)*(5*b^4-16*b^2*c^2+5*c^4)*a^2+4*(b^2-c^2)^2*b^2*c^2+2*sqrt(3)*S*a^2*((b^2+c^2)*a^2-b^4-c^4) : :
X(33478) = 5*X(1656)+X(3104) = X(33462)+2*X(33463)

The reciprocal orthologic center of these triangles is X(22687)

X(33478) lies on these lines: {2,51}, {3,22693}, {16,31701}, {18,39}, {62,22688}, {395,22691}, {629,11272}, {1656,3104}, {2782,5460}, {3106,7697}, {3107,16645}, {3934,33410}, {6114,24206}, {6248,33412}, {6683,33418}, {7804,13349}, {16966,22701}, {18581,22707}, {22687,33408}, {22695,33416}, {25167,32447}, {33388,33420}

X(33478) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22693}, {262, 22714}, {3106, 7697}, {25167, 32447}, {33463, 33479}
X(33478) = reflection of X(33462) in X(33479)
X(33478) = complement of X(22715)
X(33478) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11261, 33479), (2, 22714, 32149)


X(33479) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 1st BROCARD-REFLECTED

Barycentrics    3*(b^2+c^2)*a^6-2*((2*b^2+2*c^2)^2-b^2*c^2)*a^4+(b^2+c^2)*(5*b^4-16*b^2*c^2+5*c^4)*a^2+4*(b^2-c^2)^2*b^2*c^2-2*sqrt(3)*S*a^2*((b^2+c^2)*a^2-b^4-c^4) : :
X(33479) = 5*X(1656)+X(3105) = 2*X(33462)+X(33463)

The reciprocal orthologic center of these triangles is X(22689)

X(33479) lies on these lines: {2,51}, {3,22694}, {15,31702}, {17,39}, {61,22690}, {396,22692}, {630,11272}, {1656,3105}, {2782,5459}, {3106,16644}, {3107,7697}, {3934,33411}, {6115,24206}, {6248,33413}, {6683,33419}, {7804,13350}, {16967,22702}, {18582,22708}, {22689,33409}, {22696,33417}, {25157,32447}, {33389,33421}

X(33479) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22694}, {262, 22715}, {3107, 7697}, {25157, 32447}, {33462, 33478}
X(33479) = reflection of X(33463) in X(33478)
X(33479) = complement of X(22714)
X(33479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11261, 33478), (2, 22715, 32149)


X(33480) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 13th FERMAT-DAO

Barycentrics
a^2*(b^2*c^2*(2*a^6-5*(b^2+c^2)*a^4+(b^4-12*b^2*c^2+c^4)*a^2+2*(b^4-c^4)*(b^2-c^2))*sqrt(3)-2*S*(2*(b^4-b^2*c^2+c^4)*a^4-(b^2+c^2)*(2*b^4-11*b^2*c^2+2*c^4)*a^2-2*(b^4-3*b^2*c^2+c^4)*b^2*c^2)) : :
X(33480) = 3*X(5055)-X(25223)

The reciprocal orthologic center of these triangles is X(25165)

X(33480) lies on these lines: {2,14178}, {3,25175}, {15,31708}, {61,25161}, {373,32461}, {396,25173}, {511,618}, {512,5459}, {5055,25223}, {16241,23014}, {16967,23008}, {18582,23023}, {23303,25219}, {25177,33417}

X(33480) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 14186}, {3, 25175}
X(33480) = reflection of X(33490) in X(2)
X(33480) = complement of X(14178)


X(33481) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 14th FERMAT-DAO

Barycentrics
a^2*((2*a^6-5*(b^2+c^2)*a^4+(b^4-12*b^2*c^2+c^4)*a^2+2*(b^4-c^4)*(b^2-c^2))*sqrt(3)*b^2*c^2+2*S*(2*(b^4-b^2*c^2+c^4)*a^4-(b^2+c^2)*(2*b^4-11*b^2*c^2+2*c^4)*a^2-2*(b^4-3*b^2*c^2+c^4)*b^2*c^2)) : :
X(33481) = 3*X(5055)-X(25224)

The reciprocal orthologic center of these triangles is X(25155)

X(33481) lies on these lines: {2,14182}, {3,25180}, {16,31707}, {62,25151}, {373,32460}, {395,25178}, {511,619}, {512,5460}, {5055,25224}, {16242,23007}, {16966,22999}, {18581,23017}, {23302,25220}, {25182,33416}

X(33481) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 14188}, {3, 25180}
X(33481) = reflection of X(33491) in X(2)
X(33481) = complement of X(14182)


X(33482) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 1st NEUBERG

Barycentrics    -2*((b^2+c^2)*a^2+2*b^2*c^2)*S*sqrt(3)+(a^2+b^2+c^2)*((b^2+c^2)*a^2-2*b^2*c^2) : :
X(33482) = X(3104)-3*X(9761) = 4*X(3934)-X(33466) = 2*X(3934)+X(33467) = 3*X(7697)-X(25195)

The reciprocal orthologic center of these triangles is X(6582)

X(33482) lies on these lines: {2,39}, {3,25191}, {16,31711}, {62,7751}, {395,18806}, {633,7759}, {732,33485}, {3104,9761}, {3105,7775}, {3107,11305}, {3849,9988}, {5460,5969}, {6297,11304}, {6582,33420}, {7697,25195}, {11306,22891}, {16966,23000}, {18581,23018}, {25199,33416}, {32521,33459}

X(33482) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25191}, {76, 6294}, {33467, 33483}
X(33482) = reflection of X(i) in X(j) for these (i,j): (33466, 33483), (33483, 3934)
X(33482) = complement of X(6581)
X(33482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 6294, 32189), (2, 8149, 33483), (3934, 33467, 33466)


X(33483) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 1st NEUBERG

Barycentrics    2*((b^2+c^2)*a^2+2*b^2*c^2)*S*sqrt(3)+(a^2+b^2+c^2)*((b^2+c^2)*a^2-2*b^2*c^2) : :
X(33483) = X(3105)-3*X(9763) = 2*X(3934)+X(33466) = 4*X(3934)-X(33467) = 3*X(7697)-X(25191)

The reciprocal orthologic center of these triangles is X(6295)

X(33483) lies on these lines: {2,39}, {3,25195}, {15,31712}, {61,7751}, {396,18806}, {634,7759}, {732,33484}, {3104,7775}, {3105,9763}, {3106,11306}, {3849,9989}, {5459,5969}, {6295,33421}, {6296,11303}, {7697,25191}, {11305,22846}, {16967,23009}, {18582,23024}, {25203,33417}, {32521,33458}

X(33483) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25195}, {76, 6581}, {33466, 33482}
X(33483) = reflection of X(i) in X(j) for these (i,j): (33467, 33482), (33482, 3934)
X(33483) = complement of X(6294)
X(33483) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 6581, 32189), (2, 8149, 33482), (3934, 33466, 33467)


X(33484) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 2nd NEUBERG

Barycentrics    2*S*(2*a^4+4*(b^2+c^2)*a^2+b^4+4*b^2*c^2+c^4)*sqrt(3)-(a^2+b^2+c^2)*(2*a^4-b^4-c^4) : :
X(33484) = 4*X(6704)-X(33468) = 2*X(6704)+X(33469)

The reciprocal orthologic center of these triangles is X(6298)

X(33484) lies on these lines: {2,32}, {3,25192}, {16,31713}, {62,25158}, {395,25184}, {732,33483}, {5460,33460}, {6298,33422}, {11290,33400}, {16966,23001}, {18581,23019}, {22891,25168}, {25196,33406}, {25200,33416}

X(33484) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25192}, {83, 6297}, {33469, 33485}
X(33484) = reflection of X(i) in X(j) for these (i,j): (33468, 33485), (33485, 6704)
X(33484) = complement of X(6296)
X(33484) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 6297, 32190), (2, 8150, 33485), (6704, 33469, 33468)


X(33485) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 2nd NEUBERG

Barycentrics    -2*S*(2*a^4+4*(b^2+c^2)*a^2+b^4+4*b^2*c^2+c^4)*sqrt(3)-(a^2+b^2+c^2)*(2*a^4-b^4-c^4) : :
X(33485) = 2*X(6704)+X(33468) = 4*X(6704)-X(33469)

The reciprocal orthologic center of these triangles is X(6299)

X(33485) lies on these lines: {2,32}, {3,25196}, {15,31714}, {61,25168}, {396,25188}, {732,33482}, {5459,33461}, {6299,33423}, {11289,33401}, {16967,23010}, {18582,23025}, {22846,25158}, {25192,33407}, {25204,33417}

X(33485) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25196}, {83, 6296}, {33468, 33484}
X(33485) = reflection of X(i) in X(j) for these (i,j): (33469, 33484), (33484, 6704)
X(33485) = complement of X(6297)
X(33485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 6296, 32190), (2, 8150, 33484), (6704, 33468, 33469)


X(33486) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 1st TRI-SQUARES-CENTRAL

Barycentrics    (13*sqrt(3)+3)*S^2+(-3*sqrt(3)*SA+9*sqrt(3)*SW+3*SA-SW)*S+9*(sqrt(3)-1)*SB*SC : :

The reciprocal orthologic center of these triangles is X(13705)

X(33486) lies on these lines: {2,1327}, {3,25193}, {16,31715}, {62,25159}, {395,25185}, {530,33444}, {14813,33418}, {16966,23002}, {18581,23020}, {22891,25169}, {25201,33416}

X(33486) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25193}, {1327, 13704}, {33471, 33487}
X(33486) = reflection of X(33470) in X(33487)
X(33486) = complement of X(13706)


X(33487) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 1st TRI-SQUARES-CENTRAL

Barycentrics    (13*sqrt(3)-3)*S^2+(-3*sqrt(3)*SA+9*sqrt(3)*SW-3*SA+SW)*S+9*(1+sqrt(3))*SB*SC : :

The reciprocal orthologic center of these triangles is X(13703)

X(33487) lies on these lines: {2,1327}, {3,25197}, {15,31718}, {61,25169}, {396,25189}, {531,33446}, {14814,33419}, {16967,23011}, {18582,23026}, {22846,25159}, {25205,33417}

X(33487) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25197}, {1327, 13706}, {33470, 33486}
X(33487) = reflection of X(33471) in X(33486)
X(33487) = complement of X(13704)


X(33488) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    (13*sqrt(3)-3)*S^2+(3*sqrt(3)*SA-9*sqrt(3)*SW+3*SA-SW)*S+9*(1+sqrt(3))*SB*SC : :

The reciprocal orthologic center of these triangles is X(13825)

X(33488) lies on these lines: {2,1328}, {3,25194}, {16,31717}, {62,25160}, {395,25186}, {530,33445}, {14814,33418}, {16966,23003}, {18581,23021}, {22891,25170}, {25202,33416}

X(33488) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25194}, {1328, 13824}, {33473, 33489}
X(33488) = reflection of X(33472) in X(33489)
X(33488) = complement of X(13826)


X(33489) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 2nd TRI-SQUARES-CENTRAL

Barycentrics
((108*a^6-546*(b^2+c^2)*a^4-48*(3*b^4+37*b^2*c^2+3*c^4)*a^2+6*(b^2+c^2)*(7*b^2-4*b*c-7*c^2)*(7*b^2+4*b*c-7*c^2))*S-62*a^8-81*(b^2+c^2)*a^6+(511*b^4+1018*b^2*c^2+511*c^4)*a^4-(b^2+c^2)*(387*b^4-1270*b^2*c^2+387*c^4)*a^2+(19*b^4-358*b^2*c^2+19*c^4)*(b^2-c^2)^2)*sqrt(3)+(124*a^6+186*(b^2+c^2)*a^4-216*(b^4+c^4)*a^2-2*(b^2+c^2)*(31*b^4-46*b^2*c^2+31*c^4))*S+54*a^8-207*(b^2+c^2)*a^6+9*(9*b^4-10*b^2*c^2+9*c^4)*a^4+9*(b^2+c^2)*(11*b^4-6*b^2*c^2+11*c^4)*a^2-27*(b^2-c^2)^4 : :

The reciprocal orthologic center of these triangles is X(13823)

X(33489) lies on these lines: {2,1328}, {3,25198}, {15,31716}, {61,25170}, {396,25190}, {531,33447}, {14813,33419}, {16967,23012}, {18582,23027}, {22846,25160}, {25206,33417}

X(33489) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 25198}, {1328, 13826}, {33472, 33488}
X(33489) = reflection of X(33473) in X(33488)
X(33489) = complement of X(13824)


X(33490) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 13th FERMAT-DAO

Barycentrics
a^2*(b^2*c^2*(2*a^6+(b^2+c^2)*a^4-(5*b^4+12*b^2*c^2+5*c^4)*a^2+2*(b^4-c^4)*(b^2-c^2))*sqrt(3)+2*S*(2*(b^4+b^2*c^2+c^4)*a^4-(b^2+2*c^2)*(2*b^2+c^2)*(b^2+c^2)*a^2+2*b^2*c^2*(b^4-5*b^2*c^2+c^4))) : :
X(33490) = 3*X(5055)-X(25175)

The reciprocal parallelogic center of these triangles is X(25234)

X(33490) lies on these lines: {2,14178}, {3,25223}, {15,31720}, {61,25214}, {396,25219}, {511,5459}, {512,618}, {5055,25175}, {16241,23008}, {16967,23014}, {18582,23028}, {23303,25173}, {25227,33417}

X(33490) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 14178}, {3, 25223}
X(33490) = reflection of X(33480) in X(2)
X(33490) = complement of X(14186)


X(33491) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 14th FERMAT-DAO

Barycentrics
a^2*(-b^2*c^2*(2*a^6+(b^2+c^2)*a^4-(5*b^4+12*b^2*c^2+5*c^4)*a^2+2*(b^4-c^4)*(b^2-c^2))*sqrt(3)+2*S*(2*(b^4+b^2*c^2+c^4)*a^4-(b^2+2*c^2)*(2*b^2+c^2)*(b^2+c^2)*a^2+2*b^2*c^2*(b^4-5*b^2*c^2+c^4))) : :
X(33491) = 3*X(5055)-X(25180)

The reciprocal parallelogic center of these triangles is X(25233)

X(33491) lies on these lines: {2,14182}, {3,25224}, {16,31719}, {62,25217}, {395,25220}, {511,5460}, {512,619}, {5055,25180}, {16242,22999}, {16966,23007}, {18581,23022}, {23302,25178}, {25228,33416}

X(33491) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 14182}, {3, 25224}
X(33491) = reflection of X(33481) in X(2)
X(33491) = complement of X(14188)


X(33492) = COMPLEMENT OF X(8011)

Barycentrics    4*a*x + b*y + c*z : : , where x : y : z = -4*sin((B-C)/3)^2*(cos((B-C)/3)-cos(A+Pi/3))+sqrt(3)*sin(A) : :

X(33492) lies on these lines: {2,8010}, {3272,16271}

X(33492) = orthologic center of the 2nd half-diamonds-central triangle to these equilateral triangles: circumnormal, circumtangential, 1st/ 2nd/3rd Morley, 1st/2nd/3rd Morley-midpoint, Roussel, Stammler
X(33492) = midpoint of X(2) and X(8010)
X(33492) = reflection of X(33493) in X(2)
X(33492) = complement of X(8011)


X(33493) = COMPLEMENT OF X(8010)

Barycentrics    b*y+c*z : : , where x : y : z = -4*sin((B-C)/3)^2*(cos((B-C)/3)-cos(A+Pi/3))+sqrt(3)*sin(A) : :

X(33493) lies on the line {2,8010}

X(33493) = parallelogic center of the 2nd half-diamonds-central triangle to these equilateral triangles: circumnormal, circumtangential, 1st/ 2nd/3rd Morley, 1st/2nd/3rd Morley-midpoint, Roussel, Stammler.
X(33493) = midpoint of X(2) and X(8011)
X(33493) = reflection of X(33492) in X(2)
X(33493) = complement of X(8010)?


X(33494) = CENTER OF THE PERSPECONIC OF THESE TRIANGLES: 1st HALF-SQUARES AND 2nd HALF-SQUARES

Barycentrics    (2*R^2*(6*R^2-2*SA-3*SW)+SA^2-3*SB*SC+SW^2)*S^2-2*(3*R^2-SW)*SB*SC*SW : :

See preamble just before X(15254)

X(33494) lies on these lines:{2,15517}, {4,131}, {3091,11411}, {5133,7735}, {6564,22554}, {6565,22553}

X(33494) = anticomplement of X(15517)


X(33495) = CENTER OF THE CROSS-PERSPECONIC OF THESE TRIANGLES: 1st HALF-SQUARES AND 2nd HALF-SQUARES

Barycentrics    (2*R^2*(6*R^2-2*SA-3*SW)+SA^2+SB*SC+SW^2)*S^2-2*(8*R^4-5*R^2*SW+SW^2)*SB*SC : :

See preamble just before X(15648)

X(33495) lies on these lines:{3,254}, {4,131}, {20,11411}, {22,15512}

X(33495) = reflection of X(254) in X(3)
X(33495) = (ABC-X3 reflections)-isogonal conjugate of-X(12163)
X(33495) = X(254)-of-ABC-X3 reflections triangle


X(33496) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 2nd HALF-DIAMONDS

Barycentrics
4*S^4+(36*R^4-5*R^2*(SA+4*SW)+2*SA^2-16*SB*SC+2*SW^2)*S^2-sqrt(3)*(2*(5*R^2-SB-SC)*S^2-4*(SA+SW)*R^4-(15*SA^2-16*SA*SW-SW^2)*R^2-6*(SB+SC)*SA*SW)*S-3*(4*R^2-3*SW)*R^2*SB*SC : :

The reciprocal cyclologic center of these triangles is X(33497)

X(33496) lies on these lines: {2,8174}, {3,623}, {13,275}, {619,16336}, {5668,11126}, {8837,17035}, {10282,33497}, {20577,23872}

X(33496) = complement of X(8174)


X(33497) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 1st HALF-DIAMONDS

Barycentrics
4*S^4+(36*R^4-5*(SA+4*SW)*R^2+2*SA^2-16*SB*SC+2*SW^2)*S^2-sqrt(3)*(4*(SA+SW)*R^4+(15*SA^2-SW^2)*R^2-2*(5*R^2-SB-SC)*S^2-2*(8*R^2+3*SA-3*SW)*SA*SW)*S-3*(4*R^2-3*SW)*R^2*SB*SC : :

The reciprocal cyclologic center of these triangles is X(33496)

X(33497) lies on these lines: {2,8175}, {3,624}, {14,275}, {618,16336}, {5669,11127}, {8839,17035}, {10282,33496}, {20577,23873}

X(33497) = complement of X(8175)


X(33498) = CYCLOLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 1st HALF-DIAMONDS

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

The reciprocal cyclologic center of these triangles is X(619)

X(33498) lies on the cubic K066b and these lines: {2,1338}, {3,14}, {511,15610}, {533,3480}, {616,14921}, {6672,15778}, {8450,31703}, {16336,33500}

X(33498) = complement of X(1338)
X(33498) = inverse of X(2926) in the circumcircle
X(33498) = {X(8173), X(16242)}-harmonic conjugate of X(6105)


X(33499) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO WASAT

Barycentrics
5*S^4+(36*R^4-3*R^2*(7*SA+8*SW)+6*SA^2-7*SB*SC+3*SW^2)*S^2-sqrt(3)*((14*R^2+SA-3*SW)*S^2+36*(SA+SW)*R^4+3*R^2*(5*SA^2-12*SA*SW-7*SW^2)-SW*(2*SA+SW)*(SA-3*SW))*S-3*(3*R^2-SW)*(12*R^2-SW)*SB*SC : :

The reciprocal cyclologic center of these triangles is the complement of X(8436)

X(33499) lies on these lines: {2,5669}, {3,618}, {13,2992}, {14,471}, {110,22648}, {113,624}, {340,5668}, {621,19772}, {636,5907}, {6000,33501}, {23283,23870}

X(33499) = midpoint of X(340) and X(5668)
X(33499) = complement of X(5669)
X(33499) = inverse of X(1605) in the circumcircle


X(33500) = CYCLOLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 2nd HALF-DIAMONDS

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

The reciprocal cyclologic center of these triangles is X(618)

X(33500) lies on the cubic K066a and these lines: {2,1337}, {3,13}, {511,15609}, {532,3479}, {617,14922}, {6671,15802}, {8460,31704}, {16336,33498}

X(33500) = complement of X(1337)
X(33500) = inverse of X(2925) in the circumcircle
X(33500) = {X(8172), X(16241)}-harmonic conjugate of X(6104)


X(33501) = CYCLOLOGIC CENTER OF THESE TRIANGLES: WASAT TO 2nd HALF-DIAMONDS

Barycentrics
5*S^4+(36*R^4-3*R^2*(7*SA+8*SW)+6*SA^2-7*SB*SC+3*SW^2)*S^2+sqrt(3)*((14*R^2+SA-3*SW)*S^2+36*(SA+SW)*R^4+3*R^2*(5*SA^2-12*SA*SW-7*SW^2)-SW*(2*SA+SW)*(SA-3*SW))*S-3*(3*R^2-SW)*(12*R^2-SW)*SB*SC : :

The reciprocal cyclologic center of these triangles is the complement of X(8435)

X(33501) lies on these lines: {2,5668}, {3,619}, {13,470}, {110,22649}, {113,623}, {340,5669}, {622,19773}, {635,5907}, {5995,6671}, {6000,33499}, {23284,23871}

X(33501) = midpoint of X(340) and X(5669)
X(33501) = reflection of X(5995) in X(6671)
X(33501) = complement of X(5668)
X(33501) = inverse of X(1606) in the circumcircle


X(33502) = CENTER OF DIRECT SIMILITUDE OF THESE TRIANGLES: 1st HALF-SQUARES AND LUCAS TANGENTS

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

X(33502) lies on the Parry circle and these lines: {23,1151}, {182,7602}, {352,6221}, {6567,11673}, {11171,33503}

X(33502) = inverse of X(7602) in the Brocard circle
X(33502) = inverse of X(23) in the Lucas circles radical circle


X(33503) = CENTER OF DIRECT SIMILITUDE OF THESE TRIANGLES: 2nd HALF-SQUARES AND LUCAS(-1) TANGENTS

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

X(33503) lies on the Parry circle and these lines: {23,1152}, {182,7601}, {352,6398}, {6566,11673}, {11171,33502}

X(33503) = inverse of X(7601) in the Brocard circle
X(33503) = inverse of X(23) in the Lucas(-1) circles radical circle


X(33504) =  COMPLEMENT OF X(2867)

Barycentrics    (b-c)^2 (b+c)^2 (-a^2+b^2+c^2) (-a^4+b^4+a^2 b c-b^3 c-b c^3+c^4) (-a^4+b^4-a^2 b c+b^3 c+b c^3+c^4) (-2 a^6+a^4 b^2+b^6+a^4 c^2-b^4 c^2-b^2 c^4+c^6) : :
X(33504) = 3*X[2]-X[2867], 3 X[6793] - 2 X[15639]

See Corneliu Manescu-Avram, Ercole Suppa and Peter Moses, Hyacinthos 29137 and Hyacinthos 29138.

X(33504) lies on the nine-point circle and these lines: {2,2867}, {4,32687}, {113,15341}, {122,647}, {125,6587}, {127,525}, {132,1503}, {133,5523}, {1560,32125}, {2697,2715}, {6794,18809}, {13509,18402}, {14401,16177}, {17434,20625}

X(33504) = reflection of X(1562) in X(14117)
X(33504) = reflection of X(1562) in the van Aubel line
X(33504) = complement of X(2867)
X(33504) = X(4)-Ceva conjugate of X(2881)
X(33504) = crosspoint of X(525) and X(1503)
X(33504) = crosssum of X(112) and X(1297)
X(33504) = crossdifference of every pair of points on line {2435, 2445}
X(33504) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2881}, {2881, 10}
X(33504) = polar-circle-inverse of X(32687)
X(33504) = Moses-radical-circle-inverse of X(122)
X(33504) = orthic-isogonal conjugate of X(2881)


X(33505) =  MIDPOINT OF X(5) AND X(14611)

Barycentrics    7*S^4-(3*R^2*(63*R^2+12*SA-34*SW)-8*SA^2+5*SB*SC+13*SW^2)*S^2-(9*R^2-SW)^2*SB*SC : :
X(33505) = 3*X(110)+X(20957), X(477)+3*X(5655), X(12041)-3*X(31378), X(14480)+3*X(14643)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29140

X(33505) lies on the cubic K913 and these lines: {5, 14611}, {30, 110}, {140, 14670}, {399, 16340}, {523, 10272}, {3258, 5609}, {3470, 3628}, {5663, 31379}, {12041, 31378}, {14480, 14643}, {14702, 18571}, {16168, 16534}

X(33505) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 14611}, {399, 16340}, {3258, 5609}, {10721, 21317}
X(33505) = reflection of X(i) in X(j) for these (i,j): (140, 31945), (12079, 3628)


X(33506) =  REFLECTION OF X(396) IN X(15609)

Barycentrics    (sqrt(3)*(SB+SC)+2*S)*(3*(15*R^2-2*SA-2*SW)*S^2-6*SB*SC*SW-S*sqrt(3)*(4*S^2-3*(SW+6*SA)*R^2+6*SA^2)) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29140.

X(33506) lies on these lines: {15, 5617}, {30, 8172}, {396, 15609}, {14446, 20579}

X(33506) = reflection of X(396) in X(15609)


X(33507) =  REFLECTION OF X(395) IN X(15610)

Barycentrics    (sqrt(3)*(SB+SC) -2*S)*(3*(15*R^2-2*SA-2*SW)*S^2-6*SB*SC*SW+S*sqrt(3)*(4*S^2-3*(SW+6*SA)*R^2+6*SA^2)) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29140.

X(33507) lies on these lines: {16, 5613}, {30, 8173}, {395, 15610}, {14447, 20578}

X(33507) = reflection of X(395) in X(15610)


X(33508) =  (name pending)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29146.

X(33508) lies on this line: {758, 13464}


X(33509) =  X(2)X(525)∩X(5)X(524)

Barycentrics    2*a^10-6*(b^2+c^2)*a^8+(7*b^4+4*b^2*c^2+7*c^4)*a^6-2*(b^2+c^2)*(b^4+c^4)*a^4-(b^2-c^2)^2*(3*b^4-7*b^2*c^2+3*c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(2*b^4-7*b^2*c^2+2*c^4) : :
Barycentrics    (108*R^2+3*SA-25*SW)*S^2+6*R^2*(3*SA+SW)*(3*SA-2*SW)-3*SW*(4*SA^2-SA*SW-SW^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29146.

X(33509) lies on these lines: {2, 525}, {5, 524}


X(33510) =  X(1154)X(3850)∩X(3628)X(6368)

Barycentrics    ((51*R^2+2*SA-12*SW)*S^2+72*R^6-2*(36*SA+35*SW)*R^4+(18*SA^2+40*SA*SW+13*SW^2)*R^2-2*(2*SA+3*SW)*SA*SW)*(S^2+SB*SC) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29146.

X(33510) lies on these lines: {1154, 3850}, {3628, 6368}


X(33511) =  MIDPOINT OF X(98) AND X(113)

Barycentrics    (108*R^2+3*SA-23*SW)*S^4+(6*R^2*(9*SA^2-3*SA*SW-7*SW^2)-SW*(9*SA^2-10*SW^2))*S^2+(18*R^2-5*SW)*SB*SC*SW^2 : :
X(33511) = 3*X(2)+X(22265), X(110)+3*X(14651), 3*X(125)-X(15545), X(148)+3*X(15035), X(399)+3*X(14849), 7*X(3526)-3*X(14850), X(11005)-5*X(14061), X(11005)-3*X(23515), 2*X(11623)+X(16534), 3*X(11656)-X(22265), X(12188)+3*X(14643), X(12295)-3*X(14639), X(13172)-5*X(15051), 5*X(14061)-3*X(23515), 5*X(15059)-X(18331), X(15545)+3*X(18332), 2*X(20397)+X(31854)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29146.

X(33511) lies on these lines: {2, 11656}, {3, 16278}, {5, 542}, {98, 113}, {110, 14651}, {114, 12900}, {115, 17702}, {125, 15545}, {148, 15035}, {399, 14849}, {541, 5465}, {690, 6036}, {2777, 12042}, {2782, 5972}, {3526, 14850}, {3906, 16760}, {5642, 11632}, {6321, 16163}, {11005, 14061}, {12188, 14643}, {12295, 14639}, {13172, 15051}, {15059, 18331}, {15303, 19905}, {15342, 16003}, {15357, 20397}

X(33511) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 11656}, {3, 16278}, {98, 113}, {125, 18332}, {5465, 6055}, {5642, 11632}, {6321, 16163}, {15303, 19905}, {15342, 16003}, {15357, 31854}
X(33511) = reflection of X(i) in X(j) for these (i,j): (114, 12900), (6699, 6036), (15357, 20397), (15359, 20398)
X(33511) = complement of the complement of X(22265)
X(33511) = {X(11005), X(14061)}-harmonic conjugate of X(23515)

X(33512) =  MIDPOINT OF X(99) AND X(113)

Barycentrics    2*a^14-10*(b^2+c^2)*a^12+(17*b^4+26*b^2*c^2+17*c^4)*a^10-10*(b^2+c^2)^3*a^8-(3*b^8+3*c^8-(19*b^4+18*b^2*c^2+19*c^4)*b^2*c^2)*a^6+(b^2+c^2)*(b^4+c^4)*(7*b^4-17*b^2*c^2+7*c^4)*a^4-(b^2-c^2)^2*(4*b^8+4*c^8+(b^2+c^2)^2*b^2*c^2)*a^2+(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4) : :
Barycentrics    (36*R^2+3*SA-7*SW)*S^4-(6*R^2*(9*SA^2+SW^2-3*SA*SW)-SW*(15*SA^2-8*SA*SW+2*SW^2))*S^2-3*(6*R^2-SW)*SB*SC*SW^2 : :
X(33512) = 3*X(110)+X(18331), X(125)-3*X(15561), X(147)+3*X(15035), X(399)+3*X(14850), 7*X(3526)-3*X(14849), 3*X(5642)-X(18332), 3*X(8724)+X(18332), X(9862)-5*X(15051), X(13188)+3*X(14643), 3*X(14643)-X(16278), X(16111)-3*X(21166)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29146.

X(33512) lies on these lines: {99, 113}, {110, 18331}, {114, 17702}, {115, 12900}, {125, 15561}, {141, 542}, {147, 15035}, {399, 14850}, {541, 2482}, {690, 6132}, {2782, 5972}, {3526, 14849}, {5181, 12177}, {5477, 32661}, {5642, 8724}, {6033, 16163}, {6721, 15359}, {6723, 15535}, {7835, 15920}, {9862, 15051}, {11005, 30714}, {13188, 14643}, {15545, 24981}, {16111, 21166}

X(33512) = midpoint of X(i) and X(j) for these lines: {i,j}: {99, 113}, {5181, 12177}, {5642, 8724}, {6033, 16163}, {11005, 30714}, {13188, 16278}, {15545, 24981}
X(33512) = reflection of X(i) in X(j) for these (i,j): (115, 12900), (6699, 620), (15359, 6721), (15535, 6723)
X(33512) = {X(13188), X(14643)}-harmonic conjugate of X(16278)

leftri

Centers of bianticevian conics: X(35513)-X(35516)

rightri

Centers X(35513)-X(35516) were contributed by Vu Thanh Tung and Vu Quoc My, July 4, 2019.

Suppose that P and Q are points not on a sideline of a triangle ABC. The conic section that passes through P, Q, and the vertices of the anticevian triangle of P also passes through the vertices of the anticevian triangle of Q. This conic was introduced by Randy Hutson. Barry Wolk found coordinates for the center, and Paul Yiu and Francisco Javier Garcia found other properties. See Hyacinthos (#21109 and related posts), July 2012.

If P = p : q : r and U = u : v : w (barycentrics), then the two anticevian triangles have vertices

Pa = -p : q : r,    Pb = p :-q : r,    Pc = p : q -r      and      Ua = -u : v : w,    Ub= u : -v : w,    Uc = u : v : -w,

and the conic, which passes through P, Q, Pa, Pb, Pc, Ua, Ub, Uc, has center 1/(q^2 w^2 - r^2 v^2) : 1/(r^2 u^2 - p^2 w^2) :1/(p^2 v^2 - q^2 w^2).


X(33513) =  CENTER OF THE BIANTICEVIAN CONIC OF X(2) AND X(5)

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

X(33513) lies on the Steiner circumellipse and these lines: {290, 1173}, {547, 1494}

X(33513) = X(i)-cross conjugate of X(j) for these (i,j): {5, 23582}, {15801, 249}, {32002, 18020}
X(33513) = cevapoint of X(525) and X(3628)
X(33513) = trilinear pole of line {2, 10979}
X(33513) = X(i)-isoconjugate of X(j) for these (i,j): {140, 810}, {228, 21103}, {647, 17438}, {656, 13366}, {661, 22052}, {822, 6748}, {2616, 32078}, {3049, 20879}, {21012, 22383}
X(33513) = barycentric product X(i)*X(j) for these lines: {i,j}: {1173, 6331}, {6528, 31626}, {18831, 31610}
X(33513) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {27, 21103}, {107, 6748}, {110, 22052}, {112, 13366}, {162, 17438}, {288, 23286}, {648, 140}, {811, 20879}, {1173, 647}, {1625, 32078}, {1897, 21012}, {6331, 1232}, {31610, 6368}, {31626, 520}


X(33514) =  CENTER OF THE BIANTICEVIAN CONIC OF X(2) AND X(31)

Barycentrics    1/(b^6 - c^6) : :

X(33514) lies on the Steiner circumellipse and these lines: {99, 14574}, {110, 18829}, {251, 14970}, {290, 3114}, {670, 1576}, {671, 3407}, {827, 9063}, {3113, 14616}, {3228, 18898}, {5641, 8840}, {7305, 18827}, {18896, 19576}

X(33514) = X(i)-cross conjugate of X(j) for these (i,j): {7766, 4590}, {18906, 18020}
X(33514) = cevapoint of X(i) and X(j) for these (i,j): {523, 7792}, {824, 6679}
X(33514) = trilinear pole of line {2, 1501}
X(33514) = X(i)-isoconjugate of X(j) for these (i,j): {75, 17415}, {523, 3116}, {561, 9006}, {661, 3094}, {788, 2887}, {798, 3314}, {810, 5117}, {824, 16584}, {869, 3801}, {1491, 3778}, {1577, 3117}, {3250, 3721}, {3774, 3776}, {4122, 7032}, {8022, 30870}, {18899, 20948}, {18904, 30671}
X(33514) = barycentric product X(i)*X(j) for these lines: {i,j}: {32, 9063}, {99, 3407}, {110, 3114}, {662, 3113}, {670, 18898}, {2966, 8840}, {4577, 14617}
X(33514) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {32, 17415}, {99, 3314}, {110, 3094}, {163, 3116}, {648, 5117}, {789, 20234}, {825, 3778}, {1492, 3721}, {1501, 9006}, {1576, 3117}, {3113, 1577}, {3114, 850}, {3407, 523}, {4586, 2887}, {4613, 16886}, {4621, 3773}, {5384, 7239}, {7305, 4481}, {8840, 2799}, {9063, 1502}, {14574, 18899}, {14617, 826}, {14621, 3801}, {17743, 4122}, {17941, 9865}, {18898, 512}


X(33515) =  CENTER OF THE BIANTICEVIAN CONIC OF X(2) AND X(32)

Barycentrics    1/(b^8 - c^8) : :

X(33515) lies on the Steiner circumellipse and these lines: {290, 3115}, {670, 14574}, {827, 18829}

X(33515) = cevapoint of X(i) and X(j) for these (i,j): {826, 6680}, {4577, 4630}
X(33515) = trilinear pole of line {2, 9233}
X(33515) = X(i)-isoconjugate of X(j) for these (i,j): {626, 2084}, {688, 20627}, {798, 16893}, {826, 2085}, {1577, 3118}, {3005, 4118}, {8061, 20859}, {21110, 21814}
X(33515) = barycentric product X(110)*X(3115)
X(33515) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {99, 16893}, {827, 20859}, {1576, 3118}, {3115, 850}, {4577, 626}, {4593, 20627}, {4599, 4118}, {4630, 8265}


X(33516) =  CENTER OF THE BIANTICEVIAN CONIC OF X(2) AND X(560)

Barycentrics    1/(b^10 - c^10) : :

X(33516) lies on the Steiner circumellipse and these and on no line X(i)X(j) for 1 ≤ i < j < 33517.


X(33517) =  MIDPOINT OF X(6778) AND X(23005)

Barycentrics    sqrt(3)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2)*(-a^2+b^2+c^2)+2*S*(2*a^4-(b^2+c^2)*a^2-3*(b^2-c^2)^2) : :
X(33517) = 3*X(13)-X(16), 5*X(13)-X(6779), 2*X(16)-3*X(6108), 5*X(16)-3*X(6779), 3*X(115)-2*X(11543), 2*X(5321)-3*X(31710), 3*X(5459)-2*X(6672), 9*X(5470)-5*X(16961), 3*X(5470)-X(22998), 5*X(6108)-2*X(6779), 3*X(6778)+X(19107), 3*X(6782)-4*X(11543), 3*X(11603)-X(22856), 5*X(16961)-3*X(22998), X(19107)-3*X(23005), 3*X(22511)-X(25235)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29153.

X(33517) lies on these lines: {2, 13}, {6, 20429}, {30, 6783}, {115, 6782}, {187, 11542}, {396, 32907}, {397, 25555}, {511, 5318}, {524, 31695}, {533, 23004}, {542, 5321}, {925, 2379}, {3564, 5107}, {5470, 16961}, {5472, 14136}, {5873, 7748}, {6772, 11485}, {6778, 10722}, {7685, 16808}, {8586, 20428}, {11603, 22856}, {13103, 22513}, {13349, 20415}, {14139, 23303}, {14447, 27551}, {20412, 31687}, {22511, 25235}

X(33517) = midpoint of X(6778) and X(23005)
X(33517) = reflection of X(i) in X(j) for these (i,j): (187, 11542), (6108, 13), (6782, 115), (13349, 20415)
X(33517) = {X(5107), X(13449)}-harmonic conjugate of X(33518)
X(33517) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16, 16966, 6672), (622, 5335, 16)

X(33518) =  MIDPOINT OF X(6777) AND X(23004)

Barycentrics    sqrt(3)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2)*(-a^2+b^2+c^2)-2*S*(2*a^4-(b^2+c^2)*a^2-3*(b^2-c^2)^2) : :
X(33518) = 3*X(14)-X(15), 5*X(14)-X(6780), 2*X(15)-3*X(6109), 5*X(15)-3*X(6780), 3*X(115)-2*X(11542), 2*X(5318)-3*X(31709), 3*X(5460)-2*X(6671), 9*X(5469)-5*X(16960), 3*X(5469)-X(22997), 5*X(6109)-2*X(6780), 3*X(6777)+X(19106), 3*X(6783)-4*X(11542), 3*X(11602)-X(22900), 5*X(16960)-3*X(22997), X(19106)-3*X(23004), 3*X(22510)-X(25236)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29153.

X(33518) lies on these lines: {2, 14}, {6, 20428}, {30, 6782}, {115, 6783}, {187, 11543}, {395, 32909}, {398, 25555}, {511, 5321}, {524, 31696}, {532, 23005}, {542, 5318}, {925, 2378}, {3564, 5107}, {5469, 16960}, {5471, 14137}, {5872, 7748}, {6775, 11486}, {6777, 10722}, {7684, 16809}, {8586, 20429}, {11602, 22900}, {13102, 22512}, {13350, 20416}, {14138, 23302}, {14446, 27550}, {20411, 31688}, {22510, 25236}

X(33518) = midpoint of X(6777) and X(23004)
X(33518) = reflection of X(i) in X(j) for these (i,j): (187, 11543), (6109, 14), (6783, 115), (13350, 20416)
X(33518) = {X(5107), X(13449)}-harmonic conjugate of X(33517)
X(33518) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (15, 16967, 6671), (621, 5334, 15)

X(33519) =  REFLECTION OF X(5902) IN X(12019)

Barycentrics    a*( 2*(b+c)*a^4-4*(b^2+c^2)*a^3+2*(b+c)*b*c*a^2+(4*b^2+7*b*c+4*c^2)*(b-c)^2*a-(b^2-c^2)*(b-c)*(b+2*c)*(2*b+c)) : :
X(33519) = 3*X(11)-2*X(354), 7*X(11)-4*X(5083), 5*X(11)-2*X(17660), 11*X(11)-8*X(18240), 4*X(11)-X(27778), 7*X(354)-6*X(5083), 5*X(354)-3*X(17660), 11*X(354)-12*X(18240), 8*X(354)-3*X(27778), 4*X(3740)-3*X(6174), X(4430)-3*X(10707), 10*X(5083)-7*X(17660), 11*X(5083)-14*X(18240), 16*X(5083)-7*X(27778), 11*X(17660)-20*X(18240), 8*X(17660)-5*X(27778)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29153.

X(33519) lies on these lines: {11, 118}, {55, 1156}, {80, 1836}, {100, 3715}, {528, 3681}, {952, 3058}, {1898, 18908}, {2802, 4525}, {3740, 6174}, {4430, 10707}, {4995, 15064}, {5777, 10543}, {5851, 11246}, {5902, 12019}, {6326, 30326}, {9580, 9897}, {10176, 10609}

X(33519) = reflection of X(i) in X(j) for these (i,j): (5902, 12019), (10609, 10176)

X(33520) =  REFLECTION OF X(118) IN X(101)

Barycentrics    4*a^8-4*(b+c)*a^7-2*(3*b^2-2*b*c+3*c^2)*a^6+(b+c)*(5*b^2+2*b*c+5*c^2)*a^5+(b-3*c)*(3*b-c)*(b^2+b*c+c^2)*a^4-2*(b^2-c^2)^2*(b+c)*a^3+2*(b^2-c^2)^2*b*c*a^2+(b^2-c^2)^3*(b-c)*a-(b^2-c^2)^2*(b-c)*(b^3-c^3) : :
X(33520) = X(4)-3*X(101), 2*X(4)-3*X(118), 5*X(4)-3*X(10725), 5*X(101)-X(10725), 3*X(103)-5*X(3522), 3*X(116)-4*X(140), 5*X(118)-2*X(10725), 3*X(150)-7*X(3523), 3*X(152)+X(5059), 3*X(381)-4*X(20401), 5*X(631)-3*X(10708), X(962)-3*X(15735), 5*X(1656)-6*X(6710), 5*X(1656)-3*X(10739), X(3146)-3*X(10710), 5*X(3522)+3*X(20096), 7*X(3523)-6*X(6712), 17*X(3533)-15*X(31273), X(5073)-3*X(10741), 5*X(11522)-6*X(11728)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29153.

X(33520) lies on these lines: {3, 544}, {4, 101}, {72, 2801}, {103, 3522}, {116, 140}, {150, 3523}, {152, 5059}, {381, 20401}, {516, 6603}, {550, 2808}, {631, 10708}, {952, 31852}, {962, 15735}, {1656, 6710}, {2772, 10990}, {2774, 30714}, {2784, 3704}, {2786, 10992}, {2809, 5882}, {2810, 8550}, {3146, 10710}, {3533, 31273}, {3887, 10993}, {4292, 15730}, {4294, 4845}, {5073, 10741}, {9518, 14900}, {11522, 11728}, {11712, 13464}

X(33520) = midpoint of X(103) and X(20096)
X(33520) = reflection of X(i) in X(j) for these (i,j): (118, 101), (150, 6712), (10739, 6710), (33521,550)
X(33520) = {X(550), X(2808)}-harmonic conjugate of X(33521)

X(33521) =  REFLECTION OF X(116) IN X(103)

Barycentrics    4*a^8-4*(b+c)*a^7+4*b*c*a^6-7*(b^2-c^2)*(b-c)*a^5+(3*b^2-b*c+3*c^2)*(b-c)^2*a^4+2*(b^2-c^2)*(b-c)*(5*b^2+4*b*c+5*c^2)*a^3-2*(3*b^4+3*c^4+5*(b+c)^2*b*c)*(b-c)^2*a^2+(b^2-c^2)^3*(b-c)*a-(b^2-c^2)^2*(b-c)*(b^3-c^3) : :
X(33521) = X(4)-3*X(103), 2*X(4)-3*X(116), 5*X(4)-3*X(10727), 3*X(101)-5*X(3522), 5*X(103)-X(10727), 5*X(116)-2*X(10727), 3*X(118)-4*X(140), 3*X(150)+X(5059), 3*X(152)-7*X(3523), 5*X(631)-3*X(10710), 5*X(631)-4*X(20401), 5*X(1656)-6*X(6712), 5*X(1656)-3*X(10741), X(3146)-3*X(10708), 7*X(3523)-6*X(6710), 13*X(5068)-15*X(31273), X(5073)-3*X(10739), 3*X(10710)-4*X(20401), 5*X(11522)-6*X(11726), 3*X(11714)-2*X(13464)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29153.

X(33521) lies on these lines: {4, 103}, {20, 544}, {101, 3522}, {118, 140}, {150, 5059}, {152, 3523}, {550, 2808}, {631, 10710}, {1656, 6712}, {2772, 30714}, {2774, 10990}, {2784, 10992}, {2786, 10991}, {2801, 10993}, {2809, 5493}, {2825, 14900}, {3146, 10708}, {5068, 31273}, {5073, 10739}, {11522, 11726}, {11714, 13464}

X(33521) = reflection of X(i) in X(j) for these (i,j): (116, 103), (152, 6710), (10741, 6712), (33520, 550)
X(33521) = {X(550), X(2808)}-harmonic conjugate of X(33520)
X(33521) = {X(631), X(10710)}-harmonic conjugate of X(20401)

X(33522) =  REFLECTION OF X(11427) IN X(7494)

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

X(33522) lies on these lines: {2, 1350}, {3, 11433}, {20, 343}, {22, 69}, {25, 10519}, {51, 631}, {141, 6995}, {193, 3796}, {235, 11821}, {376, 1899}, {394, 10565}, {511, 7494}, {1370, 23293}, {1589, 11824}, {1590, 11825}, {1629, 32000}, {1992, 5012}, {2979, 7493}, {3060, 3313}, {3098, 7386}, {3220, 26872}, {3430, 25876}, {3523, 10601}, {3524, 15033}, {3528, 18950}, {3529, 11550}, {3537, 11438}, {3619, 6997}, {3917, 6353}, {4232, 17811}, {5285, 26871}, {6515, 6636}, {7378, 29181}, {7400, 17834}, {7408, 10516}, {7485, 18928}, {7499, 14853}, {7512, 18925}, {7517, 11487}, {7667, 23291}, {7735, 20859}, {8266, 26874}, {9306, 32267}, {9909, 14826}, {10323, 18909}, {11008, 15080}, {11414, 12324}, {11442, 14927}, {12289, 17538}, {12827, 13203}, {13567, 31884}, {14912, 22352}, {17825, 21167}

X(33522) = reflection of X(11427) and X(7494)
X(33522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 343, 32064}, {22, 69, 11206}, {6515, 6636, 25406}


X(33523) =  X(2)X(389)∩X(22)X(1498)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 + 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 - 4*b^4*c^4 - a^2*c^6 + b^2*c^6 + c^8) : :
X(33523) = 9 X[7998] - 4 X[17809]

X(33523) lies on these lines: {2, 389}, {22, 1498}, {25, 11459}, {66, 69}, {343, 3060}, {394, 5012}, {427, 11412}, {428, 15058}, {511, 7378}, {568, 11548}, {1092, 15246}, {1180, 22416}, {1216, 7386}, {1368, 23039}, {3567, 7539}, {3917, 6776}, {5020, 11591}, {5064, 11576}, {5876, 9909}, {5890, 7499}, {5891, 7392}, {5907, 6995}, {6636, 15072}, {6676, 18436}, {6997, 15056}, {7408, 15030}, {7484, 7592}, {7494, 13754}, {7500, 15305}, {7571, 11451}, {10154, 31834}, {11439, 16656}, {12282, 31807}, {15067, 16419}, {20806, 31521}

X(33523) = {X(2979),X(11442)}-harmonic conjugate of X(12220)


X(33524) =  EULER LINE INTERCEPT OF X(52)X(8717)

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

As a point on the Euler line, X(33524) has Shinagawa coefficients (3E+2F, -6E-2F).

X(33524) lies on the cubic K1109 and on these lines: {2, 3}, {52, 8717}, {64, 7691}, {155, 8718}, {159, 6225}, {161, 5894}, {1181, 11577}, {1232, 20477}, {1350, 12111}, {1498, 2979}, {3098, 11381}, {3100, 3303}, {3304, 4296}, {3313, 9968}, {3592, 11417}, {3594, 11418}, {5422, 13598}, {5731, 9911}, {5895, 15577}, {6800, 13346}, {7583, 9695}, {8185, 12512}, {8192, 20070}, {9778, 9798}, {9786, 15107}, {9914, 11206}, {9925, 12174}, {10625, 11456}, {11420, 22236}, {11421, 22238}, {11441, 15644}, {11477, 12220}, {12244, 25714}, {13009, 13010}, {13340, 32139}, {13348, 15066}, {15056, 15811}, {15072, 17834}, {22334, 31884}

X(33524) = anticomplement of X(1907)
X(33524) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 381, 13154}, {3, 3518, 17928}, {3, 5198, 2}, {3, 7387, 3518}, {3, 12083, 17714}, {3, 17714, 24}, {20, 22, 11413}, {20, 7488, 21312}, {20, 11414, 22}, {376, 3518, 3}, {376, 7387, 17928}, {550, 12083, 24}, {550, 17714, 3}, {3146, 16661, 3}, {3522, 12087, 25}, {5004, 5005, 7714}, {5059, 6636, 1593}, {7492, 12086, 3}, {7512, 11001, 12085}, {7530, 18369, 10594}, {12088, 17538, 3}, {13348, 26883, 15066}, {13564, 15681, 12084}, {15246, 17578, 11479}


X(33525) =  ORTHIC AXIS INTERSECT OF X(657)X(663)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29158.

X(33525) lies on these lines: {230, 231}, {657, 663}, {665, 4017}, {905, 31605}, {4130, 4990}, {4171, 6608}, {25084, 27417}

X(33525) = crossdifference of every pair of points on line X(3)X(7)
X(33525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (657, 17412, 3063), (3709, 10581, 657), (6129, 6586, 647)


X(33526) =  COMPLEMENT OF X(11600)

Barycentrics    (SB+SC)*(SA+sqrt(3)*S)*(sqrt(3)* (SB+SC)+2*S)*(3*SA^2-2*sqrt(3)*S*SA+S^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29158.

X(33526) lies on the cubic K900 and these lines: {2, 11600}, {15, 2380}, {16, 323}, {140, 619}, {532, 18803}, {618, 3479}, {624, 33496}, {630, 31376}, {3643, 22649}, {6107, 6669}, {6150, 33527}, {6671, 15609}

X(33526) = midpoint of X(15) and X(10409)
X(33526) = reflection of X(15609) in X(6671)
X(33526) = complement of X(11600)


X(33527) =  COMPLEMENT OF X(11601)

Barycentrics    (SB+SC)*(SA-sqrt(3)*S)*(sqrt(3)* (SB+SC)-2*S)*(3*SA^2+2*sqrt(3)*S*SA+S^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29158.

X(33527) lies on the cubic K900 and these lines: {2, 11601}, {15, 323}, {16, 2381}, {140, 618}, {533, 18804}, {619, 3480}, {623, 33497}, {629, 31376}, {3642, 22648}, {6106, 6670}, {6150, 33526}, {6672, 15610}, {8456, 11145}

X(33527) = midpoint of X(16) and X(10410)
X(33527) = reflection of X(15610) in X(6672)
X(33527) = complement of X(11601)


X(33528) =  X(5)X(513)∩X(10)X(3900)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29165.

X(33528) lies on these lines: {5, 513}, {10, 3900}, {522, 3634}, {4885, 6706}, {7412, 16228}

X(33528) = X(6132)-of-K798i triangle
X(33528) = center of the circle {X(i), X(j), X(k)} for these lines: {i, j, k}: {10, 946, 20418}, {140, 9955, 9956}


X(33529) =  COMPLEMENT OF X(11127)

Barycentrics    ((b^2+c^2)*a^2-(b^2-c^2)^2)*((-a^2+b^2+c^2)*sqrt(3)+2*S) : :
Barycentrics    (S^2+SB*SC)*(sqrt(3)*SA+S) : :
X(33529) = 3*X(2)+X(19778)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29165.

X(33529) lies on these lines: {2, 18}, {5, 51}, {95, 302}, {141, 16537}, {184, 5872}, {231, 396}, {298, 340}, {618, 6105}, {621, 19772}, {623, 3580}, {627, 8839}, {850, 20579}, {2041, 11090}, {2042, 11091}, {3129, 5617}, {6117, 14918}, {10601, 11311}, {13350, 13372}, {19295, 23303}

X(33529) = midpoint of X(11127) and X(19778)
X(33529) = complement of X(11127)
X(33529) = isotomic conjugate of the polar conjugate of X(6117)
X(33529) = {X(5),X(343)}-harmonic conjugate of X(33530)
X(33529) = {X(2), X(19778)}-harmonic conjugate of X(11127)


X(33530) =  COMPLEMENT OF X(11126)

Barycentrics    ((b^2+c^2)*a^2-(b^2-c^2)^2)*((-a^2+b^2+c^2)*sqrt(3)-2*S) : :
Barycentrics    (S^2+SB*SC)*(sqrt(3)*SA-S) : :
X(33530) = 3*X(2)+X(19779)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29165.

X(33530) lies on these lines: {2, 17}, {5, 51}, {95, 303}, {141, 16536}, {184, 5873}, {231, 395}, {299, 340}, {619, 6104}, {622, 19773}, {624, 3580}, {628, 8837}, {850, 20578}, {2041, 11091}, {2042, 11090}, {3130, 5613}, {6116, 14918}, {10601, 11312}, {13349, 13372}, {19294, 23302}

X(33530) = midpoint of X(11126) and X(19779)
X(33530) = complement of X(11126)
X(33530) = isotomic conjugate of the polar conjugate of X(6116)
X(33530) = {X(2), X(19779)}-harmonic conjugate of X(11126)
X(33530) = {X(5),X(343)}-harmonic conjugate of X(33529)


X(33531) =  X(2)X(31361)∩X(4)X(20208)

Barycentrics    (3*a^4-2*(b^2+c^2)*a^2-(b^2-c^2)^2)*(4*a^12-5*(b^2+c^2)*a^10-(11*b^4-30*b^2*c^2+11*c^4)*a^8+14*(b^4-c^4)*(b^2-c^2)*a^6+14*(b^2-c^2)^4*a^4-(b^4-c^4)*(b^2-c^2)*(25*b^4-34*b^2*c^2+25*c^4)*a^2+(9*b^4+22*b^2*c^2+9*c^4)*(b^2-c^2)^4) : :
Barycentrics    (S^2-2*SB*SC)*(7*S^2+16*R^2*(16*R^2-2*SA-7*SW)+8*SA^2-5*SB*SC+12*SW^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29165.

X(33531) lies on these lines: {2, 31361}, {4, 20208}, {5, 11204}, {5893, 20204}, {5895, 20207}

X(33531) = complement of the complement of X(33893)


X(33532) =  X(2)X(3)∩X(394)X(5609)

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 + 12*a^2*b^4*c^2 + 6*b^6*c^2 + 12*a^2*b^2*c^4 - 10*b^4*c^4 + 2*a^2*c^6 + 6*b^2*c^6 - c^8) : :
X(33532) = 7 X[3] - 3 X[1597],X[11472] - 3 X[31884]

As a point on the Euler line, X(33532) has Shinagawa coefficients (7E+4F,-13E-4F).

X(33532) lies on these lines: {2, 3}, {394, 5609}, {511, 8547}, {541, 12584}, {1350, 2930}, {1498, 10627}, {2777, 15577}, {2979, 14094}, {3098, 14915}, {4550, 14810}, {5473, 13859}, {5474, 13858}, {6000, 15581}, {6781, 9609}, {7706, 29317}, {9695, 18512}, {9925, 13754}, {11456, 13340}, {11472, 31884}, {11477, 13391}, {12315, 31834}, {13233, 23698}, {14128, 15811}, {15034, 26881}, {15311, 15582}, {15644, 32139}, {17702, 32305}, {18445, 23061}, {32247, 32254}

X(33532) = reflection of X(4550) and X(14810)
X(33532) = X(3)-of-tangential-triangle-of-Thomson-triangle
X(33532) = X(26)-of-Thomson-triangle
X(33532) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 23, 6644}, {3, 546, 13154}, {3, 5198, 632}, {3, 7387, 12106}, {3, 11284, 549}, {3, 12082, 7530}, {3, 12083, 23}, {3, 14070, 18571}, {3, 18534, 11284}, {3, 31861, 7514}, {20, 7492, 7464}, {23, 376, 3}, {376, 12083, 6644}, {548, 12106, 3}, {550, 11414, 26}, {1657, 10323, 7526}, {3528, 12087, 7506}, {3529, 16661, 3}, {7464, 7492, 3}, {7502, 15686, 21312}


X(33533) =  X(2)X(3581)∩X(3)X(74)

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 - 2*a^4*b^2*c^2 + 4*a^2*b^4*c^2 - b^6*c^2 - 3*a^4*c^4 + 4*a^2*b^2*c^4 + 6*b^4*c^4 + 5*a^2*c^6 - b^2*c^6 - 2*c^8) : :
X(33533) = X[6] - 3 X[7514],X[1350] + 3 X[32620],7 X[3619] - 3 X[18420],X[11472] + 3 X[31884],X[31861] - 3 X[32620]

X(33533) lies on these lines: {2, 3581}, {3, 74}, {5, 32269}, {6, 1154}, {22, 15060}, {26, 14128}, {30, 141}, {140, 11438}, {143, 7395}, {323, 14805}, {381, 15107}, {511, 12039}, {549, 11064}, {550, 16655}, {567, 11004}, {568, 7550}, {1204, 15712}, {1216, 11430}, {1350, 31861}, {1352, 12367}, {1495, 5891}, {1598, 11017}, {1656, 7691}, {1658, 11793}, {1660, 11204}, {2070, 10546}, {2937, 15056}, {3153, 18427}, {3431, 18882}, {3530, 7689}, {3531, 11479}, {3567, 12307}, {3619, 18420}, {3620, 30522}, {3917, 10564}, {5054, 5888}, {5055, 10545}, {5092, 13754}, {5447, 11250}, {5562, 32046}, {5650, 32110}, {5651, 7575}, {5889, 15037}, {5907, 7525}, {6101, 7503}, {6102, 7509}, {6636, 12112}, {6643, 13561}, {7393, 12006}, {7507, 13565}, {7512, 15052}, {7516, 13630}, {7526, 10627}, {7527, 13340}, {7712, 10540}, {9786, 13154}, {9818, 13391}, {10095, 17834}, {10170, 12106}, {10982, 13421}, {11414, 32137}, {11472, 31884}, {12017, 20806}, {13445, 15688}, {13564, 15058}, {14786, 31815}, {14810, 14915}, {15032, 18436}, {15045, 32608}, {15053, 15694}, {15062, 15696}, {17811, 18324}, {19127, 19140}

X(33533) = midpoint of X(i) and X(j) for these lines: {i,j}: {1350, 31861}, {3098, 4550}
X(33533) = X(5)-of-tangential-triangle-of-Thomson-triangle
X(33533) = X(156)-of-Thomson-triangle
X(33533) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 399, 15080}, {3, 11591, 156}, {3, 15066, 1511}, {1350, 32620, 31861}, {1511, 15067, 15066}, {11459, 15080, 399}, {11592, 32210, 3}, {14805, 23039, 323}


X(33534) =  X(3)X(5646)∩X(6)X(30)

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 - 44*a^4*b^2*c^2 + 28*a^2*b^4*c^2 + 20*b^6*c^2 + 6*a^4*c^4 + 28*a^2*b^2*c^4 - 42*b^4*c^4 - 4*a^2*c^6 + 20*b^2*c^6 + c^8) : :
X(33534) = 3 X[1597] - 4 X[5092],3 X[5085] - 4 X[8717],2 X[11472] - 3 X[31884]

X(33534) lies on these lines: {3, 5646}, {5, 16936}, {6, 30}, {20, 15052}, {74, 12082}, {154, 10564}, {161, 12379}, {323, 15683}, {394, 11001}, {399, 1498}, {511, 11820}, {550, 15811}, {1181, 5059}, {1350, 12367}, {1370, 1514}, {1495, 21312}, {1533, 31152}, {1597, 5092}, {1620, 17714}, {3098, 3426}, {3146, 15018}, {3529, 11456}, {3534, 17811}, {3830, 17825}, {4550, 20987}, {5085, 8717}, {5422, 15640}, {6000, 9924}, {9786, 14641}, {10601, 15682}, {10605, 15107}, {10606, 12083}, {11413, 15051}, {11472, 31884}, {14855, 17810}, {15068, 15704}, {15681, 18451}, {18534, 31860}

X(33534) = reflection of X(3426) in X(3098)
X(33534) = X(17834)-of-Thomson-triangle
X(33534) = X(20)-of-tangential-triangle-of-Thomson-triangle


X(33535) =  X(1)X(3024)∩X(3)X(191)

Barycentrics    a*(a^9 - a^8*b + 2*a^6*b^3 - 6*a^5*b^4 + 8*a^3*b^6 - 2*a^2*b^7 - 3*a*b^8 + b^9 - a^8*c + 2*a^7*b*c - 2*a^5*b^3*c + 2*a^4*b^4*c - 2*a^3*b^5*c + 2*a*b^7*c - b^8*c + 9*a^5*b^2*c^2 - 3*a^4*b^3*c^2 - 7*a^3*b^4*c^2 + 5*a^2*b^5*c^2 - 2*a*b^6*c^2 - 2*b^7*c^2 + 2*a^6*c^3 - 2*a^5*b*c^3 - 3*a^4*b^2*c^3 + 6*a^3*b^3*c^3 - 3*a^2*b^4*c^3 - 2*a*b^5*c^3 + 2*b^6*c^3 - 6*a^5*c^4 + 2*a^4*b*c^4 - 7*a^3*b^2*c^4 - 3*a^2*b^3*c^4 + 10*a*b^4*c^4 - 2*a^3*b*c^5 + 5*a^2*b^2*c^5 - 2*a*b^3*c^5 + 8*a^3*c^6 - 2*a*b^2*c^6 + 2*b^3*c^6 - 2*a^2*c^7 + 2*a*b*c^7 - 2*b^2*c^7 - 3*a*c^8 - b*c^8 + c^9) : :
X(33535) = 2 X[110] - 3 X[3576],4 X[113] - 5 X[8227],4 X[125] - 3 X[5587],3 X[165] - 4 X[12041],3 X[165] - 2 X[12778],4 X[1511] - 5 X[7987],5 X[1698] - 6 X[15061],3 X[1699] - 2 X[7728],3 X[1699] - 4 X[12261],3 X[3576] - 4 X[11709],2 X[3579] - 3 X[15041],7 X[3624] - 6 X[14643],3 X[5587] - 2 X[12368],4 X[5609] - 7 X[30389],2 X[5655] - 3 X[25055],3 X[5731] - X[14683],X[5881] - 4 X[16003],8 X[6699] - 7 X[31423],2 X[7978] - 3 X[16200],X[7982] + 2 X[15054],7 X[7989] - 8 X[20304],7 X[9624] - 8 X[11735],7 X[9624] - 4 X[15063],2 X[9970] - 3 X[16475],3 X[10246] - 2 X[11699],3 X[10246] - X[12308],4 X[13624] - 3 X[32609],6 X[14644] - 5 X[18492],7 X[15039] - 10 X[31666],5 X[15040] - 6 X[17502],5 X[15081] - 4 X[19925]

X(33535) lies on the circumcircle of the hexyl triangle and on these lines: {1, 3024}, {3, 191}, {4, 13605}, {40, 74}, {57, 10081}, {64, 2778}, {110, 3576}, {113, 8227}, {125, 5587}, {146, 946}, {165, 12041}, {265, 5691}, {355, 10264}, {399, 1385}, {515, 3448}, {516, 12244}, {517, 9904}, {518, 16010}, {541, 31162}, {912, 12302}, {944, 12317}, {1350, 2836}, {1420, 10091}, {1511, 7987}, {1697, 10065}, {1698, 15061}, {1699, 7728}, {2077, 13204}, {2099, 11670}, {2772, 5494}, {2784, 18331}, {2931, 9626}, {2935, 12262}, {3031, 9548}, {3043, 9622}, {3047, 9621}, {3579, 15041}, {3586, 12904}, {3601, 10088}, {3624, 14643}, {3679, 20126}, {3751, 11579}, {4297, 12383}, {5609, 30389}, {5655, 25055}, {5731, 14683}, {5847, 32247}, {5881, 13211}, {5902, 7986}, {6001, 9625}, {6264, 8674}, {6699, 31423}, {7701, 11101}, {7731, 31732}, {7978, 16200}, {7982, 7984}, {7989, 20304}, {9610, 12888}, {9611, 10118}, {9612, 12373}, {9613, 12903}, {9614, 12374}, {9615, 10819}, {9618, 10817}, {9624, 11735}, {9864, 15357}, {9928, 12901}, {9970, 16475}, {10246, 11699}, {11012, 22586}, {11710, 15342}, {11720, 14094}, {12273, 31738}, {12902, 28160}, {13171, 15177}, {13624, 32609}, {14644, 18492}, {14982, 32238}, {15039, 31666}, {15040, 17502}, {15081, 19925}, {18481, 32423}

X(33535) = midpoint of X(i) and X(j) for these lines: {i,j}: {944, 12317}, {7984, 15054}
X(33535) = reflection of X(i) in X(j) for these lines: {i,j}: {4, 13605}, {40, 74}, {110, 11709}, {146, 946}, {355, 10264}, {399, 1385}, {2935, 12262}, {2948, 3}, {3679, 20126}, {3751, 11579}, {5691, 265}, {5693, 10693}, {5881, 13211}, {7728, 12261}, {7731, 31732}, {7982, 7984}, {9864, 15357}, {9904, 10620}, {9928, 12901}, {12273, 31738}, {12308, 11699}, {12368, 125}, {12383, 4297}, {12407, 3448}, {12778, 12041}, {13211, 16003}, {14094, 11720}, {14982, 32238}, {15063, 11735}, {15342, 11710}
X(33535) = X(1141)-of-hexyl-triangle
X(33535) = X(31656)-of-excentral-triangle
X(33535) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 11709, 3576}, {125, 12368, 5587}, {7728, 12261, 1699}, {10246, 12308, 11699}, {12041, 12778, 165}


X(33536) =  X(1)X(916)∩X(4)X(9)

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

X(33536) lies on these lines: {1, 916}, {3, 25878}, {4, 9}, {5, 1715}, {55, 4551}, {57, 1779}, {64, 405}, {65, 1736}, {84, 18650}, {307, 946}, {579, 3332}, {581, 2293}, {1012, 1350}, {1213, 1547}, {1214, 10374}, {1503, 1765}, {1699, 24310}, {1709, 10319}, {1730, 8226}, {1764, 8727}, {1830, 7069}, {2328, 4219}, {2772, 5494}, {3198, 5927}, {3560, 12163}, {5733, 18164}, {5752, 6769}, {5779, 21362}, {5803, 15299}, {5805, 20367}, {6883, 11472}, {7420, 7688}, {7489, 10620}, {8053, 10902}, {8227, 18634}, {12307, 13743}, {18673, 31803}, {19541, 21363}, {25362, 31162}

X(33536) = reflection of X(i) in X(j) for these lines: {i,j}: {40, 71}, {17220, 946}
X(33536) = X(311)-of-hexyl-triangle
X(33536) = {X(11471),X(12514)}-harmonic conjugate of X(40)

leftri

Points on the Stammler reflection hyperbola: X(35537)-X(35543)

rightri

Centers X(35537)-X(35543) were contributed by Peter Moses, July 11, 2019.

The name Stammler reflection hyperbola, denoted by SRH, refers to the reflection of the Stammler hyperbola in X(3). Let T be the hexyl triangle. Then SRH is the circumhyperbola of T that passes through the orthocenter and nine-point center of T; i.e., SRH = ABCHN-of-T. Moreover,

SRH = Feuerbach hyperbola of tangential triangle of Thomson triangle
SRH = isogonal conjugate of the Euler line of ABC wrt the tangential triangle of Thomson triangle

SHR has center X(74), perspector X(2693), and equation

b^2 c^2 (b^2-c^2) ((3 a^4-2 a^2 b^2-b^4-2 a^2 c^2+2 b^2 c^2-c^4) x^2 + 4 a^2 (-a^2+b^2+c^2) y z) + (cyclic) = 0

SRH passes through the vertices of these triangles:

hexyl (TCCT 6.36)
excentral triangle of Thomson triangle (CTC Q113)
tangential triangle of Thomson triangle
anti-Hutson intouch triangle (see X(11363))

SRH passes through X(i) for these i: 3, 40, 64, 1350, 2574, 2575, 5373, 5646, 9914, 10117, 10620, 11472, 12163, 12301, 12302, 12307, 14926, 15622, 16010, 19376, 22549, 32345, 33535, 33536, 33537, 33538, 33539, 33540, 33541, 33542, 33543

Suppose that P = p : q : r (barycentrics). Define the Gibert-Euler→SRH mapping by GE(P) = a^2(8 b^2 c^2 p^2 - 2 c^2 (a^2 - c^2) q^2 - 2 b^2 (a^2 - b^2) r^2 - (a^2 (a^2 - b^2 - c^2) - 4 b^2 c^2) q r - b^2 (a^2 - b^2 - 7 c^2) r p - c^2 (a^2 - 7 b^2 - c^2) p q) : : . If P is on the Euler line, then GE(P) is on SRH. The appearance of k(i,j) in the following list means that GE(X(i)) = X(j):

(2,5646), (3,3), (4,11472), (20,1350), (21,33538), (23,10117), (30,10620), (546,33539), (550,33544), (3090, 33540), (3091,33537), (3146,64), (3529,12163), (3627,33541), (6912,33536), (7464,12302), (12086,32345), (12103,33542), (14156,2574), (15157,2575), (15704,12307), (17538,33543), (33557,40)


X(33537) =  X(2)X(64)∩X(3)X(13474)

Barycentrics    a^2*(a^4 + 2*a^2*b^2 - 3*b^4 + 2*a^2*c^2 + 6*b^2*c^2 - 3*c^4)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 6*b^2*c^2 + c^4) : :
X(33537) = 3 X[2] + X[11469],2 X[3] + X[22334],5 X[3091] - X[15741],3 X[5085] - 4 X[31521],3 X[10516] - 2 X[15435]

X(33537) lies on the Jerabek circumhyperbola of the medial triangle and on these lines: {2, 64}, {3, 13474}, {4, 141}, {5, 9786}, {6, 5907}, {20, 16656}, {26, 32620}, {40, 936}, {110, 14528}, {113, 1656}, {125, 17818}, {140, 11472}, {154, 7503}, {155, 1493}, {185, 17825}, {206, 1498}, {378, 22549}, {381, 1209}, {394, 15056}, {1147, 9818}, {1151, 10960}, {1152, 10962}, {1181, 5622}, {1192, 5020}, {1204, 11284}, {1511, 7526}, {1593, 17811}, {1597, 11793}, {1853, 6816}, {2050, 21628}, {3066, 5068}, {3090, 10605}, {3091, 15741}, {3516, 5651}, {3523, 5646}, {3763, 6823}, {3917, 11403}, {4550, 6642}, {5013, 11672}, {5059, 21766}, {5102, 10982}, {5562, 8542}, {5663, 15805}, {5895, 6815}, {6247, 6804}, {6310, 19602}, {6803, 15311}, {7392, 13568}, {7484, 11381}, {7485, 11439}, {7509, 8718}, {8567, 10117}, {9704, 11597}, {9914, 10606}, {10170, 12085}, {10323, 16261}, {10601, 12111}, {10639, 11480}, {10640, 11481}, {11017, 13861}, {11438, 11484}, {11441, 17809}, {12241, 15069}, {13093, 16836}, {13598, 29959}, {14128, 31861}, {14924, 15054}, {14926, 15720}, {19547, 31787}

X(33537) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 11821}, {11469, 15740}, {16936, 22334}
X(33537) = reflection of X(i) in X(j) for these lines: {i,j}: {9815, 5}, {16936, 3}
X(33537) = complement of X(15740)
X(33537) = medial-isogonal conjugate of X(6823)
X(33537) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 6823}, {1496, 3}, {1593, 10}, {1973, 5286}, {5065, 1214}, {17811, 18589}, {32000, 2887}
X(33537) = crosspoint of X(2) and X(32000)
X(33537) = barycentric product X(i)*X(j) for these lines: {i,j}: {3091, 17811}, {17810, 32830}
X(33537) = barycentric quotient X(5065)/X(14528)
X(33537) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11469, 15740}, {1498, 7395, 5085}, {5907, 11479, 6}, {7395, 15030, 1498}, {9818, 17814, 11425}


X(33538) =  X(21)X(40)∩X(110)X(3576)

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

X(33538) lies on these lines: {21, 40}, {110, 3576}, {1175, 3601}, {1350, 16370}, {5127, 13384}, {10620, 28443}, {11472, 28466}, {14636, 32237}, {15622, 17524}


X(33539) =  X(3)X(11439)∩X(4)X(12307)

Barycentrics    a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 + 9*a^4*b^2*c^2 + a^2*b^4*c^2 - 10*b^6*c^2 - 6*a^4*c^4 + a^2*b^2*c^4 + 26*b^4*c^4 + 8*a^2*c^6 - 10*b^2*c^6 - 3*c^8) : :
X(33539) = 5 X[1656] - 2 X[14861]

X(33539) lies on these lines: {3, 11439}, {4, 12307}, {5, 146}, {54, 399}, {64, 1656}, {74, 11017}, {185, 19348}, {195, 11424}, {381, 5449}, {382, 1350}, {546, 32608}, {575, 12162}, {631, 14926}, {2937, 4550}, {3167, 12301}, {3526, 11472}, {3851, 11704}, {5055, 18504}, {5093, 8548}, {5643, 13630}, {5663, 15047}, {5876, 12316}, {6759, 32345}, {11440, 21308}, {12017, 12315}, {12038, 12302}, {12111, 15038}, {12308, 13434}, {13564, 16194}, {15041, 15062}, {15054, 32205}, {16261, 18378}, {19362, 21650}

X(33539) = {X(74),X(11017)}-harmonic conjugate of X(22462)


X(33540) =  X(2)X(12163)∩X(3)X(32062)

Barycentrics   a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 - 12*a^4*b^2*c^2 + 28*a^2*b^4*c^2 - 16*b^6*c^2 - 6*a^4*c^4 + 28*a^2*b^2*c^4 + 38*b^4*c^4 + 8*a^2*c^6 - 16*b^2*c^6 - 3*c^8) : :

X(33540) lies on these lines: {2, 12163}, {3, 32062}, {5, 1350}, {20, 18489}, {40, 6911}, {64, 140}, {155, 5050}, {547, 17834}, {576, 11793}, {631, 11472}, {1216, 3527}, {1498, 13154}, {1656, 3574}, {3526, 6699}, {3530, 5646}, {3855, 21766}, {5092, 6759}, {5609, 10541}, {5891, 15805}, {6804, 12318}, {7395, 12301}, {7503, 12302}, {7509, 26881}, {7514, 17821}, {7526, 22549}, {11444, 12834}, {11591, 17825}, {12315, 16419}, {13565, 17846}


X(33541) =  X(3)X(6030)∩X(4)X(10264)

Barycentrics    a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 + 13*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 6*b^6*c^2 - 6*a^4*c^4 - 7*a^2*b^2*c^4 + 18*b^4*c^4 + 8*a^2*c^6 - 6*b^2*c^6 - 3*c^8) : :
X(33541) = 7 X[3] - 6 X[6030],3 X[3] - 2 X[8718],X[3] + 2 X[16835],3 X[381] - 2 X[3521],3 X[381] - 4 X[18488],9 X[6030] - 7 X[8718],3 X[6030] - 7 X[15062],3 X[6030] + 7 X[16835],X[8718] - 3 X[15062],X[8718] + 3 X[16835],3 X[11459] - X[15086]

X(33541) lies on these lines: {3, 6030}, {4, 10264}, {30, 2888}, {40, 5694}, {64, 381}, {74, 13621}, {110, 7666}, {140, 14926}, {143, 15054}, {185, 15038}, {195, 5663}, {378, 9704}, {382, 9927}, {399, 1147}, {576, 16010}, {1204, 7545}, {1350, 1657}, {1593, 2904}, {1656, 11472}, {2070, 11381}, {3357, 10117}, {3426, 7517}, {3830, 18379}, {3851, 7703}, {5050, 13093}, {5092, 10575}, {5646, 15720}, {5876, 15103}, {5899, 11440}, {6000, 10274}, {7506, 9914}, {9786, 15752}, {10539, 15040}, {11250, 32609}, {11403, 13321}, {11455, 18378}, {11459, 15086}, {12162, 18859}, {12164, 12301}, {12280, 13391}, {12834, 13630}, {13564, 14915}, {13596, 14627}, {16194, 18369}

X(33541) = midpoint of X(15062) and X(16835)
X(33541) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 15062}, {1657, 18442}, {3521, 18488}, {10620, 11559}, {15103, 5876}
X(33541) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 32137, 13621}, {3521, 18488, 381}, {11455, 32138, 18378}


X(33542) =  X(3)X(143)∩X(4)X(14926)

Barycentrics    a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 - 23*a^4*b^2*c^2 + 17*a^2*b^4*c^2 + 6*b^6*c^2 - 6*a^4*c^4 + 17*a^2*b^2*c^4 - 6*b^4*c^4 + 8*a^2*c^6 + 6*b^2*c^6 - 3*c^8) : :
X(33542) = 5 X[3] - 2 X[1173],2 X[550] + X[2889],4 X[1173] - 5 X[15047]

X(33542) lies on these lines: {3, 143}, {4, 14926}, {64, 3534}, {195, 10984}, {376, 12307}, {399, 8718}, {548, 32608}, {550, 2889}, {1593, 11817}, {1656, 5646}, {1657, 11472}, {2070, 13348}, {3431, 7525}, {7691, 15041}, {9704, 10323}, {9914, 32063}, {10117, 10282}, {11204, 32345}, {11592, 22462}, {12163, 15696}, {14093, 17834}

X(33542) = reflection of X(15047) and X(3)


X(33543) =  X(3)X(51)∩X(5)X(5646)

Barycentrics    a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 - 36*a^4*b^2*c^2 + 28*a^2*b^4*c^2 + 8*b^6*c^2 - 6*a^4*c^4 + 28*a^2*b^2*c^4 - 10*b^4*c^4 + 8*a^2*c^6 + 8*b^2*c^6 - 3*c^8) : :
X(33543) = 3 X[3] - X[3527],7 X[3] - 3 X[5644],7 X[3527] - 9 X[5644],2 X[3527] - 3 X[15805],6 X[5644] - 7 X[15805]

X(33543) lies on these lines: {3, 51}, {5, 5646}, {20, 11472}, {40, 4880}, {64, 550}, {376, 6193}, {378, 11387}, {382, 14926}, {548, 1350}, {1216, 12315}, {1511, 10117}, {5663, 16936}, {6030, 10323}, {6759, 9914}, {7667, 12293}, {8703, 17834}, {10605, 10619}, {10620, 15696}, {12084, 31884}, {12302, 15055}, {15712, 17810}, {15811, 32142}, {17822, 17846}, {19348, 32607}

X(33543) = midpoint of X(20) and X(11487)
X(33543) = reflection of X(15805) and X(3)


X(33544) =  X(3)X(5640)∩X(30)X(14926)

Barycentrics   a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 - 51*a^4*b^2*c^2 + 41*a^2*b^4*c^2 + 10*b^6*c^2 - 6*a^4*c^4 + 41*a^2*b^2*c^4 - 14*b^4*c^4 + 8*a^2*c^6 + 10*b^2*c^6 - 3*c^8) : :
X(33544) = 5 X[3] - 2 X[5643],7 X[3] - 2 X[14483],7 X[5643] - 5 X[14483]

X(33544) lies on these lines: {3, 5640}, {30, 14926}, {40, 26201}, {64, 15696}, {376, 10620}, {381, 5646}, {399, 8717}, {548, 11271}, {1350, 15688}, {3066, 15700}, {3098, 15041}, {3534, 11472}, {7712, 32609}, {9914, 14530}, {10117, 11202}, {14810, 18859}, {15681, 21766}


X(33545) =  COMPLEMENT OF X(30484)

Barycentrics    S^4-(R^2*(28*R^2+5*SA-24*SW)-2*SA^2+7*SB*SC+5*SW^2)*S^2+(20*R^4-19*R^2*SW+5*SW^2)*SB*SC : :
X(33545) = 3*X(547)-2*X(32904), 5*X(3858)-X(15619)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33545) lies on these lines: {2, 30484}, {3, 24573}, {5, 11701}, {30, 13856}, {54, 137}, {546, 8254}, {547, 32904}, {1510, 12006}, {3858, 15619}, {5501, 25340}, {10285, 25150}

X(33545) = reflection of X(32536) in X(20414)
X(33545) = complement of X(30484)

X(33546) =  COMPLEMENT OF X(3183)

Barycentrics    (-a^2+b^2+c^2)*(a^14-(b^2-c^2)^2*a^10-14*(b^4-c^4)*(b^2-c^2)*a^8+(31*b^4+18*b^2*c^2+31*c^4)*(b^2-c^2)^2*a^6-4*(b^4-c^4)*(b^2-c^2)*(5*b^4-2*b^2*c^2+5*c^4)*a^4+(b^4+14*b^2*c^2+c^4)*(b^2-c^2)^4*a^2+2*(b^2+c^2)*(b^2-c^2)^6) : :
Barycentrics    SA*((24*R^2-5*SA+SW)*S^2+2*(SB+SC)*(16*(2*R^2-SA-SW)*R^2+3*SA^2-3*SB*SC+2*SW^2)) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33546) lies on these lines: {2, 3183}, {3, 1661}, {4, 1073}, {5, 6523}, {30, 20329}, {64, 122}, {381, 14059}, {382, 10745}, {1032, 3348}, {1657, 6760}, {1853, 8798}, {5895, 14379}, {5925, 12096}, {6260, 18589}

X(33546) = midpoint of X(4) and X(3346)
X(33546) = reflection of X(6523) in X(5)
X(33546) = complement of X(3183)
X(33546) = {X(5894), X(31377)}-harmonic conjugate of X(3)

X(33547) =  COMPLEMENT OF X(12893)

Barycentrics    SA*(8*(4*R^2-SA)*S^2+(SB+SC)*((54*R^2-33*SA-29*SW)*R^2+8*SA^2-8*SB*SC+4*SW^2)) : :
X(33547) = X(68)-5*X(15081), 3*X(381)+X(12302), 5*X(1656)-X(2931), 3*X(2072)+X(32123), 7*X(3090)+X(12319), X(3448)+3*X(5654), 9*X(5055)-X(12310), X(5504)+3*X(14644), X(7689)-3*X(15061), X(9927)-3*X(14644), X(13293)-3*X(18281), 3*X(14643)+X(15133), 5*X(15027)+X(15083), 9*X(23515)-X(32263)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33547) lies on these lines: {2, 12893}, {3, 19479}, {4, 12901}, {5, 1511}, {68, 15081}, {110, 7577}, {113, 1594}, {125, 1568}, {381, 12302}, {403, 12295}, {539, 11804}, {541, 23315}, {542, 20300}, {858, 16111}, {1209, 10170}, {1656, 2931}, {2777, 13371}, {3047, 25739}, {3090, 12319}, {3448, 5654}, {3564, 20301}, {3574, 16222}, {5055, 12310}, {5448, 5663}, {5449, 11591}, {5504, 9927}, {6639, 22109}, {6699, 11585}, {7689, 15061}, {7741, 12888}, {7951, 19469}, {9820, 32423}, {10024, 16163}, {10182, 13406}, {10254, 12121}, {10264, 22660}, {10576, 12891}, {10577, 12892}, {10663, 16966}, {10664, 16967}, {10721, 31074}, {10733, 16868}, {13289, 18569}, {13293, 18281}, {14643, 15133}, {14708, 18388}, {14915, 15125}, {14984, 15088}, {15027, 15083}, {18404, 32607}, {23336, 25564}

X(33547) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 19479}, {4, 12901}, {5, 23306}, {5504, 9927}, {7687, 15115}, {10264, 22660}, {13289, 18569}
X(33547) = reflection of X(i) in X(j) for these (i,j): (5449, 20304), (25564, 23336), (32743, 10224)
X(33547) = complement of X(12893)
X(33547) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (125, 1568, 7723), (5504, 14644, 9927)

X(33548) =  X(5)X(39)∩X(125)X(33330)

Barycentrics    S^6-(20*R^2*SW-SB*SC-4*SW^2)*S^4-(2*R^2*(3*SA^2-5*SA*SW+3*SW^2)-SW*(2*SA^2-2*SA*SW+SW^2))*SW*S^2-(2*R^2-SW)*SB*SC*SW^3 : :
X(33548) = 5*X(1656)-X(3511)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33548) lies on these lines: {5, 39}, {125, 33330}, {290, 7752}, {626, 5449}, {1656, 3511}


X(33549) =  COMPLEMENT OF X(15319)

Barycentrics    (S^2+(4*R^2+2*SA-3*SW)*SA)*(3*S^2-SB*SC)*SB*SC : :
X(33549) = X(4)-5*X(3462)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33549) lies on the cubic K569 and these lines: {2, 15319}, {4, 54}, {133, 16252}, {548, 3184}, {800, 11062}, {1075, 10182}, {3526, 6709}, {5878, 16253}, {10192, 14363}, {10303, 20213}

X(33549) = complement of X(15319)
X(33549) = complementary conjugate of X(32767)

X(33550) =  X(6)X(5054)∩X(18800)X(32455)

Barycentrics    (8*a^2-b^2-c^2)*(2*a^4-7*(b^2+c^2)*a^2+3*(b^2-c^2)^2) : :
Barycentrics    (9*SA-7*SW)*(6*S^2+(SB+SC)*SW) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33550) lies on these lines: {6, 5054}, {18800, 32455}


X(33551) =  X(55)X(16296)∩X(72)X(519)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33551) lies on these lines: {55, 16296}, {72, 519}, {145, 6018}, {390, 1682}, {3601, 21214}, {3664, 17609}, {5903, 12109}


X(33552) =  X(511)X(26869)∩X(1196)X(9177)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33552) lies on these lines: {511, 26869}, {1196, 9177}, {7484, 9734}


X(33553) =  COMPLEMENT OF X(18848)

Barycentrics    (-a^2+b^2+c^2)*(a^6-3*(b^2-c^2)^2*a^2+2*(b^4-c^4)*(b^2-c^2))*(4*a^8-5*(b^2+c^2)*a^6-(b^4-10*b^2*c^2+c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4) : :
Barycentrics    SA*(16*R^2-SA-3*SW)*(2*S^2+(SB+SC)*(16*R^2-SA-4*SW)) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33553) lies on these lines: {2, 18848}, {4, 12096}, {20, 6389}, {185, 520}, {216, 31829}, {550, 10600}, {5894, 15526}

X(33553) = complement of X(18848)

X(33554) =  X(6)X(5055)∩X(193)X(26613)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33554) lies on these lines: {6, 5055}, {193, 26613}, {3054, 15850}, {3629, 18800}, {5107, 6776}


X(33555) =  X(5)X(7743)∩X(5882)X(30198)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33555) lies on these lines: {5, 7743}, {5882, 30198}


X(33556) =  COMPLEMENT OF X(32533)

Barycentrics    a^2*(3*a^4-6*(b^2+c^2)*a^2+3*b^4+4*b^2*c^2+3*c^4)*(3*a^4-(b^2+c^2)*a^2-2*(b^2-c^2)^2) : :
Barycentrics    (SB+SC)*(S^2-5*SA^2)*(S^2-5*SB*SC) : :
X(33556) = 5*X(631)+3*X(25712)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29169.

X(33556) lies on these lines: {2, 32533}, {6, 12038}, {20, 113}, {110, 11270}, {140, 16254}, {141, 3530}, {184, 10937}, {206, 14810}, {548, 2883}, {631, 1209}, {960, 17502}, {1092, 11597}, {1511, 7689}, {1658, 6593}, {3526, 18396}, {3528, 6030}, {5206, 11672}, {5447, 6293}, {6759, 11598}, {7488, 17713}, {8542, 20190}, {8717, 17821}, {15083, 15646}, {15606, 18324}, {22966, 32171}

X(33556) = complement of X(32533)


X(33557) =  MIDPOINT OF X(6361) AND X(16116)

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 - 7*a^4*b*c + 4*a^2*b^3*c + a*b^4*c + 3*b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 + 4*a^2*b*c^3 - 6*b^3*c^3 + a^2*c^4 + a*b*c^4 - a*c^5 + 3*b*c^5) : :
X(33557) = 4 X[3] - 3 X[21],2 X[3] - 3 X[3651],7 X[3] - 6 X[5428],2 X[4] - 3 X[6175],7 X[21] - 8 X[5428],3 X[165] - 2 X[3647],6 X[442] - 5 X[3091],2 X[546] - 3 X[5499],3 X[1699] - 4 X[6701],3 X[2475] - X[3146],4 X[3579] - X[10308],X[3648] - 3 X[9778],7 X[3651] - 4 X[5428],3 X[5731] - 2 X[10543],X[7982] - 3 X[16132],X[7991] + 3 X[16143],7 X[15020] - 6 X[16164],2 X[22798] - 3 X[26446].

As a point on the Euler line, X(33557) has Shinagawa coefficients (2S2+3abc$a$, -2S2-6abc$a$).

X(33557) lies on these lines: {2, 3}, {35, 3947}, {40, 3681}, {46, 10394}, {79, 516}, {100, 16113}, {144, 3650}, {153, 31799}, {165, 3647}, {191, 2938}, {515, 5178}, {758, 6765}, {962, 3303}, {1155, 16141}, {1476, 21578}, {1479, 7677}, {1490, 3984}, {1621, 16125}, {1699, 6701}, {1770, 16152}, {2771, 15054}, {3058, 27197}, {3085, 7676}, {3219, 3579}, {3295, 11544}, {3304, 5731}, {3587, 3876}, {3648, 6223}, {3871, 5905}, {4297, 5441}, {5260, 7688}, {5284, 18483}, {5691, 12511}, {5709, 11220}, {5732, 10122}, {5752, 15072}, {7282, 20291}, {7701, 10860}, {7966, 7982}, {9943, 17637}, {10306, 20084}, {10884, 11518}, {10902, 28150}, {11495, 18253}, {12699, 31019}, {15020, 16164}, {16006, 20214}, {16138, 17613}, {22798, 26446}, {26202, 31663}

X(33557) = midpoint of X(6361) and X(16116)
X(33557) = reflection of X(i) in X(j) for these lines: {i,j}: {21, 3651}, {962, 3649}, {3652, 3579}, {5441, 4297}, {10308, 3652}, {11684, 40}, {12528, 31938}, {16113, 31730}, {16138, 22937}, {17637, 9943}, {26202, 31663}
X(33557) = anticomplement of X(37447)
X(33557) = crosssum of X(3270) and X(4979)
X(33557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4, 5047}, {3, 3146, 6912}, {3, 3149, 17572}, {3, 3627, 6920}, {3, 5047, 6986}, {3, 12104, 21161}, {3, 13743, 12104}, {3, 16862, 3523}, {3, 19541, 16862}, {3, 21669, 21}, {4, 7411, 6986}, {20, 411, 6909}, {20, 7580, 411}, {376, 6985, 404}, {404, 15678, 21}, {631, 16617, 15671}, {3522, 17572, 3}, {3651, 21669, 3}, {5047, 7411, 3}, {5428, 28461, 21}, {6895, 6907, 7548}, {6908, 10431, 6828}, {7688, 31673, 5260}, {13743, 21161, 21}


X(33558) =  MIDPOINT OF X(7) AND X(2886)

Barycentrics    2*a^5-2*(b+c)*a^4-(3*b^2-4*b*c+3*c^2)*a^3+(b+c)*(b^2-6*b*c+c^2)*a^2+(5*b^2+4*b*c+5*c^2)*(b-c)^2*a-3*(b^2-c^2)*(b-c)^3 : :
X(33558) = X(144)-5*X(31245), 3*X(6173)-X(8255)

See César Lozada, Hyacinthos 29171.

X(33558) lies on these lines: {1, 528}, {7, 2886}, {142, 6690}, {144, 31245}, {527, 3838}, {1376, 30275}, {2550, 5855}, {5173, 15587}, {5735, 28628}, {6667, 8257}, {20008, 30340}

X(33558) = midpoint of X(i) and X(j) for these lines: {i,j}: {7, 2886}, {5173, 15587}
X(33558) = reflection of X(6690) in X(142)
X(33558) = complement of complement of X(36971)


X(33559) =  MIDPOINT OF X(8) AND X(1329)

Barycentrics    (2*a^3-2*(b+c)*a^2-(b^2-8*b*c+c^2)*a+3*(b^2-c^2)*(b-c))*(-a+b+c) : :
X(33559) = 3*X(8)+X(2098), 3*X(10)-X(24928), X(46)-9*X(3679), X(46)-3*X(8256), X(56)-5*X(3617), X(145)-5*X(31246), 3*X(1329)-X(2098), X(3436)+7*X(4678), 3*X(3679)-X(8256), 3*X(4669)+X(21616), 3*X(5790)-X(7681), 3*X(6691)-2*X(24928)

See César Lozada, Hyacinthos 29171.

X(33559) lies on these lines: {8, 11}, {10, 6691}, {46, 529}, {56, 3617}, {145, 31246}, {496, 32426}, {517, 546}, {1145, 11010}, {2646, 6735}, {2829, 5690}, {3035, 21842}, {3333, 32049}, {3436, 4678}, {3625, 11545}, {3812, 11035}, {4669, 21616}, {5046, 13996}, {5790, 7681}, {6667, 22837}, {9711, 12647}, {11009, 17757}, {17768, 24393}

X(33559) = midpoint of X(8) and X(1329)
X(33559) = reflection of X(6691) in X(10)
X(33559) = complement of complement of X(36972)

X(33560) =  MIDPOINT OF X(13) AND X(623)

Barycentrics    2*a^6-8*(b^2+c^2)*a^4+(b^4-24*b^2*c^2+c^4)*a^2+5*(b^4-c^4)*(b^2-c^2)-2*sqrt(3)*S*(2*a^4+4*(b^2+c^2)*a^2-3*b^4+8*b^2*c^2-3*c^4) : :
Barycentrics    5*S^2-sqrt(3)*(SA-3*SW)*S+9*SB*SC : :
X(33560) = 3*X(13)+X(298), 5*X(13)+3*X(21359), X(298)-3*X(623), 5*X(298)-9*X(21359), X(396)-3*X(5459), X(396)+3*X(31693), X(621)+3*X(16267), 5*X(623)-3*X(21359), 3*X(5470)+X(5978)

See César Lozada, Hyacinthos 29171.

X(33560) lies on these lines: {2, 10646}, {3, 6673}, {5, 6670}, {13, 298}, {14, 7797}, {17, 617}, {30, 6669}, {115, 396}, {511, 20252}, {530, 625}, {533, 11542}, {546, 6694}, {547, 6672}, {618, 5318}, {619, 11303}, {621, 16267}, {629, 16965}, {633, 33465}, {3589, 5066}, {3642, 18582}, {3643, 11305}, {5470, 5978}, {11300, 16966}, {16241, 31704}, {16644, 22917}, {16645, 18584}, {20253, 25555}, {20377, 20415}

X(33560) = midpoint of X(i) and X(j) for these lines: {i,j}: {13, 623}, {618, 5318}, {619, 31709}, {5459, 31693}
X(33560) = reflection of X(6671) in X(6669)
X(33560) = complement of complement of X(36969)
X(33560) = {X(3589),X(5066)}-harmonic conjugate of X(33561)


X(33561) =  MIDPOINT OF X(14) AND X(624)

Barycentrics    2*a^6-8*(b^2+c^2)*a^4+(b^4-24*b^2*c^2+c^4)*a^2+5*(b^4-c^4)*(b^2-c^2)+2*sqrt(3)*S*(2*a^4+4*(b^2+c^2)*a^2-3*b^4+8*b^2*c^2-3*c^4) : :
Barycentrics    5*S^2+sqrt(3)*(SA-3*SW)*S+9*SB*SC : :
X(33561) = 3*X(14)+X(299), 5*X(14)+3*X(21360), X(299)-3*X(624), 5*X(299)-9*X(21360), X(395)-3*X(5460), X(395)+3*X(31694), X(622)+3*X(16268), 5*X(624)-3*X(21360), 3*X(5469)+X(5979)

See César Lozada, Hyacinthos 29171.

X(33561) lies on these lines: {2, 10645}, {3, 6674}, {5, 6669}, {13, 7797}, {14, 299}, {18, 616}, {30, 6670}, {115, 395}, {511, 20253}, {531, 625}, {532, 11543}, {546, 6695}, {547, 6671}, {618, 11304}, {619, 5321}, {622, 16268}, {630, 16964}, {634, 33464}, {3589, 5066}, {3642, 11306}, {3643, 18581}, {5469, 5979}, {11299, 16967}, {16242, 31703}, {16644, 18584}, {16645, 22872}, {20252, 25555}, {20378, 20416}

X(33561) = midpoint of X(i) and X(j) for these lines: {i,j}: {14, 624}, {618, 31710}, {619, 5321}, {5460, 31694}
X(33561) = reflection of X(6672) in X(6670)
X(33561) = complement of complement of X(36970)
X(33561) = {X(3589),X(5066)}-harmonic conjugate of X(33560)


X(33562) =  MIDPOINT OF X(11) AND X(59)

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

See César Lozada, Hyacinthos 29171.

X(33562) lies on these lines: {11, 59}, {521, 3035}, {1090, 5723}, {6129, 23593}

X(33562) = midpoint of X(11) and X(59)
X(33562) = center of pedal circle of X(11) (and of X(59))

X(33563) =  MIDPOINT OF X(24) AND X(68)

Barycentrics    SA*((12*R^2-SA-SW)*S^2+(SB+SC)*(R^2*(2*R^2-7*SA-SW)+SA^2-SB*SC)) : :

See César Lozada, Hyacinthos 29171.

X(33563) lies on these lines: {468, 12421}, {597, 8254}, {1147, 13292}, {1495, 32145}, {1899, 32048}, {6353, 12420}, {10020, 22663}, {12134, 32539}, {12163, 31725}

X(33563) = midpoint of X(i) and X(j) for these lines: {i,j}: {24, 68}, {12163, 31725}
X(33563) = reflection of X(i) in X(j) for these (i,j): (1147, 16238), (11585, 5449)
X(33563) = center of pedal circle of X(24) (and of X(68))

X(33564) =  (name pending)

Barycentrics    a^2 (a^24 b^2-10 a^22 b^4+44 a^20 b^6-110 a^18 b^8+165 a^16 b^10-132 a^14 b^12+132 a^10 b^16-165 a^8 b^18+110 a^6 b^20-44 a^4 b^22+10 a^2 b^24-b^26+a^24 c^2-18 a^22 b^2 c^2+101 a^20 b^4 c^2-279 a^18 b^6 c^2+425 a^16 b^8 c^2-338 a^14 b^10 c^2+84 a^12 b^12 c^2+20 a^10 b^14 c^2+109 a^8 b^16 c^2-220 a^6 b^18 c^2+167 a^4 b^20 c^2-61 a^2 b^22 c^2+9 b^24 c^2-10 a^22 c^4+101 a^20 b^2 c^4-356 a^18 b^4 c^4+581 a^16 b^6 c^4-404 a^14 b^8 c^4-23 a^12 b^10 c^4+166 a^10 b^12 c^4-69 a^8 b^14 c^4+114 a^6 b^16 c^4-206 a^4 b^18 c^4+138 a^2 b^20 c^4-32 b^22 c^4+44 a^20 c^6-279 a^18 b^2 c^6+581 a^16 b^4 c^6-430 a^14 b^6 c^6-34 a^12 b^8 c^6+99 a^10 b^10 c^6+86 a^8 b^12 c^6-91 a^6 b^14 c^6+103 a^4 b^16 c^6-135 a^2 b^18 c^6+56 b^20 c^6-110 a^18 c^8+425 a^16 b^2 c^8-404 a^14 b^4 c^8-34 a^12 b^6 c^8+84 a^10 b^8 c^8+39 a^8 b^10 c^8+78 a^6 b^12 c^8-83 a^4 b^14 c^8+50 a^2 b^16 c^8-45 b^18 c^8+165 a^16 c^10-338 a^14 b^2 c^10-23 a^12 b^4 c^10+99 a^10 b^6 c^10+39 a^8 b^8 c^10+18 a^6 b^10 c^10+63 a^4 b^12 c^10-28 a^2 b^14 c^10+5 b^16 c^10-132 a^14 c^12+84 a^12 b^2 c^12+166 a^10 b^4 c^12+86 a^8 b^6 c^12+78 a^6 b^8 c^12+63 a^4 b^10 c^12+52 a^2 b^12 c^12+8 b^14 c^12+20 a^10 b^2 c^14-69 a^8 b^4 c^14-91 a^6 b^6 c^14-83 a^4 b^8 c^14-28 a^2 b^10 c^14+8 b^12 c^14+132 a^10 c^16+109 a^8 b^2 c^16+114 a^6 b^4 c^16+103 a^4 b^6 c^16+50 a^2 b^8 c^16+5 b^10 c^16-165 a^8 c^18-220 a^6 b^2 c^18-206 a^4 b^4 c^18-135 a^2 b^6 c^18-45 b^8 c^18+110 a^6 c^20+167 a^4 b^2 c^20+138 a^2 b^4 c^20+56 b^6 c^20-44 a^4 c^22-61 a^2 b^2 c^22-32 b^4 c^22+10 a^2 c^24+9 b^2 c^24-c^26) : :
Barycentrics    (10 R^4-30 R^2 SB-30 R^2 SC+22 R^2 SW+8 SB SW+8 SC SW-8 SW^2)S^4 + (180 R^8-15 R^6 SB-15 R^6 SC+50 R^4 SB SC-189 R^6 SW+14 R^4 SB SW+14 R^4 SC SW-38 R^2 SB SC SW+60 R^4 SW^2-2 R^2 SB SW^2-2 R^2 SC SW^2+8 SB SC SW^2-6 R^2 SW^3)S^2 + 100 R^8 SB SC-139 R^6 SB SC SW+64 R^4 SB SC SW^2-10 R^2 SB SC SW^3 : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29174.

X(33564) lies on this line: {1154,10126}


X(33565) =  ISOGONAL CONJUGATE OF X(2070)

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+a^2 b^4 c^2-2 b^6 c^2-a^2 b^2 c^4+2 a^2 c^6+2 b^2 c^6-c^8) (a^8-2 a^6 b^2+2 a^2 b^6-b^8-2 a^6 c^2+a^4 b^2 c^2-a^2 b^4 c^2+2 b^6 c^2+2 a^4 c^4+a^2 b^2 c^4-2 a^2 c^6-2 b^2 c^6+c^8) : :
Barycentrics    (12 R^4+7 R^2 SB+7 R^2 SC-11 R^2 SW-2 SB SW-2 SC SW+2 SW^2)S^2 + 9 R^4 SB SC-9 R^2 SB SC SW+2 SB SC SW^2 : :
Barycentrics    1/(sin B sin 3B + sin C sin 3C - sin A sin 3A) : :
Trilinears    1/((J^2 - 2) cos A + 4 cos B cos C) : :, where J is as at X(1113)

X(33565) = 3*X[2]-2*X[11597], X[54]-2*X[125], X[110]-2*X[1209], 3*X[381]-2*X[11805], 2*X[1493]-5*X[15027], 4*X[6689]-5*X[15059], X[7728]-2*X[22804], 2*X[10113]-X[15800], 2*X[10610]-3*X[15061], X[10721]-2*X[32340], X[11562]-2*X[11802], X[11702]-2*X[20304], 2*X[11801]-X[20424], X[12307]+X[12902], X[13368]+X[15101], 4*X[13565]-3*X[14643], 3*X[15035]-4*X[32348], 2*X[15647]-X[32359], X[19150]-2*X[20301]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29177.

X(33565) lies on the Jerabek hyperbola, the circumconic centered at X(1209), and also on these lines: {2,11597}, {3,2888}, {4,7730}, {6,2914}, {30,11559}, {54,125}, {64,12244}, {67,32353}, {68,12319}, {70,32346}, {71,21092}, {74,10421}, {110,1209}, {146,18550}, {195,10224}, {265,1154}, {381,11805}, {399,3410}, {511,18125}, {539,5504}, {542,1176}, {895,5965}, {1173,3574}, {1352,20125}, {1493,15027}, {1899,3431}, {1987,15340}, {2777,16835}, {2781,15321}, {3024,12956}, {3028,12946}, {3527,7547}, {3531,18386}, {4846,11442}, {5663,6288}, {6145,6242}, {6391,31180}, {6689,15059}, {6776,19151}, {7687,14483}, {7691,17702}, {7728,22804}, {9920,13171}, {10113,15800}, {10274,14940}, {10610,15061}, {10721,32340}, {10821,11245}, {11270,11457}, {11271,15317}, {11562,11802}, {11702,20304}, {11801,20424}, {12307,12902}, {12903,18984}, {12904,13079}, {13198,32377}, {13202,13603}, {13368,15101}, {13418,21660}, {13423,18381}, {13452,14216}, {13472,18912}, {13565,14643}, {14542,32334}, {15035,32348}, {15041,15332}, {15089,16867}, {15100,18474}, {15110,18434}, {15647,32359}, {15738,22466}, {16665,20379}, {16868,17824}, {17835,18559}, {18377,21400}, {19150,20301}, {22336,32274}

X(33565) = midpoint of X(13368) and X(15101)
X(33565) = reflection of X(i) in X(j) for these lines: {i,j}: {54,125}, {110,1209}, {195,11804}, {7728,22804}, {11562,11802}, {11702,20304}, {13417,11808}, {15800,10113}, {19150,20301}, {20424,11801}, {32359,15647}
X(33565) = isogonal conjugate of X(2070)
X(33565) = isotomic conjugate of isogonal conjugate of X(34448)
X(33565) = anticomplement of X(11597)
X(33565) = antigonal image of X(54)
X(33565) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {1,2070}, {1725,11557}, {6149,11597}
X(33565) = antipode in Jerabek hyperbola of X(54)
X(33565) = trilinear pole of line X(570)X(647)
X(33565) = polar conjugate of X(37766)
X(33565) = pole wrt polar circle of trilinear polar of X(37766) (line X(10214)X(11557))
X(33565) = X(12380)-of-orthocentroidal-triangle
X(33565) = X(7730)-of-anti-orthocentroidal-triangle
X(33565) = barycentric product X(3)*X(9381)
X(33565) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {6,2070}, {50,11597}, {184,9380}, {523,24978}, {2963,19552}, {3003,11557}, {9381,264}
X(33565) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {54,14076,6143}


X(33566) =  REFLECTION OF X(3) IN X(25640)

Barycentrics    a^13-a^12 b-2 a^11 b^2+2 a^10 b^3-a^9 b^4+a^8 b^5+4 a^7 b^6-4 a^6 b^7-a^5 b^8+a^4 b^9-2 a^3 b^10+2 a^2 b^11+a b^12-b^13-a^12 c+7 a^11 b c-4 a^10 b^2 c-8 a^9 b^3 c+13 a^8 b^4 c-12 a^7 b^5 c-6 a^6 b^6 c+14 a^5 b^7 c-5 a^4 b^8 c+5 a^3 b^9 c+2 a^2 b^10 c-6 a b^11 c+b^12 c-2 a^11 c^2-4 a^10 b c^2+20 a^9 b^2 c^2-14 a^8 b^3 c^2-18 a^7 b^4 c^2+30 a^6 b^5 c^2-14 a^5 b^6 c^2+2 a^4 b^7 c^2+12 a^3 b^8 c^2-18 a^2 b^9 c^2+2 a b^10 c^2+4 b^11 c^2+2 a^10 c^3-8 a^9 b c^3-14 a^8 b^2 c^3+52 a^7 b^3 c^3-20 a^6 b^4 c^3-22 a^5 b^5 c^3+30 a^4 b^6 c^3-40 a^3 b^7 c^3+6 a^2 b^8 c^3+18 a b^9 c^3-4 b^10 c^3-a^9 c^4+13 a^8 b c^4-18 a^7 b^2 c^4-20 a^6 b^3 c^4+46 a^5 b^4 c^4-28 a^4 b^5 c^4-10 a^3 b^6 c^4+40 a^2 b^7 c^4-17 a b^8 c^4-5 b^9 c^4+a^8 c^5-12 a^7 b c^5+30 a^6 b^2 c^5-22 a^5 b^3 c^5-28 a^4 b^4 c^5+70 a^3 b^5 c^5-32 a^2 b^6 c^5-12 a b^7 c^5+5 b^8 c^5+4 a^7 c^6-6 a^6 b c^6-14 a^5 b^2 c^6+30 a^4 b^3 c^6-10 a^3 b^4 c^6-32 a^2 b^5 c^6+28 a b^6 c^6-4 a^6 c^7+14 a^5 b c^7+2 a^4 b^2 c^7-40 a^3 b^3 c^7+40 a^2 b^4 c^7-12 a b^5 c^7-a^5 c^8-5 a^4 b c^8+12 a^3 b^2 c^8+6 a^2 b^3 c^8-17 a b^4 c^8+5 b^5 c^8+a^4 c^9+5 a^3 b c^9-18 a^2 b^2 c^9+18 a b^3 c^9-5 b^4 c^9-2 a^3 c^10+2 a^2 b c^10+2 a b^2 c^10-4 b^3 c^10+2 a^2 c^11-6 a b c^11+4 b^2 c^11+a c^12+b c^12-c^13 : :
X(33566) = 3*X[3]-4*X[6717], 2*X[5]-X[1295], 2*X[123]-3*X[381], 2*X[3627]-X[10731], 2*X[3845]-X[10715], X[10702]-2*X[22791], X[10763]-2*X[21850], X[10776]-2*X[22938], 2*X[11719]-X[18481], 4*X[11733]-5*X[18493]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29177.

X(33566) lies on these lines: {3,6717}, {4,280}, {5,1295}, {30,108}, {123,381}, {265,2778}, {382,2829}, {517,15499}, {1359,1479}, {1478,3318}, {2791,6321}, {2798,6033}, {2804,10742}, {2812,10741}, {2817,10747}, {2823,10739}, {2834,15521}, {2840,15522}, {2845,22337}, {2849,10740}, {2850,7728}, {2851,22338}, {3627,10731}, {3845,10715}, {9521,10743}, {9525,10744}, {9528,10745}, {9531,10748}, {10702,22791}, {10763,21850}, {10776,22938}, {11719,18481}, {11733,18493}

X(33566) = reflection of X(i) in X(j) for these lines: {i,j}: {3,25640}, {1295,5}, {10702,22791}, {10715,3845}, {10731,3627}, {10746,4}, {10763,21850}, {10776,22938}, {18481,11719}

X(33567) =  X(399)X(18319)∩X(1117)X(5663)

Barycentrics    (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^20-4 a^18 b^2-3 a^16 b^4+48 a^14 b^6-126 a^12 b^8+168 a^10 b^10-126 a^8 b^12+48 a^6 b^14-3 a^4 b^16-4 a^2 b^18+b^20-4 a^18 c^2+19 a^16 b^2 c^2-47 a^14 b^4 c^2+85 a^12 b^6 c^2-101 a^10 b^8 c^2+49 a^8 b^10 c^2+31 a^6 b^12 c^2-53 a^4 b^14 c^2+25 a^2 b^16 c^2-4 b^18 c^2+9 a^16 c^4-17 a^14 b^2 c^4+45 a^12 b^4 c^4-111 a^10 b^6 c^4+160 a^8 b^8 c^4-195 a^6 b^10 c^4+165 a^4 b^12 c^4-53 a^2 b^14 c^4-3 b^16 c^4-24 a^14 c^6-23 a^12 b^2 c^6+75 a^10 b^4 c^6-19 a^8 b^6 c^6+107 a^6 b^8 c^6-195 a^4 b^10 c^6+31 a^2 b^12 c^6+48 b^14 c^6+54 a^12 c^8+25 a^10 b^2 c^8-140 a^8 b^4 c^8-19 a^6 b^6 c^8+160 a^4 b^8 c^8+49 a^2 b^10 c^8-126 b^12 c^8-72 a^10 c^10+25 a^8 b^2 c^10+75 a^6 b^4 c^10-111 a^4 b^6 c^10-101 a^2 b^8 c^10+168 b^10 c^10+54 a^8 c^12-23 a^6 b^2 c^12+45 a^4 b^4 c^12+85 a^2 b^6 c^12-126 b^8 c^12-24 a^6 c^14-17 a^4 b^2 c^14-47 a^2 b^4 c^14+48 b^6 c^14+9 a^4 c^16+19 a^2 b^2 c^16-3 b^4 c^16-4 a^2 c^18-4 b^2 c^18+c^20) (a^20-4 a^18 b^2+9 a^16 b^4-24 a^14 b^6+54 a^12 b^8-72 a^10 b^10+54 a^8 b^12-24 a^6 b^14+9 a^4 b^16-4 a^2 b^18+b^20-4 a^18 c^2+19 a^16 b^2 c^2-17 a^14 b^4 c^2-23 a^12 b^6 c^2+25 a^10 b^8 c^2+25 a^8 b^10 c^2-23 a^6 b^12 c^2-17 a^4 b^14 c^2+19 a^2 b^16 c^2-4 b^18 c^2-3 a^16 c^4-47 a^14 b^2 c^4+45 a^12 b^4 c^4+75 a^10 b^6 c^4-140 a^8 b^8 c^4+75 a^6 b^10 c^4+45 a^4 b^12 c^4-47 a^2 b^14 c^4-3 b^16 c^4+48 a^14 c^6+85 a^12 b^2 c^6-111 a^10 b^4 c^6-19 a^8 b^6 c^6-19 a^6 b^8 c^6-111 a^4 b^10 c^6+85 a^2 b^12 c^6+48 b^14 c^6-126 a^12 c^8-101 a^10 b^2 c^8+160 a^8 b^4 c^8+107 a^6 b^6 c^8+160 a^4 b^8 c^8-101 a^2 b^10 c^8-126 b^12 c^8+168 a^10 c^10+49 a^8 b^2 c^10-195 a^6 b^4 c^10-195 a^4 b^6 c^10+49 a^2 b^8 c^10+168 b^10 c^10-126 a^8 c^12+31 a^6 b^2 c^12+165 a^4 b^4 c^12+31 a^2 b^6 c^12-126 b^8 c^12+48 a^6 c^14-53 a^4 b^2 c^14-53 a^2 b^4 c^14+48 b^6 c^14-3 a^4 c^16+25 a^2 b^2 c^16-3 b^4 c^16-4 a^2 c^18-4 b^2 c^18+c^20) : :
Barycentrics    (3 R^2+2 SB+2 SC-2 SW) (2 S^4 + (-54 R^4-18 R^2 SC+6 SC^2+36 R^2 SW-6 SW^2)S^2-243 R^6 SC+324 R^4 SC^2-108 R^2 SC^2 SW+18 R^2 SC SW^2+6 SC^2 SW^2) (4 S^4 +(378 R^4+18 R^2 SB+6 SB SC+6 SC^2-144 R^2 SW-6 SB SW-6 SC SW+12 SW^2)S^2 + 243 R^6 SB+324 R^4 SB SC+324 R^4 SC^2-324 R^4 SB SW-324 R^4 SC SW-108 R^2 SB SC SW-108 R^2 SC^2 SW+90 R^2 SB SW^2+108 R^2 SC SW^2+6 SB SC SW^2+6 SC^2 SW^2-6 SB SW^3-6 SC SW^3) : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29177.

X(33567) lies on these lines: {399,18319}, {1117,5663}

X(33567) = antigonal image of X(3470)

X(33568) =  X(2)X(824)∩X(4809)X(14402)

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

See Angel Montesdeoca, Hyacinthos 29181 and HG100719.

X(33568) lies on the cubic K219 and these lines: {2, 824}, {4809, 14402}


X(33569) =  X(2)X(647)∩X(684)X(2491)

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

See Angel Montesdeoca, Hyacinthos 29181 and HG100719.

X(33569) lies on the cubic K219 and these lines: {2, 647}, {684, 2491}


X(33570) =  X(2)X(650)∩X(647)X(1962)

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

See Angel Montesdeoca, Hyacinthos 29181 and HG100719.

X(33570) lies on the cubic K219 and these lines: {2, 650}, {647, 1962}


X(33571) =  X(2)X(216)∩X(1636)X(2972)

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

See Angel Montesdeoca, Hyacinthos 29181 and HG100719.

X(33571) lies on the cubic K219 and these lines: {2, 216}, {1636, 2972}


X(33572) =  X(2)X(92)∩X(7004)X(7117)

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

See Angel Montesdeoca, Hyacinthos 29181 and HG100719.

X(33572) lies on the cubic K219 and these lines: {2, 92}, {7004, 7117}


X(33573) =  REFLECTION OF X(14477) IN X(2)

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

See Angel Montesdeoca, Hyacinthos 29181 and HG100719.

X(33573) lies on the cubic K219 and these lines: {2, 7}, {11, 1146}

X(33573) = reflection of X(14477) in X(2)


X(33574) =  X(1)X(3)∩X(140)X(9947)

Barycentrics    a (-a^5 (b+c)+a^4 (b^2-20 b c+c^2)+2 a^3 (b^3+2 b^2 c+2 b c^2+c^3)-2 a^2 (b^4-11 b^3 c+4 b^2 c^2-11 b c^3+c^4)-a (b-c)^2 (b^3+5 b^2 c+5 b c^2+c^3)+(b-c)^4 (b+c)^2) : :
X(33574) = (4R+r) I + (8R-r) O

See Angel Montesdeoca, Hyacinthos 29188 and AoPS.

X(33574) lies on these lines: {1,3}, {140,9947}, {515,10156}, {551,10178}, {631,18908}, {971,10165}, {1125,15726}, {2801,5044}, {3555,15717}, {3646,12684}, {3817,3824}, {3848,28164}, {5265,7671}, {5886,21151}, {5918,25055}, {5927,16845}, {6916,18527}, {9858,30478}, {10864,16853}, {11220,17558}, {13369,31821}

X(33574) = midpoint of X(i) and X(j), for these lines: {i, j}: {165, 5049}, {551, 10178}, {3576, 11227}

X(33575) =  X(3)X(9)∩X(72)X(15717)

Barycentrics    a (a^5 (b+c)-a^4 (b^2+20 b c+c^2)-2 a^3 (b^3+c^3)+2 a^2 (b^4+11 b^3 c+11 b c^3+c^4)+a (b^5-b^4 c-b c^4+c^5)-(b-c)^2 (b+c)^4) : :
X(33575) = (8R-r) X(3) + (4R+r) X(9)

See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 29192.

X(33575) lies on these lines: {3,9}, {72,15717}, {140,5806}, {165,16417}, {376,10157}, {517,549}, {631,31793}, {912,12100}, {942,3523}, {1071,10299}, {2800,31787}, {3524,11227}, {3530,9940}, {3579,22753}, {3628,31822}, {3646,24644}, {3940,10857}, {5447,31816}, {5927,10304}, {6924,31663}, {6961,31786}, {9729,31819}, {10167,15692}, {10176,10178}, {10202,15693}, {10855,16371}, {11220,15705}, {15712,31837}, {16192,25917}

X(33575) = reflection of X(10156) in X(549)

X(33576) =  X(1)X(5927)∩X(4)X(9949)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29189.

X(33576) lies on the Feuerbach hyperbola and these lines: {1, 5927}, {4, 9949}, {7, 3832}, {8, 9580}, {9, 3983}, {21, 5438}, {72, 4900}, {80, 9589}, {84, 19541}, {90, 10860}, {104, 10864}, {226, 5558}, {950, 7320}, {1000, 5881}, {1155, 7285}, {1156, 5128}, {1172, 16670}, {1320, 11523}, {1728, 3065}, {1864, 5665}, {2320, 5436}, {2335, 16676}, {2346, 10384}, {3062, 5729}, {3296, 5714}, {3427, 31673}, {3577, 9856}, {3586, 5559}, {5225, 6601}, {5557, 9612}, {5560, 30286}, {7091, 17604}, {7160, 9947}, {7655, 23838}, {8581, 10390}, {9948, 10309}, {10398, 31507}


X(33577) =  (name pending)

Barycentrics    (SB+SC)*(S^2+SB*SC)*(5*(SA+SB)*R^2+SA*SB+SC^2-SW^2)*(5*(SA+SC)*R^2+SA*SC+SB^2-SW^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29189.

X(33577) lies on the line {1593, 18439}


X(33578) =  X(25)X(800)∩X(32)X(682)

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

X(33578) lies on these lines: {25, 800}, {32, 682}, {184, 13342}, {237, 5065}, {577, 19136}, {4232, 15594}, {5007, 19125}, {5158, 9969}, {5481, 14484}, {6467, 20897}, {13345, 18374}, {17810, 26880}, {19132, 30435}

X(33578) = isogonal conjugate of isotomic conjugate of X(17810)
X(33578) = X(561)-isoconjugate of X(14528)
X(33578) = crosssum of X(i) and X(j) for these (i,j): {20, 3618}, {69, 32830}, {394, 7485}
X(33578) = crossdifference of every pair of points on line {3267, 20580}
X(33578) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 17810}, {32, 3091}, {217, 19169}, {393, 26880}
X(33578) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {1501, 14528}, {3091, 1502}, {17810, 76}, {26880, 3926}


X(33579) =  X(3)X(206)∩X(253)X(6995)

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

X(33579) lies on the cubic K1110 and these lines: {3,206}, {253,6995}, {6523,18855}

X(33579) = barycentric quotient X(26880)/X(23115)


X(33580) =  X(3)X(3589)∩X(25)X(1249)

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

X(33580 lies on the cubic K1110 and these lines: {3,3589}, {25,1249}, {133,18535}, {1486,15621}, {1597,16253}, {1598,6523}, {1995,30698}, {7669,8573}, {9969,15851}, {17810,26880}

X(33580) = X(i)-complementary conjugate of X(j) for these (i,j): {2155, 3763}, {6995, 20308}, {19614, 7386}
X(33580) = X(107)-Ceva conjugate of X(3800)
X(33580) = barycentric product X(i)*X(j) for these lines: {i,j}: {3091, 30435}, {3618, 17810}
X(33580) = barycentric quotient X(17810)/X(18840)


X(33581) =  ISOGONAL CONJUGATE OF X(14615)

Barycentrics    a^4*(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) : :

X(33581) lies on the cubics K236 and K1111, and on these lines: {3, 64}, {6, 1661}, {20, 801}, {25, 800}, {31, 1410}, {98, 459}, {184, 5065}, {228, 1253}, {253, 1799}, {577, 1660}, {878, 8651}, {1402, 2212}, {1495, 2351}, {2200, 14827}, {3089, 6526}, {10154, 13157}

The trilinear polar of X(33581) passes through X(3049).

X(33581) = isogonal conjugate of X(14615)
X(33581) = isogonal conjugate of the anticomplement of X(800)
X(33581) = isogonal conjugate of the isotomic conjugate of X(64)
X(33581) = polar conjugate of the isotomic of X(14642)
X(33581) = X(i)-Ceva conjugate of X(j) for these (i,j): {64, 14642}, {14642, 32}
X(33581) = X(1974)-cross conjugate of X(32)
X(33581) = crosssum of X(i) and X(j) for these (i,j): {2, 6225}, {69, 6527}, {394, 11413}
X(33581) = crossdifference of every pair of points on line {6587, 20580}
X(33581) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14615}, {2, 18750}, {20, 75}, {63, 15466}, {69, 1895}, {76, 610}, {85, 27382}, {99, 17898}, {122, 23999}, {154, 561}, {204, 305}, {253, 1097}, {274, 8804}, {304, 1249}, {310, 3198}, {312, 18623}, {314, 5930}, {326, 14249}, {668, 21172}, {799, 6587}, {811, 8057}, {823, 20580}, {1394, 3596}, {1969, 15905}, {4554, 14331}, {4625, 14308}, {6063, 7070}, {28660, 30456}
X(33581) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 2155}, {4, 14642}, {6, 64}, {19, 19614}, {25, 1073}, {31, 2184}, {32, 253}, {41, 8809}, {56, 30457}, {184, 459}, {393, 14379}, {577, 6526}, {647, 1301}, {1973, 19611}, {2207, 15394}, {3269, 15384}, {8749, 11589}, {8798, 8882}, {15905, 31942}, {28785, 31956}
X(33581) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 14615}, {25, 15466}, {31, 18750}, {32, 20}, {64, 76}, {92, 37669}, {253, 1502}, {459, 18022}, {560, 610}, {669, 6587}, {798, 17898}, {1073, 305}, {1301, 6331}, {1397, 18623}, {1501, 154}, {1918, 8804}, {1919, 21172}, {1973, 1895}, {1974, 1249}, {2155, 75}, {2175, 27382}, {2184, 561}, {2205, 3198}, {2207, 14249}, {3049, 8057}, {6526, 18027}, {8798, 28706}, {8809, 20567}, {9447, 7070}, {14379, 3926}, {14575, 15905}, {14642, 69}, {19614, 304}, {30457, 3596}


X(33582) =  X(3)X(66)∩X(22)X(6527)

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

X(33582) lies on the cubic K1111 and these lines: {3, 66}, {22, 6527}, {25, 393}, {32, 7716}, {154, 216}, {197, 1604}, {577, 9924}, {1486, 2385}, {1598, 6750}, {1609, 7669}, {2393, 15905}, {2847, 14673}, {3148, 19459}, {3155, 5595}, {3156, 5594}, {3172, 11397}, {5158, 19132}, {6090, 20819}, {7819, 15435}, {8553, 19596}, {8651, 22260}, {8667, 9909}, {8969, 13889}, {9756, 14767}, {9969, 20993}, {10934, 20999}, {11641, 12918}, {12167, 14575}, {15851, 19153}, {19118, 20975}, {19125, 23635}

X(33582) = isogonal conjugate of the isotomic conjugate of X(32064)
X(33582) = tangential-isogonal conjugate of X(1661)
X(33582) = X(253)-Ceva conjugate of X(6)
X(33582) = crosspoint of X(1301) and X(15388)
X(33582) = crosssum of X(i) and X(j) for these (i,j): {69, 32006}, {127, 8057}
X(33582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {157, 159, 3}, {7669, 20987, 1609}
X(33582) = barycentric product X(6) and X(32064),barycentric quotient X(32064)/X(76)


X(33583) =  X(25)X(64)∩X(1073)X(31978)

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

X(33583) lies on the cubic K1111 and these lines: {25, 64}, {1073, 31978}

X(33583) = {X(64),X(28785)}-harmonic conjugate of X(9914)
X(33583) = X(17510)-cross conjugate of X(14390)
X(33583) = barycentric product X(i)*X(j) for these lines: {i,j}: {253, 14390}, {2063, 31942}
X(33583) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {14390, 20}, {17510, 1249}


X(33584) =  X(45)X(31367)∩X(25)X(800)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 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 + 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(33584) lies on the cubic K1111 and these lines: {4, 31367}, {25, 800}, {64, 66}, {253, 6995}, {1301, 1995}, {1843, 14642}, {2393, 14390}, {3089, 31362}, {5198, 8798}

X(33584) = reflection of X(17807) and X(15259)
X(33584) = barycentric product X(i)/X(j) for these lines: {i,j}: {159, 459}, {253, 3162}, {6526, 23115}
X(33584) = barycentric quotient X(3162)/X(20)


X(33585) =  X(610)-ISOCONJUGATE OF X(32831)

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

X(33585) lies on the cubic K1111 and this line: {64, 3146}

X(33585) = X(610)-isoconjugate of X(32831)
X(33585) = barycentric quotient X(64)/X(32831)


X(33586) =  MIDPOINT OF X(6515) AND X(7500)

Barycentrics    a^2*(a^4 + 2*a^2*b^2 - 3*b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 3*c^4) : :
X(33586) = 5 X[25] - 3 X[6090],3 X[25] - 2 X[9306],5 X[394] - 6 X[6090],3 X[394] - 4 X[9306],9 X[6090] - 10 X[9306]

X(33586) lies on these lines: {2, 1350}, {3, 51}, {4, 343}, {6, 22}, {20, 9786}, {23, 154}, {25, 394}, {26, 5944}, {30, 1899}, {52, 1181}, {64, 3146}, {68, 7553}, {69, 6995}, {141, 6997}, {155, 6243}, {156, 13421}, {161, 19149}, {182, 9777}, {184, 1351}, {193, 9924}, {263, 7467}, {373, 16419}, {382, 9927}, {389, 11414}, {427, 31670}, {428, 1352}, {568, 12083}, {573, 20835}, {576, 11402}, {578, 9715}, {611, 5310}, {613, 5322}, {858, 26958}, {991, 11350}, {1004, 1730}, {1092, 3517}, {1112, 15462}, {1147, 9714}, {1154, 7530}, {1160, 5408}, {1161, 5409}, {1184, 3981}, {1192, 11413}, {1216, 7529}, {1370, 13567}, {1495, 3167}, {1498, 5889}, {1503, 6515}, {1583, 11825}, {1584, 11824}, {1593, 13598}, {1598, 5562}, {1599, 12305}, {1600, 12306}, {1611, 3124}, {1619, 2393}, {1629, 9308}, {1763, 16465}, {1853, 3580}, {1994, 5102}, {1995, 2979}, {2353, 6464}, {3053, 20977}, {3098, 5943}, {3101, 10394}, {3129, 5864}, {3130, 5865}, {3155, 5406}, {3156, 5407}, {3231, 8770}, {3292, 8780}, {3515, 13346}, {3529, 18950}, {3564, 31383}, {3567, 10323}, {3819, 11284}, {3830, 11472}, {3832, 33537}, {3917, 5020}, {3920, 10387}, {4121, 7776}, {4186, 10441}, {5013, 20965}, {5050, 15004}, {5064, 21243}, {5079, 33540}, {5085, 5422}, {5093, 13366}, {5198, 5907}, {5640, 7485}, {5752, 13730}, {5890, 12082}, {5899, 18445}, {6101, 13861}, {6146, 31305}, {6353, 11064}, {6525, 6820}, {6642, 10625}, {6644, 13391}, {6676, 21850}, {6759, 12160}, {6815, 11745}, {6816, 15873}, {7392, 10519}, {7394, 10516}, {7395, 10110}, {7488, 11425}, {7493, 23292}, {7494, 14853}, {7499, 14561}, {7509, 9781}, {7516, 10095}, {7519, 15069}, {7539, 19130}, {7592, 12088}, {7691, 11743}, {7714, 14826}, {7728, 15085}, {8547, 8584}, {8567, 12086}, {9591, 16473}, {9919, 21649}, {9922, 19462}, {9973, 27365}, {10391, 24611}, {10446, 14004}, {10541, 15019}, {10565, 11427}, {10574, 33524}, {10594, 11412}, {10733, 17835}, {10984, 11432}, {11411, 16655}, {11438, 21312}, {11673, 21001}, {11800, 13171}, {11807, 12168}, {12111, 15811}, {12161, 14449}, {12164, 14531}, {12310, 13417}, {12410, 16980}, {13142, 19467}, {13352, 14070}, {13367, 16195}, {13410, 15815}, {13428, 13748}, {13439, 13749}, {13595, 15066}, {13724, 19782}, {13754, 18534}, {14852, 31723}, {15030, 18535}, {15360, 23293}, {15394, 32001}, {15488, 17516}, {15534, 32220}, {15761, 31815}, {15801, 17846}, {16982, 32046}, {17845, 31304}, {19924, 31152}, {21970, 30771}, {22129, 26892}, {22534, 22972}, {23332, 31099}, {24320, 26893}, {26032, 26530}, {26096, 26579}, {26869, 29317}, {26898, 30258}

X(33586) = midpoint of X(6515) and X(7500)
X(33586) = reflection of X(i) in X(j) for these lines: {i,j}: {394, 25}, {1370, 13567}, {18451, 7530}, {21312, 11438}
X(33586) = isogonal conjugate of X(34285)
X(33586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17810, 3066}, {3, 51, 10601}, {3, 5446, 10982}, {6, 22, 3796}, {22, 3060, 6}, {23, 1993, 154}, {52, 7387, 1181}, {154, 11477, 1993}, {182, 21849, 9777}, {184, 21969, 1351}, {1350, 17810, 2}, {1351, 9909, 184}, {1994, 6800, 17809}, {1995, 2979, 17811}, {3060, 15107, 22}, {3098, 5943, 7484}, {3155, 9733, 5406}, {3156, 9732, 5407}, {3167, 20850, 1495}, {3580, 7391, 1853}, {3981, 5017, 1184}, {5102, 17809, 1994}, {5422, 6636, 5085}, {5640, 7485, 17825}, {6243, 7517, 155}, {6636, 11002, 5422}, {6800, 16981, 5102}, {10565, 11427, 13394}, {10594, 11412, 17814}, {14449, 17714, 12161}, {14531, 26883, 12164}, {15004, 22352, 5050}, {17825, 31884, 7485}
X(33586) = isogonal conujgate of the isotomic conjugate of X(32816)
X(33586) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {64, 21289}, {82, 6225}, {2155, 2896}, {2184, 1369}
X(33586) = barycentric product X(i) X(j) for these lines: {i,j}: {1, 18713}, {6, 32816},barycentric quotient X(i) / X(j) for these lines: {i,j}: {18713, 75}, {32816, 76}


X(33587) =  X(1)X(4222)∩X(6)X(41)

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

X(33587) lies on the cubic K1112 and these lines: {1, 4222}, {3, 17978}, {6, 41}, {40, 758}, {72, 26934}, {78, 7289}, {197, 1042}, {603, 23154}, {610, 951}, {976, 3827}, {1038, 3942}, {1457, 8192}, {1473, 22072}, {1802, 23620}, {2933, 9316}, {3057, 3938}, {3304, 17810}, {3876, 16560}, {4101, 9028}, {18162, 19767}, {19765, 24328}, {20277, 20323}


X(33588) =  X(6)X(31)∩X(165)X(6765)

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

X(33588) lies in the cubic K1112 and these lines: {6, 31}, {165, 6765}

X(33588) = crosssum of X(12632) and X(18228)


X(33589) =  X(6)X(1201)∩X(9)X(32577)

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

X(35589) lies on the cubic K1112 and these lines: {6, 1201}, {9, 32577}, {106, 3973}, {244, 2324}, {612, 1962}, {2321, 9350}, {3731, 7963}, {9458, 30693}, {17299, 21950}

X(35589) = crossdifference of every pair of points on line {3667, 25020}


X(33590) =  X(9)X(55)∩X(1108)X(1696)

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

X(33590) lies on the cubic K1112 and these lines: {9, 55}, {1108, 1696}, {1436, 2183}, {1466, 1743}, {1604, 5204}, {3973, 10310}


X(33591) =  EULER LINE INTERCEPT OF X(524)X(10282)

Barycentrics    -10 a^10+21 a^8 (b^2+c^2)-2 a^6 (b^4+4 b^2 c^2+c^4)-4 a^4 (5 b^6-b^4 c^2-b^2 c^4+5 c^6)+4 a^2 (b^2-c^2)^2 (3 b^4+b^2 c^2+3 c^4)-(b^2-c^2)^4 (b^2+c^2) : :

As a point on the Euler line, X(33591) has Shinagawa coefficients (2E+11F,-6E-9F).

See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 29196.

X(33591) lies on these lines: {2,3}, {524,10282}, {5907,32267}, {6146,32225}, {10182,29181}

X(33591) = midpoint of X(i) and X(j), for these lines: {i, j}: {549,9909}, {10154,14070}
X(33591) = reflection of X(5066) in X(10201)

X(33592) =  COMPLEMENT OF X(16139)

Barycentrics    (b+c)*a^6-2*b*c*a^5-3*(b^3+c^3)*a^4-2*b^2*c^2*a^3+(b^2-c^2)*(b-c)*(3*b^2+b*c+3*c^2)*a^2+2*(b^2-c^2)^2*b*c*a-(b^2-c^2)^3*(b-c) : :
X(33592) = X(3)-3*X(26725), X(21)-3*X(5886), X(79)+5*X(18493), X(191)-5*X(8227), 3*X(1699)+X(16132), X(2475)+3*X(5603), X(3649)+2*X(9955), 2*X(3649)+X(22798), 3*X(5426)-7*X(9624), 3*X(5587)+X(16126), 3*X(5886)+X(16159), 2*X(5901)+X(16125), 2*X(6675)-3*X(11230), 2*X(6701)+X(22791), 4*X(9955)-X(22798), 3*X(11230)-X(22937), 2*X(11544)+X(26202), X(13743)-5*X(18493), X(16113)-3*X(28443), X(16150)+3*X(28453)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29203.

X(33592) lies on these lines: {1, 18407}, {2, 16139}, {3, 26725}, {5, 758}, {11, 113}, {21, 5886}, {30, 551}, {55, 16155}, {56, 79}, {191, 8227}, {442, 517}, {496, 10122}, {1125, 5428}, {1482, 31140}, {1519, 13373}, {1621, 3651}, {1699, 16132}, {2094, 3652}, {2475, 5603}, {3338, 7701}, {3487, 18517}, {3579, 6690}, {3647, 4999}, {3656, 5330}, {3850, 21635}, {3884, 5499}, {5249, 13624}, {5426, 9624}, {5441, 9668}, {5443, 16142}, {5587, 16126}, {5714, 18516}, {5885, 6831}, {6265, 11604}, {6583, 26470}, {6675, 11230}, {7743, 16193}, {8070, 17605}, {8071, 16153}, {9956, 21677}, {10543, 14526}, {10785, 16116}, {11277, 28174}, {11544, 26202}, {12053, 15174}, {13374, 20288}, {13407, 28204}, {13464, 19907}, {16113, 28443}, {16150, 28453}, {16617, 17768}, {18253, 21616}, {18481, 31019}, {24220, 29097}, {24390, 31938}, {25055, 28460}, {26446, 31254}

X(33592) = midpoint of X(i) and X(j) for these lines: {i,j}: {21, 16159}, {79, 13743}, {946, 11263}, {3649, 6841}, {3651, 12699}, {3652, 14450}, {3656, 6175}, {5499, 22791}, {6265, 11604}, {16116, 16138}
X(33592) = reflection of X(i) in X(j) for these (i,j): (1385, 11281), (3647, 10021), (5428, 1125), (5499, 6701), (6841, 9955), (21677, 9956), (22798, 6841), (22936, 16617), (22937, 6675)
X(33592) = complement of X(16139)
X(33592) = (K798e)-anticomplement of-X(6675)
X(33592) = X(6288)-of-3rd Euler triangle
X(33592) = X(10610)-of-Wasat triangle
X(33592) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3649, 9955, 22798), (9955, 12047, 12611)

X(33593) =  MIDPOINT OF X(11) AND X(3649)

Barycentrics    (b+c)*a^6-2*b*c*a^5-(b+c)*(3*b^2-5*b*c+3*c^2)*a^4+(b^2+c^2)*b*c*a^3+(b^2-c^2)*(b-c)*(3*b^2-b*c+3*c^2)*a^2+(b^2-c^2)^2*b*c*a-(b^2-c^2)^3*(b-c) : :
X(33593) = X(79)+3*X(16173), 3*X(442)-X(1145), X(1320)+3*X(6175), X(1749)-3*X(3582), X(3647)-3*X(32557), X(3648)-9*X(32558), X(6224)+3*X(11604), 3*X(11263)+X(21630), X(11684)-5*X(31272)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29203.

X(33593) lies on these lines: {1, 149}, {7, 3065}, {11, 113}, {12, 6797}, {21, 16153}, {30, 1319}, {36, 17009}, {56, 16159}, {79, 104}, {80, 226}, {100, 12609}, {142, 10090}, {191, 499}, {214, 5249}, {354, 1484}, {442, 1145}, {495, 17636}, {496, 13751}, {498, 11024}, {758, 908}, {952, 13407}, {1125, 4996}, {1320, 6175}, {1479, 16132}, {1519, 15528}, {1749, 3218}, {1768, 6847}, {1770, 10058}, {2802, 6701}, {2932, 5880}, {3057, 5499}, {3086, 14450}, {3091, 9803}, {3336, 6972}, {3647, 32557}, {3648, 32558}, {3651, 14798}, {3671, 11571}, {4293, 16118}, {4857, 18444}, {5428, 16142}, {5433, 22937}, {5441, 12053}, {5533, 10122}, {5541, 10056}, {5572, 25558}, {5840, 24299}, {5902, 6830}, {6147, 17660}, {6326, 6826}, {6667, 18253}, {6904, 15015}, {6964, 15017}, {6982, 10051}, {7680, 17654}, {7972, 21620}, {8104, 16151}, {8674, 13158}, {9614, 16143}, {10057, 12531}, {10087, 12855}, {10404, 12773}, {10523, 17665}, {10543, 15178}, {10572, 13273}, {10573, 16126}, {10948, 17653}, {10957, 13852}, {11376, 13743}, {11684, 21616}, {11715, 16125}, {12331, 17718}, {12701, 16117}, {13267, 16147}, {14986, 18224}

X(33593) = midpoint of X(i) and X(j) for these lines: {i,j}: {11, 3649}, {11715, 16125}
X(33593) = reflection of X(i) in X(j) for these (i,j): (10122, 18240), (18253, 6667)
X(33593) = incircle-inverse-of X(5620)
X(33593) = X(11597)-of-intouch triangle
X(33593) = X(33565)-of-inverse-in-incircle triangle
X(33593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 11263, 14526), (8068, 12736, 1737)

X(33594) =  MIDPOINT OF X(442) AND X(1537)

Barycentrics    (b+c)*a^9-(b^2+4*b*c+c^2)*a^8-(b+c)*(4*b^2-7*b*c+4*c^2)*a^7+2*(b^2+3*b*c+c^2)*(2*b^2-3*b*c+2*c^2)*a^6+(b^2-c^2)*(b-c)*(6*b^2-5*b*c+6*c^2)*a^5-2*(3*b^6+3*c^6-(b^4+c^4+2*(2*b^2-3*b*c+2*c^2)*b*c)*b*c)*a^4-(b^2-c^2)*(b-c)*(4*b^4+4*c^4-(5*b^2-6*b*c+5*c^2)*b*c)*a^3+2*(b^4-c^4)*(b^2-c^2)*(2*b^2-3*b*c+2*c^2)*a^2+(b^2-c^2)^2*(b-c)^2*(b^3+c^3)*a-(b^2-c^2)^4*(b-c)^2 : :
Trilinears    16*q*p^5-8*(2*q^2+1)*p^4-4*(4*q^2-3)*q*p^3+2*(8*q^4-4*q^2+1)*p^2+4*(q^2-1)*q*p-4*q^2+3 : :, where p=sin(A/2), q=cos((B-C)/2)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29203.

X(33594) lies on these lines: {11, 113}, {30, 1519}, {119, 7686}, {226, 10742}, {381, 21635}, {392, 5499}, {442, 1537}, {946, 6265}, {1125, 17009}, {2829, 11281}, {5450, 5886}, {6866, 9803}, {7701, 23708}, {12248, 31019}, {12515, 12609}, {14526, 15950}, {16139, 21616}, {16159, 22753}, {20288, 26470}, {22935, 28452}

X(33594) = midpoint of X(442) and X(1537)
X(33594) = reflection of X(17009) in X(1125)

X(33595) =  REFLECTION OF X(3916) IN X(17549)

Barycentrics    a*(6*a^3-3*(b+c)*a^2-2*(3*b^2+2*b*c+3*c^2)*a+(b+c)*(3*b^2-4*b*c+3*c^2)) : :
X(33595) = R*X(2)-2*(R+r)*X(24929)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29203.

X(33595) lies on these lines: {1, 4004}, {2, 3419}, {3, 11520}, {57, 19705}, {72, 3601}, {78, 16418}, {214, 3748}, {228, 19251}, {376, 5758}, {392, 4428}, {519, 2646}, {549, 24299}, {551, 17614}, {936, 17542}, {942, 13587}, {1385, 3241}, {2094, 19708}, {3534, 31164}, {3555, 3612}, {3653, 11240}, {3655, 11239}, {3689, 4669}, {3740, 5426}, {3742, 15015}, {3746, 19524}, {3873, 17502}, {3897, 31145}, {3916, 17549}, {3928, 19704}, {3957, 5126}, {3984, 17571}, {4018, 5217}, {4855, 5439}, {4881, 5049}, {5044, 16858}, {5249, 9945}, {5436, 19536}, {5777, 28461}, {6940, 15178}, {6942, 24680}, {7483, 12437}, {10609, 13405}, {10707, 22935}, {11518, 19537}, {11523, 19535}, {12100, 13151}, {13411, 17530}, {15174, 24982}, {22836, 31165}, {28443, 31837}

X(33595) = reflection of X(i) in X(j) for these (i,j): (3916, 17549), (17530, 13411)
X(33595) = {X(3928), X(30282)}-harmonic conjugate of X(19704)

X(33596) =  MIDPOINT OF X(4) AND X(11015)

Barycentrics    a*(2*a^6-3*(b+c)*a^5-3*(b-c)^2*a^4+6*(b^3+c^3)*a^3-4*(b^2-b*c+c^2)*b*c*a^2-3*(b^4-c^4)*(b-c)*a+(b^2-c^2)^2*(b-c)^2): :
X(33596) = R*X(3)-2*(R+r)*X(24929), 3*X(35)-X(40), 3*X(5086)-5*X(5818), 5*X(8227)-3*X(31159)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29203.

X(33596) lies on these lines: {1, 3}, {4, 11015}, {5, 5440}, {8, 6892}, {20, 5761}, {21, 26878}, {72, 6914}, {78, 3560}, {145, 5770}, {214, 10993}, {443, 10596}, {912, 6906}, {938, 6961}, {944, 11239}, {946, 28452}, {950, 6882}, {1455, 5399}, {1519, 20420}, {1621, 31838}, {1858, 10058}, {1900, 7497}, {3419, 6862}, {3487, 6948}, {3488, 6891}, {3555, 32153}, {3635, 11715}, {3649, 24466}, {3811, 22758}, {3868, 6950}, {3897, 12245}, {4304, 7491}, {4313, 6827}, {4855, 6911}, {5044, 7489}, {5086, 5552}, {5175, 6859}, {5270, 12119}, {5534, 18519}, {5554, 6857}, {5603, 6885}, {5691, 11929}, {5703, 6850}, {5719, 31775}, {5722, 6958}, {5777, 13743}, {5789, 12645}, {5804, 6970}, {5840, 12047}, {5887, 22836}, {5901, 17614}, {6326, 31937}, {6675, 24982}, {6684, 28465}, {6826, 7704}, {6842, 13411}, {6847, 10528}, {6851, 12115}, {6861, 26364}, {6881, 25639}, {6893, 27383}, {6909, 13369}, {6923, 11374}, {6935, 12648}, {6977, 12649}, {7330, 28444}, {7548, 9963}, {8227, 11928}, {8727, 10942}, {9945, 11729}, {9955, 10738}, {10525, 11375}, {10915, 12437}, {14988, 20612}, {15556, 17010}, {16113, 18244}, {16370, 26921}, {17857, 18761}, {31649, 31835}

X(33596) = midpoint of X(4) and X(11015)
X(33596) = reflection of X(6842) in X(13411)
X(33596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 10679, 23340), (10202, 23340, 24474), (10284, 11567, 5048)

X(33597) =  REFLECTION OF X(3916) IN X(3)

Barycentrics    a*(-a^2+b^2+c^2)*(2*a^4-3*(b+c)*a^3-(b-c)^2*a^2+3*(b^2-c^2)*(b-c)*a-(b^2-c^2)^2) : :
X(33597) = R*X(4)-2*(R+r)*X(24929), 2*X(946)-3*X(4870)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29203.

X(33597) lies on these lines: {1, 227}, {2, 355}, {3, 63}, {4, 4313}, {5, 24299}, {8, 6988}, {12, 515}, {20, 5812}, {21, 5777}, {35, 6001}, {36, 12675}, {40, 4421}, {55, 6261}, {65, 6796}, {84, 30282}, {100, 17654}, {104, 6986}, {125, 18641}, {140, 13151}, {214, 6700}, {392, 10267}, {404, 9940}, {405, 5720}, {411, 517}, {474, 18443}, {500, 28381}, {518, 11012}, {535, 4297}, {631, 5768}, {908, 31789}, {936, 958}, {938, 6049}, {942, 6905}, {946, 3058}, {950, 1532}, {952, 6734}, {956, 5534}, {960, 6326}, {971, 6906}, {993, 14872}, {1006, 5044}, {1012, 1490}, {1064, 5266}, {1155, 5884}, {1158, 5217}, {1210, 1319}, {1519, 15171}, {1537, 10624}, {1538, 31795}, {1858, 5172}, {2077, 9943}, {2095, 11520}, {2096, 3522}, {2801, 5267}, {3305, 5780}, {3419, 6825}, {3428, 3811}, {3436, 5731}, {3488, 6848}, {3530, 13226}, {3555, 11249}, {3560, 5927}, {3612, 12114}, {3616, 6864}, {3651, 31793}, {3683, 20117}, {3689, 11362}, {3748, 13464}, {3753, 11499}, {3824, 6901}, {3870, 22770}, {3880, 11014}, {4189, 12528}, {4304, 6260}, {4305, 12667}, {4511, 31786}, {4640, 5693}, {4857, 22835}, {5010, 15071}, {5122, 26877}, {5220, 21153}, {5258, 5531}, {5428, 12691}, {5432, 12616}, {5438, 8726}, {5439, 6911}, {5450, 12680}, {5657, 20007}, {5691, 10894}, {5705, 5881}, {5719, 20420}, {5722, 6834}, {5761, 6869}, {5779, 17571}, {5787, 6833}, {5811, 11111}, {5842, 12047}, {5886, 6835}, {5887, 20846}, {6174, 6684}, {6256, 10953}, {6259, 6938}, {6284, 12608}, {6828, 18480}, {6836, 10526}, {6855, 10585}, {6875, 31445}, {6894, 9955}, {6895, 28160}, {6915, 15178}, {6918, 10246}, {6920, 10157}, {6922, 10942}, {6924, 10202}, {6935, 9799}, {6940, 11227}, {6943, 26287}, {6962, 12649}, {6991, 11230}, {7330, 16370}, {7498, 18283}, {8069, 12711}, {8071, 17625}, {10165, 24953}, {10310, 12520}, {10523, 10572}, {10806, 11373}, {10954, 15844}, {11507, 12709}, {12005, 32636}, {12119, 13272}, {12650, 13384}, {12700, 20075}, {13607, 20323}, {14110, 22836}, {16139, 31663}, {16293, 19861}, {17563, 31657}, {17613, 26285}, {17718, 26332}, {18180, 27653}, {21161, 26878}, {23961, 26201}

X(33597) = midpoint of X(11491) and X(21740)
X(33597) = reflection of X(i) in X(j) for these (i,j): (3916, 3), (6831, 13411)
X(33597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18446, 1071), (944, 10786, 355), (4855, 10884, 3)

X(33598) =  REFLECTION OF X(2646) IN X(214)

Barycentrics    a*(2*a^6-3*(b+c)*a^5-(3*b^2-4*b*c+3*c^2)*a^4+(b+c)*(6*b^2-7*b*c+6*c^2)*a^3-4*(b-c)^2*b*c*a^2-(b^3+c^3)*(3*b^2-4*b*c+3*c^2)*a+(b^4-c^4)*(b^2-c^2)) : :
X(33598) = X(35)-3*X(15015)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29203.

X(33598) lies on these lines: {11, 214}, {35, 392}, {72, 2949}, {100, 517}, {149, 24929}, {952, 6734}, {956, 5531}, {960, 14794}, {1145, 6737}, {1319, 33337}, {1385, 5086}, {1484, 24299}, {2771, 3916}, {2802, 11011}, {3555, 22560}, {3582, 10073}, {3897, 20085}, {4855, 11849}, {5289, 11010}, {5541, 11009}, {5687, 11014}, {5886, 6901}, {9945, 11729}, {10087, 17652}, {10090, 13750}, {10914, 12331}

X(33598) = midpoint of X(i) and X(j) for these lines: {i,j}: {5086, 6224}, {5541, 11009}, {6326, 11012}
X(33598) = reflection of X(i) in X(j) for these (i,j): (2646, 214), (3916, 4996)
X(33598) = {X(100), X(22935)}-harmonic conjugate of X(5440)

X(33599) =  REFLECTION OF X(36) IN X(13141)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29206.

X(33599) lies on the cubic K529 and these lines: {1, 15529}, {36, 13141}, {355, 1836}, {14008, 33140}

X(33599) = reflection of X(36) in X(13141)
X(33599) = antigonal conjugate of X(36)


X(33600) =  TRILINEAR POLE OF THE LINE X(6)X(563)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29206.

X(33600) lies on the circumcircle and this line: {925,4575}

X(33600) = trilinear pole of the line X(6)X(563)


X(33601) =  ISOGONAL CONJUGATE OF X(11643)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29206.

X(33601) lies on the cubic K300 and this line: {381, 576}

X(33601) = isogonal conjugate of X(11643)
X(33601) = antigonal conjugate of X(187)


leftri

Fermat-Dao-Nhi triangles and related centers: X(33602)-X(33627)

rightri

This preamble and centers X(33602)-X(33627) were contributed by César Eliud Lozada, July 19, 2019.

Dao Thanh Oai and Hoang Le Ngoc Nhi have presented the following configurations:

Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf.

  1. Let A* = reflection of G in Af; let A1 = reflection of A* in A. Define B1 and C1 cyclically.
  2. Let A* = reflection of G in A; let A2 = reflection of A* in Af . Define B2 and C2 cyclically.
  3. Let A* = reflection of A in G; let A3 = midpoint of A*Af . Define B3 and C3 cyclically.
  4. Let A* = reflection of Af in G; let A4 = midpoint of A*A. Define B4 and C4 cyclically.
Then triangles A1B1C1, A2B2C2, A3B3C3, A4B4C4 are equilateral and perspective to ABC.

Added by César Lozada:

For the outer-Fermat triangle, barycentrics coordinates of A1...A4 are:

A1 = -7*S-3*sqrt(3)*a^2 : 2*S+3*sqrt(3)*SC : 2*S+3*sqrt(3)*SB

A2 = -5*S-3*sqrt(3)*a^2 : 4*S+3*sqrt(3)*SC : 4*S+3*sqrt(3)*SB

A3 = 4*S-3*sqrt(3)*a^2 : -5*S+3*sqrt(3)*SC : -5*S+3*sqrt(3)*SB

A4 = 8*S-3*sqrt(3)*a^2 : -S+3*sqrt(3)*SC : -S+3*sqrt(3)*SB

For the inner-Fermat triangle, just replace S → -S in these coordinates.

The preceding triangles are here named here the 1st, 2nd, 3rd and 4th outer-Fermat-Dao-Nhi triangles, respectively, and their correspondents built from the inner-Fermat triangle are here named the 1st, 2nd, 3rd and 4th inner-Fermat-Dao-Nhi triangles, respectively. All these triangles have center X(2).

Observe that given A-barycentrics have all the form Aλ, μ = λ*S - a^2 : μ*S + SC : μ*S + SB, where λ, μ are real numbers. It results that, for all real numbers (λ, μ), the triangle 𝔽(λ, μ) = Aλ, μBλ, μCλ, μ is perspective to each triangle in the following set: {ABC, anti-Artzt, 1st anti-Brocard, anti-McCay, anticomplementary, Artzt, 1st Brocard-reflected, 1st Brocard, inner-Fermat, outer-Fermat, 1st half-diamonds-central, 2nd half-diamonds-central, 1st half-diamonds, 2nd half-diamonds, 1st half-squares, 2nd half-squares, McCay, medial, inner-Napoleon, outer-Napoleon, 1st Neuberg, 2nd Neuberg, inner-Vecten, outer-Vecten}. Also 𝔽(λ, μ) and 𝔽(λ', μ') are perspective for any combination of (λ, μ, λ', μ'). The perspector of ABC and 𝔽(λ, μ) has barycentric coordinates Q = (μ*S+SB)*(μ*S+SC) : :, not dependending on λ. Q lies on the Kiepert hyperbola of ABC.

With the last notation we have: A1B1C1 = 𝔽(-7*k, 2*k), A2B2C2 = 𝔽(-5*k, 4*k), A3B3C3 = 𝔽(4*k, -5*k), A4B4C4 = 𝔽(8*k, -k), where k = ±sqrt(3)/9 (plus and minus signs for outer- and inner- triangles, respectively). Similarly: 1st/2nd half-diamonds triangles = 𝔽( ±2*sqrt(3)/3, ±sqrt(3)/3 ), 1st/2nd half-diamonds-central triangles = 𝔽( ∓2*sqrt(3), ∓sqrt(3) ), 1st/2nd half-squares triangles = 𝔽( ∓1, 0 ), outer-/inner-Fermat = 𝔽( 0, ±sqrt(3)/3 ).

The condition for 𝔽(λ, μ) being equilateral is |λ - μ| = sqrt(3).

Note that every original construction is made from two reflections. Going further, if homothecies are used instead of reflections then configurations 1 to 4 can be combined and generalized by writing:

Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf.

  1. Let A* be the homothecy of G with factor p and center A, 𝔸1 the homothecy of A* with factor q and center Af. Build 𝔹1 and ℂ1 cyclically. Then, for each value of p∉{0, 3} there exist two values of q∈{1/p, 2/(3-p)} such that 𝔸1𝔹11 is equilateral and perspective to ABC.
  2. Let A* be the homothecy of G with factor p and center Af, 𝔸2 the homothecy of A* with factor q and center A. Build 𝔹2 and ℂ2 cyclically. Then, for each value of p∉{0, 3/2} there exist two values of q∈{1/p, 1/(3-2*p)} such that 𝔸2𝔹22 is equilateral and perspective to ABC.
Perspective triangles with perspectors in ETC (where *, *- mean directly and inversely homothetic, respectively, and $, $- mean directly and inversely similar, respectively):

Fermat-Dao-Nhi triangle From outer-Fermat triangle From inner-Fermat triangle
1st (ABC, 33602), (anticomplementary, 33608), (1st inner-Fermat-Dao-Nhi$-, 15682), (2nd inner-Fermat-Dao-Nhi$-, 5862), (3rd inner-Fermat-Dao-Nhi*, 2), (4th inner-Fermat-Dao-Nhi*, 2), (2nd outer-Fermat-Dao-Nhi*, 2), (3rd outer-Fermat-Dao-Nhi$-, 33622), (4th outer-Fermat-Dao-Nhi$-, 33623), (1st half-diamonds-central*, 2), (medial, 33614), (outer-Napoleon*, 2) (ABC, 33603), (anticomplementary, 33609), (2nd inner-Fermat-Dao-Nhi*, 2), (3rd inner-Fermat-Dao-Nhi$-, 33624), (4th inner-Fermat-Dao-Nhi$-, 33625), (1st outer-Fermat-Dao-Nhi$-, 15682), (2nd outer-Fermat-Dao-Nhi$-, 5863), (3rd outer-Fermat-Dao-Nhi*, 2), (4th outer-Fermat-Dao-Nhi*, 2), (2nd half-diamonds-central*, 2), (medial, 33615), (inner-Napoleon*, 2)
2nd (ABC, 33604), (anticomplementary, 33610), (1st inner-Fermat-Dao-Nhi$-, 5863), (2nd inner-Fermat-Dao-Nhi$-, 11001), (3rd inner-Fermat-Dao-Nhi*, 2), (4th inner-Fermat-Dao-Nhi*, 2), (1st outer-Fermat-Dao-Nhi*, 2), (3rd outer-Fermat-Dao-Nhi$-, 33610), (4th outer-Fermat-Dao-Nhi$-, 33626), (1st half-diamonds-central*, 2), (medial, 33616), (outer-Napoleon*, 2) (ABC, 33605), (anticomplementary, 33611), (1st inner-Fermat-Dao-Nhi*, 2), (3rd inner-Fermat-Dao-Nhi$-, 33611), (4th inner-Fermat-Dao-Nhi$-, 33627), (1st outer-Fermat-Dao-Nhi$-, 5862), (2nd outer-Fermat-Dao-Nhi$-, 11001), (3rd outer-Fermat-Dao-Nhi*, 2), (4th outer-Fermat-Dao-Nhi*, 2), (2nd half-diamonds-central*, 2), (medial, 33617), (inner-Napoleon*, 2)
3rd (ABC, 33606), (anticomplementary, 33610), (inner-Fermat, 5858), (12th Fermat-Dao*, 5066), (1st inner-Fermat-Dao-Nhi*, 2), (2nd inner-Fermat-Dao-Nhi*, 2), (3rd inner-Fermat-Dao-Nhi$-, 3534), (4th inner-Fermat-Dao-Nhi$-, 5858), (1st outer-Fermat-Dao-Nhi$-, 33622), (2nd outer-Fermat-Dao-Nhi$-, 33610), (4th outer-Fermat-Dao-Nhi*, 2), (2nd half-diamonds-central*, 2), (medial, 33618), (inner-Napoleon*, 2) (ABC, 33607), (anticomplementary, 33611), (outer-Fermat, 5859), (11th Fermat-Dao*, 5066), (1st inner-Fermat-Dao-Nhi$-, 33624), (2nd inner-Fermat-Dao-Nhi$-, 33611), (4th inner-Fermat-Dao-Nhi*, 2), (1st outer-Fermat-Dao-Nhi*, 2), (2nd outer-Fermat-Dao-Nhi*, 2), (3rd outer-Fermat-Dao-Nhi$-, 3534), (4th outer-Fermat-Dao-Nhi$-, 5859), (1st half-diamonds-central*, 2), (medial, 33619), (outer-Napoleon*, 2)
4th (ABC, 12817), (anticomplementary, 33612), (outer-Fermat, 5859), (12th Fermat-Dao*, 3845), (1st inner-Fermat-Dao-Nhi*, 2), (2nd inner-Fermat-Dao-Nhi*, 2), (3rd inner-Fermat-Dao-Nhi$-, 5859), (4th inner-Fermat-Dao-Nhi$-, 3830), (1st outer-Fermat-Dao-Nhi$-, 33623), (2nd outer-Fermat-Dao-Nhi$-, 33626), (3rd outer-Fermat-Dao-Nhi*, 2), (2nd half-diamonds-central*, 2), (medial, 33620), (inner-Napoleon*, 2) (ABC, 12816), (anticomplementary, 33613), (inner-Fermat, 5858), (11th Fermat-Dao*, 3845), (1st inner-Fermat-Dao-Nhi$-, 33625), (2nd inner-Fermat-Dao-Nhi$-, 33627), (3rd inner-Fermat-Dao-Nhi*, 2), (1st outer-Fermat-Dao-Nhi*, 2), (2nd outer-Fermat-Dao-Nhi*, 2), (3rd outer-Fermat-Dao-Nhi$-, 5858), (4th outer-Fermat-Dao-Nhi$-, 3830), (1st half-diamonds-central*, 2), (medial, 33621), (outer-Napoleon*, 2)

The following four generalizations were contributed by Dao Thanh Oai, June 29, 2022.

1. Generalization of the First Fermat-Dao-Nhi equilateral triangle

Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf. P be arbitrary point in the plane.

Let A* = reflection of P in Af; let A1 = reflection of A* in A; define B1 and C1 cyclically.

1) Then A1B1C1 is an equilateral triangle homothetic to the outer (inner) Napoleon equilateral triangle, with homothetic center H1.

2) H1 lies on the segment PG, and |PH1|=6|H1G|.

3) Area(A1B1C1) = 36*(area of outer [or inner] Napoleon equilateral triangle).

2. Generalization of the second Fermat-Dao-Nhi equilateral triangle

Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf, and let P be an arbitrary point in the plane of ABC. Let A* = reflection of P in A; let A2 = reflection of A* in Af. Define B2 and C2 cyclically.

1) Then A2B2C2 is an equilateral triangle homothetic with the outer (inner) Napoleon equilateral triangle, with homothetic center H2.

2) G lies on segment PH2, and |PG} = 5|GH2|.

3) Area(A2B2C2)=36*(area of outer [or inner] Napoleon equilateral triangle).

3. Generalization of the third Fermat-Dao-Nhi equilateral triangle

Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf, and let P be an arbitrary point in the plane of ABC. Let A* = reflection of A in P; let A3 = midpoint of A*Af. Define B3 and C3 cyclically.

1) Then A3B3C3 is an equilateral triangle homothetic to the outer (inner) Napoleon equilateral triangle, with homothetic center H3.

2) G lies on segment PH3, and 2|PG| = |GH3|.

3) Area(A3B3C3) = (9/4)*(area of outer (inner) Napoleon equilateral triangle).

4. Generalization of the fourth Fermat-Dao-Nhi equilateral triangle

Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf. P be arbitrary point in the plane

Let A* = reflection of Af in P; let A4 = midpoint of A*A. Define B4 and C4 cyclically.

1) Then A4B4C4 is an equilateral homothetic to the outer (inner) Napoleon equilateral triangle, with homothetic center H4.

2) H4 lies on segment PG, and 2|PH4|=3|H4G|.

3) Area(A4B4C4)=(9/4)*(area of outer (inner) Napoleon equilateral triangle).

Sketches for the four generalizations:

1. Generalization of the first Fermat-Dao-Nhi equilateral triangle - GeoGebra
See also png file: X(33602x1).png

2. Generalization of the second Fermat-Dao-Nhi equilateral triangle - GeoGebra
See also png file: X(33602x2).png

3. Generalization of the third Fermat-Dao-Nhi equilateral triangle - GeoGebra
See also png file: X(33602x3).png

4. Generalization of the fourth Fermat-Dao-Nhi equilateral triangle - GeoGebra
See also png file: X(33602x4).png


X(33602) = PERSPECTOR OF THESE TRIANGLES: ABC AND 1st OUTER-FERMAT-DAO-NHI

Barycentrics    (2*S+3*sqrt(3)*SC)*(2*S+3*sqrt(3)*SB) : :

X(33602) lies on the Kiepert hyperbola and these lines: {2,33619}, {6,33603}, {13,15682}, {17,376}, {18,3545}, {30,22235}, {381,22237}, {396,33604}, {631,10188}, {2043,3590}, {2044,3591}, {3090,10187}, {3524,5344}, {5071,5340}, {5318,11001}, {5485,5859}, {10654,12820}, {15709,16965}, {15719,18582}

X(33602) = anticomplement of X(33619)


X(33603) = PERSPECTOR OF THESE TRIANGLES: ABC AND 1st INNER-FERMAT-DAO-NHI

Barycentrics    (-2*S+3*sqrt(3)*SC)*(-2*S+3*sqrt(3)*SB) : :

X(33603) lies on the Kiepert hyperbola and these lines: {2,33618}, {6,33602}, {14,15682}, {17,3545}, {18,376}, {30,22237}, {381,22235}, {395,33605}, {631,10187}, {2043,3591}, {2044,3590}, {3090,10188}, {3524,5343}, {5071,5339}, {5321,11001}, {5485,5858}, {10653,12821}, {11543,15640}, {15709,16964}, {15719,18581}

X(33603) = anticomplement of X(33618)


X(33604) = PERSPECTOR OF THESE TRIANGLES: ABC AND 2nd OUTER-FERMAT-DAO-NHI

Barycentrics    (4*S+3*sqrt(3)*SC)*(4*S+3*sqrt(3)*SB) : :

X(33604) lies on the Kiepert hyperbola and these lines: {2,33621}, {6,33605}, {13,11001}, {17,3524}, {18,5071}, {376,22235}, {396,33602}, {3525,10188}, {3545,22237}, {5067,10187}, {5485,33458}, {11488,33607}, {11541,16962}, {11542,15682}

X(33604) = anticomplement of X(33621)


X(33605) = PERSPECTOR OF THESE TRIANGLES: ABC AND 2nd INNER-FERMAT-DAO-NHI

Barycentrics    (-4*S+3*sqrt(3)*SC)*(-4*S+3*sqrt(3)*SB) : :

X(33605) lies on the Kiepert hyperbola and these lines: {2,33620}, {6,33604}, {14,11001}, {17,5071}, {18,3524}, {376,22237}, {395,33603}, {3525,10187}, {3545,22235}, {5067,10188}, {5485,33459}, {11489,33606}, {11541,16963}, {11543,15682}

X(33605) = anticomplement of X(33620)


X(33606) = PERSPECTOR OF THESE TRIANGLES: ABC AND 3rd OUTER-FERMAT-DAO-NHI

Barycentrics    (-5*S+3*sqrt(3)*SC)*(-5*S+3*sqrt(3)*SB) : :

X(33606) lies on the Kiepert hyperbola and these lines: {2,33609}, {4,3411}, {6,33607}, {13,5066}, {14,3534}, {15,11540}, {16,15640}, {17,5055}, {18,549}, {62,23046}, {395,12817}, {671,32553}, {3526,10187}, {3628,10188}, {3830,12821}, {3845,12820}, {5463,11121}, {5469,10612}, {10109,16960}, {10159,21359}, {10304,16964}, {11122,33622}, {11489,33605}, {12816,16809}, {15684,16963}, {15698,16242}

X(33606) = isogonal conjugate of X(34755)
X(33606) = complement of X(33609)


X(33607) = PERSPECTOR OF THESE TRIANGLES: ABC AND 3rd INNER-FERMAT-DAO-NHI

Barycentrics    (5*S+3*sqrt(3)*SC)*(5*S+3*sqrt(3)*SB) : :

X(33607) lies on the Kiepert hyperbola and these lines: {2,33608}, {4,3412}, {6,33606}, {13,3534}, {14,5066}, {15,15640}, {16,11540}, {17,549}, {18,5055}, {61,23046}, {396,12816}, {671,32552}, {3526,10188}, {3628,10187}, {3830,12820}, {3845,12821}, {5464,11122}, {5470,10611}, {10109,16961}, {10159,21360}, {10304,16965}, {11121,33624}, {11488,33604}, {12817,16808}, {15684,16962}, {15698,16241}

X(33607) = isogonal conjugate of X(34754)
X(33607) = complement of X(33608)


X(33608) = PERSPECTOR OF THESE TRIANGLES: ANTICOMPLEMENTARY AND 1st OUTER-FERMAT-DAO-NHI

Barycentrics    26*S^2+15*sqrt(3)*SA*S-27*SB*SC : :

X(33608) lies on these lines: {2,33607}, {69,33609}, {140,33405}, {298,15685}, {381,627}, {616,15682}, {617,8703}, {622,10109}, {628,3524}, {633,15689}, {634,15721}, {3090,33404}, {5463,33622}, {6777,8591}, {15716,33612}

X(33608) = anticomplement of X(33607)
X(33608) = anticomplement of isogonal conjugate of X(34754)
X(33608) = X(33623)-of-2nd half-diamonds triangle


X(33609) = PERSPECTOR OF THESE TRIANGLES: ANTICOMPLEMENTARY AND 1st INNER-FERMAT-DAO-NHI

Barycentrics    26*S^2-15*sqrt(3)*SA*S-27*SB*SC : :

X(33609) lies on these lines: {2,33606}, {69,33608}, {140,33404}, {299,15685}, {381,628}, {616,8703}, {617,15682}, {621,10109}, {627,3524}, {633,15721}, {634,15689}, {3090,33405}, {5464,33624}, {6778,8591}, {15716,33613}

X(33609) = anticomplement of X(33606)
X(33609) = anticomplement of isogonal conjugate of X(34755)


X(33610) = PERSPECTOR OF THESE TRIANGLES: ANTICOMPLEMENTARY AND 2nd OUTER-FERMAT-DAO-NHI

Barycentrics    14*S^2+3*sqrt(3)*SA*S-27*SB*SC : :
X(33610) = 4*X(12816)-3*X(33623)

X(33610) lies on these lines: {2,10646}, {3,33405}, {4,33404}, {30,627}, {69,33611}, {147,5473}, {298,15685}, {299,15690}, {376,628}, {530,33626}, {531,33622}, {616,11001}, {617,3534}, {622,8703}, {633,15681}

X(33610) = reflection of X(33623) in X(2)
X(33610) = anticomplementary conjugate of the anticomplement of X(10645)
X(33610) = anticomplement of X(12816)
X(33610) = X(5863)-of-2nd half-diamonds triangle


X(33611) = PERSPECTOR OF THESE TRIANGLES: ANTICOMPLEMENTARY AND 2nd INNER-FERMAT-DAO-NHI

Barycentrics    14*S^2-3*sqrt(3)*SA*S-27*SB*SC : :
X(33611) = 4*X(12817)-3*X(33625)

X(33611) lies on these lines: {2,10645}, {3,33404}, {4,33405}, {30,628}, {69,33610}, {147,5474}, {298,15690}, {299,15685}, {376,627}, {530,33624}, {531,33627}, {616,3534}, {617,11001}, {621,8703}, {634,15681}

X(33611) = reflection of X(33625) in X(2)
X(33611) = anticomplementary conjugate of the anticomplement of X(10646)
X(33611) = anticomplement of X(12817)


X(33612) = PERSPECTOR OF THESE TRIANGLES: ANTICOMPLEMENTARY AND 4th OUTER-FERMAT-DAO-NHI

Barycentrics    38*S^2-21*sqrt(3)*SA*S-27*SB*SC : :

X(33612) lies on these lines: {69,33613}, {299,15690}, {549,627}, {616,19708}, {617,3830}, {628,3545}, {1656,33405}, {3525,33404}, {5464,33626}, {8591,32552}, {15716,33608}


X(33613) = PERSPECTOR OF THESE TRIANGLES: ANTICOMPLEMENTARY AND 4th INNER-FERMAT-DAO-NHI

Barycentrics    38*S^2+21*sqrt(3)*SA*S-27*SB*SC : :

X(33613) lies on these lines: {69,33612}, {298,15690}, {549,628}, {616,3830}, {617,19708}, {627,3545}, {1656,33404}, {3525,33405}, {5463,33627}, {8591,32553}, {15716,33609}


X(33614) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 1st OUTER-FERMAT-DAO-NHI

Barycentrics    (7*S+6*sqrt(3)*SA)*(7*S+3*sqrt(3)*(SB+SC)) : :

X(33614) lies on these lines: {141,33615}, {618,15682}, {629,5071}, {630,15709}, {19710,33619}, {22892,33622}


X(33615) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 1st INNER-FERMAT-DAO-NHI

Barycentrics    (-6*sqrt(3)*SA+7*S)*(7*S-3*sqrt(3)*(SB+SC)) : :

X(33615) lies on these lines: {141,33614}, {619,15682}, {629,15709}, {630,5071}, {19710,33618}, {22848,33624}


X(33616) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 2nd OUTER-FERMAT-DAO-NHI

Barycentrics    (5*S+6*sqrt(3)*SA)*(5*S+3*sqrt(3)*(SB+SC)) : :

X(33616) lies on these lines: {141,33617}, {618,11001}, {619,15719}, {629,3545}, {630,15702}, {15690,33619}, {19711,33618}, {22892,33626}


X(33617) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 2nd INNER-FERMAT-DAO-NHI

Barycentrics    (5*S-6*sqrt(3)*SA)*(5*S-3*sqrt(3)*(SB+SC)) : :

X(33617) lies on these lines: {141,33616}, {618,15719}, {619,11001}, {629,15702}, {630,3545}, {15690,33618}, {19711,33619}, {22848,33627}


X(33618) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 3rd OUTER-FERMAT-DAO-NHI

Barycentrics    (-3*sqrt(3)*SA+2*S)*(4*S-3*sqrt(3)*(SB+SC)) : :

X(33618) lies on these lines: {2,33603}, {141,33619}, {381,630}, {618,15693}, {619,3534}, {629,5054}, {2482,6778}, {5464,22848}, {11165,33458}, {15685,33620}, {15690,33617}, {15722,33621}, {15764,33364}, {19710,33615}, {19711,33616}, {22489,22892}, {30472,33622}

X(33618) = complement of X(33603)


X(33619) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 3rd INNER-FERMAT-DAO-NHI

Barycentrics    (2*S+3*sqrt(3)*SA)*(4*S+3*sqrt(3)*(SB+SC)) : :

X(33619) lies on these lines: {2,33602}, {141,33618}, {381,629}, {618,3534}, {619,15693}, {630,5054}, {2482,6777}, {11165,33459}, {22490,22848}, {30471,33624}

X(33619) = complement of X(33602)


X(33620) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 4th OUTER-FERMAT-DAO-NHI

Barycentrics    (4*S-3*sqrt(3)*SA)*(8*S-3*sqrt(3)*(SB+SC)) : :

X(33620) lies on these lines: {2,33605}, {141,33621}, {618,15701}, {619,3830}, {629,15694}, {630,5055}, {15685,33618}, {15722,33619}, {30472,33626}

X(33620) = complement of X(33605)


X(33621) = PERSPECTOR OF THESE TRIANGLES: MEDIAL AND 4th INNER-FERMAT-DAO-NHI

Barycentrics    (4*S+3*sqrt(3)*SA)*(8*S+3*sqrt(3)*(SB+SC)) : :

X(33621) lies on these lines: {2,33604}, {141,33620}, {618,3830}, {619,15701}, {629,5055}, {630,15694}, {15685,33619}, {15722,33618}, {30471,33627}

X(33621) = complement of X(33604)


X(33622) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 3rd OUTER-FERMAT-DAO-NHI

Barycentrics    8*S^2-9*SB*SC+sqrt(3)*(9*SA-2*SW)*S : :
X(33622) = 7*X(2)-6*X(17) = 2*X(2)-3*X(627) = 11*X(2)-12*X(629) = 5*X(2)-3*X(22113) = X(2)-6*X(22844) = 17*X(2)-12*X(33465) = 4*X(17)-7*X(627) = 11*X(17)-14*X(629) = 10*X(17)-7*X(22113) = X(17)-7*X(22844) = 17*X(17)-14*X(33465) = 12*X(17)-7*X(33626) = 11*X(627)-8*X(629) = 25*X(627)-16*X(6673) = 5*X(627)-2*X(22113) = X(627)-4*X(22844) = 17*X(627)-8*X(33465) = 3*X(627)-X(33626) = 20*X(629)-11*X(22113) = 4*X(4745)-3*X(22652)

X(33622) lies on these lines: {2,17}, {530,33623}, {531,33610}, {616,5862}, {622,33459}, {4745,22652}, {5066,16629}, {5463,33608}, {5965,19708}, {8703,22532}, {11122,33606}, {14144,15533}, {15697,22890}, {22892,33614}, {30472,33618}

X(33622) = reflection of X(33626) in X(2)
X(33622) = complement of X(36326)
X(33622) = anticomplement of X(36366)
X(33622) = X(15682)-of-2nd half-diamonds triangle
X(33622) = {X(627), X(33626)}-harmonic conjugate of X(2)


X(33623) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 4th OUTER-FERMAT-DAO-NHI

Barycentrics    4*S^2-27*SB*SC+sqrt(3)*(3*SA-2*SW)*S : :
X(33623) = 4*X(12816)-X(33610)

X(33623) lies on these lines: {2,10646}, {30,16629}, {530,33622}, {531,33626}, {617,19106}, {1992,33625}

X(33623) = reflection of X(i) in X(j) for these (i,j): (2, 12816), (33610, 2)
X(33623) = X(5862)-of-2nd half-diamonds triangle


X(33624) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 3rd INNER-FERMAT-DAO-NHI

Barycentrics    8*S^2-9*SB*SC-sqrt(3)*(9*SA-2*SW)*S : :
X(33624) = 7*X(2)-6*X(18) = 2*X(2)-3*X(628) = 11*X(2)-12*X(630) = 5*X(2)-3*X(22114) = X(2)-6*X(22845) = 17*X(2)-12*X(33464) = 4*X(18)-7*X(628) = 11*X(18)-14*X(630) = 10*X(18)-7*X(22114) = X(18)-7*X(22845) = 17*X(18)-14*X(33464) = 12*X(18)-7*X(33627) = 11*X(628)-8*X(630) = 25*X(628)-16*X(6674) = 5*X(628)-2*X(22114) = X(628)-4*X(22845) = 17*X(628)-8*X(33464) = 3*X(628)-X(33627) = 20*X(630)-11*X(22114) = 4*X(4745)-3*X(22651)

X(33624) lies on these lines: {2,18}, {530,33611}, {531,33625}, {617,5863}, {621,33458}, {4745,22651}, {5066,16628}, {5464,33609}, {5965,19708}, {8703,22531}, {11121,33607}, {14145,15533}, {15697,22843}, {22848,33615}, {30471,33619}

X(33624) = reflection of X(33627) in X(2)
X(33624) = complement of X(36324)
X(33624) = anticomplement of X(36368)
X(33624) = X(15682)-of-1st half-diamonds triangle
X(33624) = {X(628), X(33627)}-harmonic conjugate of X(2)


X(33625) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 4th INNER-FERMAT-DAO-NHI

Barycentrics    4*S^2-27*SB*SC-sqrt(3)*(3*SA-2*SW)*S : :
X(33625) = 4*X(12817)-X(33611)

X(33625) lies on these lines: {2,10645}, {30,16628}, {530,33627}, {531,33624}, {616,19107}, {1992,33623}

X(33625) = reflection of X(i) in X(j) for these (i,j): (2, 12817), (33611, 2)


X(33626) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 4th OUTER-FERMAT-DAO-NHI

Barycentrics    2*S^2+9*SB*SC-sqrt(3)*(9*SA-4*SW)*S : :
X(33626) = 5*X(2)-6*X(17) = 4*X(2)-3*X(627) = 13*X(2)-12*X(629) = X(2)-3*X(22113) = 11*X(2)-6*X(22844) = 7*X(2)-12*X(33465) = 8*X(17)-5*X(627) = 13*X(17)-10*X(629) = 23*X(17)-20*X(6673) = 2*X(17)-5*X(22113) = 11*X(17)-5*X(22844) = 7*X(17)-10*X(33465) = 12*X(17)-5*X(33622) = 13*X(627)-16*X(629) = X(627)-4*X(22113) = 11*X(627)-8*X(22844) = 7*X(627)-16*X(33465) = 3*X(627)-2*X(33622) = 4*X(629)-13*X(22113) = 2*X(3534)-3*X(22532)

X(33626) lies on these lines: {2,17}, {530,33610}, {531,33623}, {617,5859}, {3180,19569}, {3534,22532}, {3845,16629}, {4669,22652}, {5464,33612}, {5965,20423}, {11122,12817}, {21359,33413}, {22892,33616}, {30472,33620}

X(33626) = reflection of X(33622) in X(2)
X(33626) = complement of X(36352)
X(33626) = anticomplement of X(36386)
X(33626) = X(11001)-of-2nd half-diamonds triangle
X(33626) = {X(2), X(33622)}-harmonic conjugate of X(627)


X(33627) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 4th INNER-FERMAT-DAO-NHI

Barycentrics    2*S^2+9*SB*SC+sqrt(3)*(9*SA-4*SW)*S : :
X(33627) = 5*X(2)-6*X(18) = 4*X(2)-3*X(628) = 13*X(2)-12*X(630) = X(2)-3*X(22114) = 11*X(2)-6*X(22845) = 7*X(2)-12*X(33464) = 8*X(18)-5*X(628) = 13*X(18)-10*X(630) = 23*X(18)-20*X(6674) = 2*X(18)-5*X(22114) = 11*X(18)-5*X(22845) = 7*X(18)-10*X(33464) = 12*X(18)-5*X(33624) = 13*X(628)-16*X(630) = X(628)-4*X(22114) = 11*X(628)-8*X(22845) = 7*X(628)-16*X(33464) = 3*X(628)-2*X(33624) = 4*X(630)-13*X(22114) = 2*X(3534)-3*X(22531)

X(33627) lies on these lines: {2,18}, {530,33625}, {531,33611}, {616,5858}, {3181,19569}, {3534,22531}, {3845,16628}, {4669,22651}, {5463,33613}, {5965,20423}, {11121,12816}, {21360,33412}, {22848,33617}, {30471,33621}

X(33627) = reflection of X(33624) in X(2)
X(33627) = complement of X(36346)
X(33627) = anticomplement of X(36388)
X(33627) = X(11001)-of-1st half-diamonds triangle
X(33627) = {X(2), X(33624)}-harmonic conjugate of X(628)

leftri

Perspectors of triangles inscribed in the circumcircle: X(33628)-X(33636)

rightri

This preamble and centers X(33628)-X(33636) were contributed by Clark Kimberling and Peter Moses, July 21, 2019. Suppose that P = p : q : r is a point. The points

q - r : r - p : p - q    and     2p - q - r : 2q - r - p : 2r - p - q

clearly lie on the line at infinity, so that their isogonal conjugates,

g(P) = a^2/(q-r) : b^2/(r-p) : c^2/(p-q)     and     h(P) = a^2/(2p-q-r) : b^2/(2q-r-p) : c^2/(2r-p-q),

lie on the circumcircle. Thus, if T is a central triangle Then g(T) and h(T) are central triangles inscribed in the circumcircle. Suppose that X = x : y : z is a triangle center. Let T(1) be the central triangle with A-vertex -x : y : z, and let T(2) be the central triangle with A-vertex 0 : 1/y : 1/z.

Theorem: the triangles g(T(1)) and h(T(2)) are perspective, and their perspector is

M(X) = a^2(-3x+y+z)/(y+z) : b^2(-3y+z+x)/(z+x) : c^2(-3z-x+y)/(x+y).

If X is on the circumcircle, then M(X) is on the line X(6)X', where X' is the X(3)-cross conjugate of X. If X is on the line at infinity, then M(X) = X(6). The appearance of (i,j) in the following list means that M(X(i)) = X(j):

(1,33628), (2,2), (3,33629), (4,33630), (5,33631), (6,33632), (7,33633), (8,3973), (9,33634), (10, 33635), (20,33636)

If X is on the Kiepert circumhyperbola, KCH, of the anticomplementary triangle, then M(X) is on the Brocard axis. Points on KCH include X(i) for these i: {1, 2 , 20, 63, 147, 194, 368, 487, 488, 616, 617, 627, 628, 1670, 1671, 1764, 2128, 2582, 2583, 2896, 3413, 3414, 6194, 6462, 6463, 7616, 8591, 8782, 9742, 10336, 11148, 13174, 13678, 13798, 16552, 16563, 17147, 18301, 18596, 20371, 21378, 30562, 30564, 30579, 33404, 33405, 33608, 33609, 33610, 33611, 33612, 33613}

See César Lozada, Perspectivities involving the g and h mappings.


X(33628) = M(X(1))

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

X(33628) lies on these lines: {3, 6}, {21, 3731}, {28, 16485}, {48, 595}, {81, 18186}, {106, 112}, {110, 17222}, {163, 16947}, {230, 32431}, {604, 7031}, {609, 2268}, {727, 26714}, {741, 26716}, {759, 26715}, {849, 7054}, {902, 2206}, {1169, 16785}, {1743, 4855}, {2273, 24047}, {2287, 3973}, {2303, 3247}, {2327, 5526}, {2360, 16483}, {2712, 2715}, {3052, 20818}, {3620, 24632}, {3729, 16046}, {4234, 17355}, {4483, 19623}, {4877, 16814}, {7419, 17945}, {14953, 17189}, {16470, 22054}, {17398, 18907}, {21287, 30851}


X(33629) = M(X(3))

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

X(33629) lies on these lines: {6, 24}, {74, 15664}, {95, 3619}, {97, 1073}, {571, 1614}, {577, 14371}, {2165, 12289}, {3484, 10979}, {8745, 26882}, {8883, 11456}, {8972, 16032}, {13509, 22052}, {13941, 16037}, {19210, 28783}


X(33630) = M(X(4))

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

X(33630) lies on these lines: {4, 6}, {19, 10977}, {24, 1033}, {111, 30249}, {216, 3525}, {281, 1886}, {297, 20080}, {323, 6820}, {577, 17538}, {648, 11008}, {1068, 8755}, {1093, 6621}, {1495, 3079}, {1595, 22246}, {1785, 3973}, {1870, 7129}, {2331, 6198}, {3091, 15851}, {3284, 11541}, {3518, 8573}, {3524, 10979}, {3528, 22052}, {3529, 15905}, {3535, 8972}, {3536, 13941}, {3619, 17907}, {3620, 9308}, {3731, 7952}, {5064, 14930}, {5304, 7714}, {6353, 16318}, {6618, 14569}, {6819, 15018}, {7487, 21309}, {11001, 18487}, {11547, 14361}, {12090, 14572}, {14091, 14580}

X(33630) = isogonal conjugate of X(36609)
X(33630) = polar conjugate of X(35510)
X(33630) = pole wrt polar circle of trilinear polar of X(35510) (line X(525)X(7658))
X(33630) = crosssum of X(3) and X(33636)
X(33630) = X(63)-isoconjugate of X(3532)
X(33630) = polar conjugate of isotomic conjugate of X(3146)


X(33631) = M(X(5))

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

X(33631) lies on these lines: {2, 10979}, {6, 1173}, {53, 1487}, {112, 14579}, {232, 3108}, {251, 10985}, {393, 7755}, {3199, 8882}, {3228, 33513}, {5421, 26863}, {6748, 26862}, {10641, 21462}, {10642, 21461}

X(33631) = polar conjugate of X(1232)


X(33632) = M(X(6))

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

X(33632) lies on these lines: {6, 22}, {83, 5033}, {187, 28724}, {206, 1627}, {1384, 10547}, {1691, 8601}, {1799, 3620}, {3619, 10130}, {5092, 8152}


X(33633) = M(X(7))

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

X(33633) lies on these lines: {1, 31391}, {6, 57}, {9, 1443}, {77, 3247}, {241, 3973}, {738, 1055}, {1406, 5128}, {1420, 1456}, {1429, 19604}, {1464, 13384}, {2124, 4350}, {3731, 6180}, {3945, 4654}, {4306, 16485}, {4334, 16491}, {5018, 16496}, {7290, 32577}, {9312, 17116}, {9436, 20080}, {16670, 17092}

X(33633) = isogonal conjugate of X(36627)


X(33634) = M(X(9))

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

X(33634) lies on these lines: {6, 1174}, {2346, 3247}


X(33635) = M(X(10))

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

X(33635) lies on these lines: {6, 595}, {9, 3871}, {19, 3731}, {37, 2160}, {55, 7064}, {57, 1255}, {101, 17454}, {284, 1334}, {333, 2321}, {673, 1268}, {1751, 6539}, {2161, 16814}, {2164, 4262}, {2177, 2258}, {2259, 5526}, {2268, 2364}, {2269, 2316}, {2291, 8701}, {3723, 5030}, {5124, 9327}, {16777, 24047}

X(33635) = isogonal conjugate of X(553)


X(33636) = M(X(20))

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

X(33636) lies on these lines: {3, 6}, {30, 33630}, {323, 6617}, {393, 5073}, {441, 20080}, {1249, 1657}, {3087, 3851}, {3630, 20208}, {10313, 20850}, {19588, 23164}, {22124, 23070}

X(33636) = isogonal conjugate of polar conjugate of X(5059)


X(33637) =  TRILINEAR POLE OF LINE X(6)X(1731)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29211.

X(33637) lies on the circumcircle and these lines: {3, 14987}, {46, 15530}, {104, 411}, {105, 29681}, {106, 21842}, {109, 13589}, {915, 7412}, {1018, 29115}, {1897, 30250}, {3799, 29337}, {4242, 26704}, {6099, 14513}, {7424, 12030}

X(33637) = reflection of X(14987) in X(3)
X(33637) = circumperp conjugate of X(14987)
X(33637) = antipode of X(14987) in the circumcircle
X(33637) = trilinear pole of line X(6)X(1731)
X(33637) = barycentric quotient X(i)/X(j) for these (i,j): (100, 33113), (101, 22836)
X(33637) = trilinear quotient X(i)/X(j) for these (i,j): (100, 22836), (190, 33113)
X(33637) = X(12092)-of-1st circumperp triangle
X(33637) = X(14103)-of-excentral triangle
X(33637) = X(14987)-of-ABC-X3 reflections triangle
X(33637) = X(22751)-of-2nd circumperp triangle


X(33638) =  TRILINEAR POLE OF LINE X(6)X(9716)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29211.

X(33638) lies on the circumcircle and these lines: {98, 3534}, {111, 7492}, {376, 13530}, {843, 8586}, {2374, 5094}, {2770, 10989}, {4563, 6082}, {5966, 15744}, {5970, 10631}, {11634, 11636}

X(33638) = trilinear pole of line X(6)X(9716)
X(33638) = barycentric quotient X(110)/X(15534)
X(33638) = trilinear quotient X(662)/X(15534)


X(33639) =  ISOGONAL CONJUGATE OF X(13152)

Barycentrics    (SB+SC)*(SA-SB)*(SA-SC)*(4*SB-R^2-2*SW)*(4*SC-R^2-2*SW) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29211.

See ADGEOM #2795 and related posts (Ngo Quang Duong, Tsihong Lau, Angel Montesdeoca, Nikos Dergiades, September 16, 2015). X(33639) is the point of concurrence when P = X(5). (Randy Hutson, August 19, 2019)

Let T be any of these homothetic triangles: polar triangle of nine-point circle, orthoanticevian triangle of X(2), orthic axes triangle (see X(2501)), Yiu tangents triangle (see X(7495)). Then X(33639) = Λ(orthic axis of T). (Randy Hutson, August 19, 2019)

X(33639) lies on the circumcircle and these lines: {74, 12291}, {2383, 3520}, {5966, 6636}

X(33639) = isogonal conjugate of X(13152)
X(33639) = anticomplement of the complementary conjugate of X(13152)
X(33639) = complement of the anticomplementary conjugate of X(13152)
X(33639) = trilinear pole of line {6, 22462}


X(33640) =  TRILINEAR POLE OF LINE X(6)X(3520)

Barycentrics    SB*SC*(SB+SC)*(SA-SB)*(SA-SC)*(S^2-5*SA*SB)*(S^2-5*SA*SC) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29211.

X(33640) lies on the circumcircle and these lines: {4, 20480}, {74, 6759}, {107, 5502}, {1294, 1657}, {2693, 6760}, {2697, 30745}, {5896, 14379}, {12092, 30510}, {12107, 18401}

X(33640) = trilinear pole of line {6, 3520}
X(33640) = barycentric product X(648)*X(11270)
X(33640) = barycentric quotient X(i)/X(j) for these (i,j): (112, 382), (162, 14212)
X(33640) = trilinear product X(162)*X(11270)
X(33640) = trilinear quotient X(i)/X(j) for these (i,j): (162, 382), (648, 14212)


X(33641) =  ANTIGONAL CONJUGATE OF X(11589)

Barycentrics    SA*(S^2-3*SB*SC)*(S^2+(40*R^2-12*SW+5*SB)*SB)*(S^2+(40*R^2-12*SW+5*SC)*SC) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29211.

X(33641) lies on the cubic K427 and this line {382, 1853}

X(33641) = antigonal conjugate of X(11589)


X(33642) = X(35)X(37)∩X(65)X(16118)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29212.

X(33642) lies on these lines: {35, 37}, {65, 16118}, {5663, 5903}

X(33642) = {X(267), X(1717)}-harmonic conjugate of X(35)


X(33643) = X(4)X(30248)∩X(5)X(930)

Barycentrics    (SB+SC)*((4*SB+R^2-2*SW)*S^2-(3*R^2-2*SW)*SA*SC)*((4*SC+R^2-2*SW)*S^2-(3*R^2-2*SW)*SA*SB) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29213.

Let T be any of these homothetic triangles: polar triangle of nine-point circle, orthoanticevian triangle of X(2), orthic axes triangle (see X(2501)), Yiu tangents triangle (see X(7495)). Then X(33643) = Λ(Euler line of T). (Randy Hutson, August 19, 2019)

X(33643) lies on the circumcircle, the cubics K067, K464, and these lines: {4, 30248}, {5, 930}, {110, 143}, {112, 14577}, {933, 10214}, {1291, 6150}

X(33643) = reflection of X(74) in the line X(3)X(15532)
X(33643) = (ABC-X3 reflections)-isogonal conjugate of-X(13152)


X(33644) = X(3)X(1075)∩X(14249)X(18400)

Barycentrics    (S^4-2*(16*R^4+SB*SC-SW^2)*S^2-(4*R^2-SW)*(16*(36*R^2+8*SA-23*SW)*R^4+4*(2*SA^2-18*SA*SW+19*SW^2)*R^2+(6*SA^2+2*SA*SW-5*SW^2)*SW))*SB*SC : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29221.

X(33644) lies on these lines: {3, 1075}, {14249, 18400}


X(33645) =  MIDPOINT OF X(65) AND X(3025)

Barycentrics    a*(a^8*b - 3*a^7*b^2 - 2*a^6*b^3 + 9*a^5*b^4 - 9*a^3*b^6 + 2*a^2*b^7 + 3*a*b^8 - b^9 + a^8*c - 2*a^7*b*c + 8*a^6*b^2*c - 8*a^5*b^3*c - 16*a^4*b^4*c + 22*a^3*b^5*c + 4*a^2*b^6*c - 12*a*b^7*c + 3*b^8*c - 3*a^7*c^2 + 8*a^6*b*c^2 - 10*a^5*b^2*c^2 + 17*a^4*b^3*c^2 - 25*a^2*b^5*c^2 + 13*a*b^6*c^2 - 2*a^6*c^3 - 8*a^5*b*c^3 + 17*a^4*b^2*c^3 - 26*a^3*b^3*c^3 + 19*a^2*b^4*c^3 + 12*a*b^5*c^3 - 8*b^6*c^3 + 9*a^5*c^4 - 16*a^4*b*c^4 + 19*a^2*b^3*c^4 - 32*a*b^4*c^4 + 6*b^5*c^4 + 22*a^3*b*c^5 - 25*a^2*b^2*c^5 + 12*a*b^3*c^5 + 6*b^4*c^5 - 9*a^3*c^6 + 4*a^2*b*c^6 + 13*a*b^2*c^6 - 8*b^3*c^6 + 2*a^2*c^7 - 12*a*b*c^7 + 3*a*c^8 + 3*b*c^8 - c^9) : :
X(33645) = 3 X[354] - X[13756],5 X[18398] - X[23153]

See Antreas Hatzipolakis, Peter Moses and and César Lozada, Hyacinthos 29224 and Hyacinthos 29227.

X(33645) lies on these lines: {1, 901}, {57, 953}, {65, 3025}, {226, 31841}, {354, 13756}, {513, 12736}, {517, 5083}, {942, 24201}, {1210, 3259}, {2800, 14115}, {13411, 22102}, {18398, 23153}

X(33645) = midpoint of X(65) and X(3025)
X(33645) = reflection of X(24201) in X(942)
X(33645) = reflection of X(12736) in the OI line
X(33645) = incircle inverse of X(2718)
X(33645) = (inverse-in-incircle)-isogonal conjugate of-X(952)
X(33645) = (intouch)-complement of-X(13756)
X(33645) = X(477)-of-inverse-in-incircle triangle
X(33645) = X(25641)-of-intouch triangle
X(33645) = X(31379)-of-Ursa-minor triangle

X(33646) =  COMPLEMENT OF X(15632)

Barycentrics    a*(-a+b+c)*(b-c)^2*(a^5-(2*b-c)*(b-2*c)*a^3-3*(b+c)*b*c*a^2+(b^4+c^4-b*c*(5*b^2-12*b*c+5*c^2))*a+3*(b^2-c^2)*(b-c)*b*c) : :
X(33646) = 3*X(11)+X(3025), X(3025)-3*X(14115), 9*X(16173)-X(23153)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29227.

Let LA, LB, LC be the lines through A, B, C, resp. parallel to line X(1)X(3). Let MA, MB, MC be the reflections of BC, CA, AB in LA, LB, LC, resp. Let A' = MB∩MC, and define B' and C' cyclically. Triangle A'B'C' is inversely similar to, and 3 times the size of, ABC. X(33646) is the center of inverse similitude of ABC and A'B'C'; see Hyacinthos #16741/16782, September 2008. (Randy Hutson, August 19, 2019)

X(33646) lies on these lines: {2, 15632}, {11, 513}, {244, 6129}, {517, 1387}, {650, 2170}, {1086, 3326}, {1149, 5048}, {3011, 18839}, {3022, 14027}, {3086, 31849}, {3660, 11028}, {15608, 21252}, {16173, 23153}

X(33646) = midpoint of X(i) and X(j) for these lines: {i,j}: {11, 14115}, {3259, 15635}
X(33646) = complement of X(15632)
X(33646) = X(3233)-of-intouch triangle

X(33647) =  MIDPOINT OF X(3025) AND X(14115)

Barycentrics    a*(b-c)^2*(-a+b+c)*(3*a^5-(6*b^2-7*b*c+6*c^2)*a^3-(b+c)*b*c*a^2+(3*b^4+3*c^4-b*c*(7*b^2-12*b*c+7*c^2))*a+(b^2-c^2)*(b-c)*b*c) : :
X(33647) = X(11)+3*X(3025), X(11)-3*X(14115)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29227.

X(33647) lies on these lines: {11, 513}, {517, 5083}, {1155, 1458}, {1357, 3328}, {4162, 7004}, {4293, 31849}

X(33647) = midpoint of X(3025) and X(14115)

X(33648) = (name pending)

Barycentrics    a*( 2*a^14-3*(b+c)*a^13-(11*b^2-14*b*c+11*c^2)*a^12+6*(b+c)*(3*b^2-4*b*c+3*c^2)*a^11+12*(2*b^4+2*c^4-(4*b^2-5*b*c+4*c^2)*b*c)*a^10-(b+c)*(45*b^4+45*c^4-8*(11*b^2-13*b*c+11*c^2)*b*c)*a^9-(25*b^6+25*c^6-7*(10*b^4+10*c^4-(15*b^2-16*b*c+15*c^2)*b*c)*b*c)*a^8+2*(b+c)*(30*b^6+30*c^6-(64*b^4+64*c^4-(85*b^2-96*b*c+85*c^2)*b*c)*b*c)*a^7+2*(5*b^8+5*c^8-(32*b^6+32*c^6-(49*b^4+49*c^4-(36*b^2-29*b*c+36*c^2)*b*c)*b*c)*b*c)*a^6-(b+c)*(45*b^8+45*c^8-(96*b^6+96*c^6-(94*b^4+94*c^4-(88*b^2-93*b*c+88*c^2)*b*c)*b*c)*b*c)*a^5+(3*b^8+3*c^8+(48*b^6+48*c^6+(22*b^4+22*c^4-(8*b^2+21*b*c+8*c^2)*b*c)*b*c)*b*c)*(b-c)^2*a^4+2*(b^2-c^2)*(b-c)*(9*b^8+9*c^8-(2*b^4+2*c^4+(7*b^2-16*b*c+7*c^2)*b*c)*(b+c)^2*b*c)*a^3-2*(b^2-c^2)^2*(b-c)^2*(2*b^6+2*c^6+(12*b^4+12*c^4+(9*b^2+10*b*c+9*c^2)*b*c)*b*c)*a^2-(b^4-c^4)*(b^2-c^2)^3*(b+c)*(3*b^2-8*b*c+3*c^2)*a+(b^2-c^2)^6*(b+c)^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29226.

X(33648) lies on this line: {36, 3065}


X(33649) =  MIDPOINT OF X(109) AND X(1807)

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

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29235.

X(33649) lies on these lines: {1, 3}, {37, 1983}, {109, 1807}, {201, 22937}, {651, 12738}, {952, 11700}, {1104, 6788}, {1411, 6797}, {1455, 28204}, {1777, 31828}, {5081, 27529}, {5840, 15252}, {6198, 7012}, {6796, 32047}, {18340, 28160}, {24433, 31445}

X(33649) = midpoint of X(109) and X(1807)
X(33649) = crossdifference of every pair of points on line {650, 7297}
X(33649) = inverse-in-circumconic-centered-at-X(1) of X(484)


X(33650) = X(2)X(109)∩X(4)X(151)

Barycentrics    a^6 - a^5*b - a^4*b^2 + a^2*b^4 + a*b^5 - b^6 - a^5*c + 3*a^4*b*c - 3*a*b^4*c + b^5*c - a^4*c^2 - 2*a^2*b^2*c^2 + 2*a*b^3*c^2 + b^4*c^2 + 2*a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 - 3*a*b*c^4 + b^2*c^4 + a*c^5 + b*c^5 - c^6 : :
X(33650) = 3 X[2] - 4 X[124],9 X[2] - 8 X[6718],3 X[4] - 2 X[10740],3 X[109] - 4 X[6718],X[109] - 3 X[10716],4 X[117] - 5 X[3091],3 X[124] - 2 X[6718],2 X[124] - 3 X[10716],3 X[151] - 4 X[10740],X[151] - 4 X[10747],7 X[3523] - 8 X[6711],3 X[3543] - 2 X[10726],5 X[3616] - 4 X[11700],7 X[3622] - 8 X[11734],3 X[3839] - 2 X[10709],3 X[5731] - 4 X[11713],4 X[6718] - 9 X[10716],X[10740] - 3 X[10747],8 X[29008] - 9 X[32558]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29235.

X(33650) lies on the circumcircle of the anticomplementary triangle and these lines: {2, 109}, {4, 151}, {8, 153}, {20, 102}, {63, 147}, {92, 1836}, {117, 3091}, {144, 31091}, {145, 10703}, {146, 2779}, {148, 2785}, {149, 3738}, {150, 928}, {152, 2807}, {189, 9812}, {193, 10764}, {221, 17555}, {329, 2835}, {388, 1361}, {497, 1364}, {651, 23541}, {908, 4645}, {914, 3685}, {938, 12016}, {962, 2817}, {1330, 3869}, {1331, 27542}, {1456, 17923}, {1795, 3086}, {1845, 4295}, {2550, 3042}, {2551, 3040}, {2773, 3448}, {2841, 3436}, {2852, 14360}, {2853, 13219}, {3146, 10732}, {3523, 6711}, {3543, 10726}, {3616, 11700}, {3622, 11734}, {3839, 10709}, {4468, 14732}, {5081, 6001}, {5174, 12688}, {5698, 6350}, {5731, 11713}, {8048, 10446}, {8677, 21293}, {9364, 26010}, {9532, 12384}, {11109, 20306}, {11681, 15050}, {12699, 20220}, {14594, 26611}, {17615, 32850}, {18662, 33100}, {20557, 20562}, {29008, 32558}

X(33650) = reflection of X(i) in X(j) for these lines: {i,j}: {2, 10716}, {4, 10747}, {8, 13532}, {20, 102}, {109, 124}, {145, 10703}, {149, 10777}, {151, 4}, {193, 10764}, {3146, 10732}
X(33650) = isogonal conjugate of X(34189)
X(33650) = anticomplement of X(109)
X(33650) = orthoptic circle of the Steiner circumellipse inverse of X(1311)
X(33650) = anticomplement of the isogonal of X(522)
X(33650) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 522}, {2, 693}, {4, 521}, {6, 17496}, {7, 3900}, {8, 513}, {9, 514}, {11, 149}, {21, 523}, {29, 7253}, {33, 25259}, {41, 21225}, {55, 17494}, {57, 4025}, {75, 21302}, {78, 20294}, {80, 3738}, {81, 4467}, {84, 8058}, {87, 4449}, {88, 4453}, {101, 4552}, {104, 2804}, {108, 1897}, {162, 14544}, {189, 4131}, {190, 21272}, {200, 4468}, {210, 31290}, {256, 3907}, {261, 17166}, {274, 4374}, {277, 24002}, {278, 17896}, {280, 4397}, {281, 4391}, {282, 6332}, {284, 4560}, {291, 2254}, {294, 918}, {312, 20295}, {314, 512}, {318, 20293}, {329, 20297}, {333, 7192}, {346, 4462}, {513, 145}, {514, 7}, {521, 20}, {522, 8}, {523, 2475}, {525, 2897}, {643, 4427}, {644, 190}, {646, 668}, {647, 18667}, {649, 3210}, {650, 2}, {651, 664}, {652, 6360}, {653, 4566}, {656, 3152}, {657, 3177}, {661, 17778}, {662, 17136}, {663, 192}, {666, 883}, {668, 3888}, {693, 3434}, {885, 518}, {905, 347}, {941, 23880}, {983, 3810}, {1018, 3882}, {1019, 3875}, {1021, 63}, {1022, 1266}, {1024, 239}, {1039, 23874}, {1156, 6366}, {1169, 15420}, {1172, 525}, {1320, 900}, {1392, 4926}, {1577, 2893}, {1635, 30577}, {1639, 30578}, {1783, 651}, {1812, 6563}, {1896, 520}, {1929, 4458}, {1946, 3164}, {2170, 4440}, {2185, 17161}, {2194, 31296}, {2298, 3910}, {2299, 17498}, {2316, 21222}, {2319, 649}, {2320, 4777}, {2335, 23882}, {2344, 824}, {2346, 6362}, {2481, 926}, {2648, 2785}, {2766, 4242}, {2804, 153}, {2997, 8676}, {3063, 194}, {3064, 5905}, {3223, 23655}, {3239, 329}, {3254, 3887}, {3261, 21285}, {3271, 9263}, {3307, 3308}, {3308, 3307}, {3309, 7674}, {3596, 21301}, {3669, 4452}, {3680, 3667}, {3683, 14779}, {3699, 3952}, {3700, 2895}, {3709, 1655}, {3716, 17794}, {3737, 1}, {3738, 6224}, {3835, 20537}, {3900, 144}, {3952, 3909}, {4041, 1654}, {4086, 1330}, {4130, 30695}, {4391, 69}, {4397, 3436}, {4516, 148}, {4521, 8055}, {4560, 75}, {4581, 65}, {4594, 3903}, {4608, 20292}, {4612, 99}, {4631, 4576}, {4636, 6758}, {4768, 21290}, {4814, 17488}, {4858, 150}, {4866, 4778}, {4876, 812}, {4895, 17487}, {4900, 6006}, {4985, 2891}, {4997, 21297}, {5548, 2397}, {6332, 4329}, {6557, 4106}, {6591, 30699}, {6598, 6003}, {6601, 3309}, {6728, 7057}, {6729, 16018}, {6730, 16017}, {7105, 656}, {7110, 1577}, {7155, 4083}, {7192, 3873}, {7199, 20244}, {7220, 4724}, {7252, 17147}, {7253, 3869}, {7281, 4088}, {7649, 12649}, {7658, 31527}, {8047, 30613}, {8056, 3676}, {8058, 6223}, {8611, 3151}, {8641, 21218}, {8702, 12849}, {8851, 659}, {9282, 21105}, {9368, 6615}, {9375, 6129}, {9445, 6608}, {9503, 2400}, {10266, 8702}, {10309, 30201}, {10492, 4146}, {10495, 188}, {10566, 20247}, {11604, 8674}, {11609, 2787}, {12641, 2827}, {13426, 6365}, {13454, 6364}, {13486, 6742}, {14224, 2771}, {14298, 20211}, {14304, 151}, {14837, 5932}, {16612, 18632}, {17096, 17158}, {17420, 5484}, {17926, 92}, {18101, 25048}, {18108, 3891}, {18155, 17135}, {18191, 17154}, {18344, 193}, {19605, 3239}, {20906, 20350}, {21044, 21221}, {23189, 20222}, {23696, 3100}, {23836, 3880}, {23838, 519}, {23893, 527}, {24002, 6604}, {27527, 17149}, {28659, 21304}, {28660, 17217}, {30479, 8678}, {30513, 9001}, {30571, 4804}, {30610, 4554}, {31343, 3699}, {31623, 850}, {31628, 4998}, {32635, 4977}
X(33650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 124, 2}, {109, 10716, 124}

X(33651) =  X(2)X(32)∩X(22)X(99)

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

X(33651) lies on these lines: {2, 32}, {22, 99}, {23, 8024}, {25, 76}, {69, 1974}, {95, 1007}, {98, 3222}, {183, 5020}, {316, 427}, {325, 6676}, {376, 19583}, {385, 1196}, {394, 9419}, {468, 7768}, {491, 18289}, {492, 18290}, {524, 2056}, {858, 16275}, {1184, 6179}, {1194, 7760}, {1236, 13595}, {1368, 7750}, {1370, 7802}, {1383, 16952}, {1629, 18022}, {1975, 9909}, {2862, 8709}, {2979, 4563}, {3228, 8667}, {3266, 6636}, {3926, 10565}, {3933, 10154}, {3972, 11324}, {3978, 7467}, {4176, 33522}, {5094, 7860}, {5133, 11056}, {5206, 30793}, {5207, 21243}, {5971, 15246}, {6394, 6638}, {6573, 9076}, {6677, 7767}, {6995, 11185}, {7386, 14907}, {7392, 32832}, {7394, 15031}, {7398, 32828}, {7484, 7771}, {7485, 11059}, {7493, 7796}, {7494, 7763}, {7499, 7769}, {7873, 30777}, {8889, 32006}, {8891, 16950}, {11057, 31152}, {16951, 30749}, {30786, 31101}

X(33651) = isotomic conjuage of the isogonal conjugate of X(19121)
X(33651) = X(250)-Ceva conjugate of X(99)
X(33651) = crosspoint of X(689) and X(18020)
X(33651) = crosssum of X(688) and X(20975)
X(33651) = barycentric product X(i)*X(j) for these lines: {i,j}: {76, 19121}, {1502, 15257}
X(33651) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {15257, 32}, {19121, 6}
X(33651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1799, 1078}, {2, 26233, 1799}, {22, 305, 99}, {23, 8024, 16276}


X(33652) =  X(2)X(66)∩X(110)X(22135)

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

X(33652) lies on these lines: {2, 66}, {110, 22135}


X(33653) =  X(1)X(16)∩X(14)X(80)

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

X(33653) lies on the Feuerbach circumhyperbola and these lines: {1, 16}, {4, 1833}, {6, 11073}, {7, 554}, {8, 5240}, {14, 80}, {21, 5239}, {37, 2154}, {55, 199}, {61, 3467}, {79, 10651}, {84, 10649}, {90, 2307}, {104, 18469}, {177, 30372}, {203, 3065}, {256, 30364}, {1100, 7127}, {1652, 30300}, {1953, 3130}, {3062, 30292}, {3296, 30344}, {7005, 7161}, {8609, 10636}, {11087, 21011}

X(33653) = isogonal conjugate of X(559)
X(33653) = X(i)-cross conjugate of X(j) for these (i,j): {1100, 1251}, {7127, 7126}, {30377, 7}
X(33653) = X(i)-isoconjugate of X(j) for these (i,j): {1, 559}, {7, 10638}, {35, 1081}, {554, 7005}, {1251, 1442}, {2306, 3219}
X(33653) = barycentric product X(i)*X(j) for these lines: {i,j}: {9, 554}, {14, 5239}, {1082, 7110}, {1250, 30690}
X(33653) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 559}, {41, 10638}, {554, 85}, {1082, 17095}, {1250, 3219}, {2160, 1081}, {2307, 1442}, {3458, 7052}, {5239, 299}, {6186, 2306}
X(33653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 10638, 7126}, {55, 16777, 1251}, {2160, 7073, 1251}


X(33654) =  X(1)X(16)∩X(14)X(79)

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

X(33654) lies on the conic {{A,B,C,X(1),X(2)}} and these lines: {1, 16}, {2, 554}, {6, 1406}, {14, 79}, {56, 11073}, {57, 2307}, {61, 3336}, {62, 5902}, {65, 2154}, {81, 15772}, {202, 5903}, {203, 3337}, {277, 30281}, {395, 3649}, {398, 11246}, {484, 7005}, {559, 1255}, {942, 7127}, {1082, 25417}, {3130, 6186}, {3579, 10638}, {5131, 5238}, {5239, 5253}, {5367, 11684}, {5442, 16241}, {5714, 30328}, {7006, 18398}, {7051, 32636}, {11543, 11544}

X(33654) = {X(6),X(5221)}-harmonic conjugate of X(2306)
X(33654) = X(i)-cross conjugate of X(j) for these (i,j): {7051, 7052}, {32636, 2306}
X(33654) = X(i)-isoconjugate of X(j) for these (i,j): {2, 10638}, {9, 559}, {16, 7043}, {1251, 3219}, {2306, 4420}, {5239, 7150}, {5357, 7026}
X(33654) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 554}, {79, 1082}, {2307, 30690}
X(33654) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {31, 10638}, {56, 559}, {554, 75}, {1082, 319}, {1250, 4420}, {2154, 7043}, {2307, 3219}, {3458, 7126}, {6186, 1251}, {11073, 7026}


X(33655) =  X(1)X(62)∩X(13)X(80)

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

X(33655) lies on the conic {{A,B,C,X(1),X(2)}} and these lines: {1, 62}, {2, 559}, {6, 1411}, {13, 80}, {14, 18393}, {15, 484}, {17, 18395}, {18, 5443}, {56, 11073}, {57, 7051}, {61, 5903}, {65, 2153}, {81, 1082}, {203, 5902}, {395, 15950}, {397, 10950}, {1250, 24929}, {1319, 19373}, {1929, 10648}, {3129, 6187}, {5119, 10638}, {5353, 5425}, {5444, 16242}, {5697, 7005}, {11542, 11545}

X(33655) = isogonal conjugate of X(5240)
X(33655) = X(1168)-Ceva conjugate of X(7052)
X(33655) = X(i)-cross conjugate of X(j) for these (i,j): {1319, 7052}, {19373, 2306}
X(33655) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5240}, {8, 19373}, {36, 7043}, {202, 7026}, {283, 1832}, {3218, 7126}, {4511, 7052}
X(33655) = cevapoint of X(2307) and X(19373)
X(33655) = crosssum of X(1) and X(11789)
X(33655) = barycentric product X(i)*X(j) for these lines: {i,j}: {7, 19551}, {13, 1082}, {57, 7026}, {2006, 5239}, {7051, 18359}, {7127, 18815}
X(33655) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 5240}, {604, 19373}, {1082, 298}, {1880, 1832}, {2161, 7043}, {3457, 1251}, {5239, 32851}, {6187, 7126}, {7026, 312}, {7051, 3218}, {7127, 4511}, {19551, 8}
X(33655) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2099, 7052}, {65, 2307, 2306}, {1411, 2161, 7052}


X(33656) = X(500)X(1064)∩X(517)X(13630)

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

See Antreas Hatzipolakis, César Lozada and Ercole Suppa, Hyacinthos 29238 and Hyacinthos 29240.

X(33656) lies on these lines: {500, 1064}, {517, 13630}


X(33657) = X(1)X(3)∩X(5)X(33337)

Barycentrics    a*(4*a^6-7*(b+c)*a^5-5*(b^2-4*b*c+c^2)*a^4+(b+c)*(14*b^2-25*b*c+14*c^2)*a^3-2*(b^4+c^4+b*c*(7*b^2-15*b*c+7*c^2))*a^2-(b^2-c^2)*(b-c)*(7*b^2-11*b*c+7*c^2)*a+3*(b^2-c^2)^2*(b-c)^2) : :
X(33657) = 3*X(1)+X(26285)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29242.

X(33657) lies on these lines: {1, 3}, {5, 33337}, {1483, 10265}, {5901, 16174}, {10283, 11263}

X(33657) = midpoint of X(i) and X(j) for these {i,j}: {1, 26287}, {1385, 11567}, {24680, 26086}
X(33657) = X(26287)-of-anti-Aquila triangle
X(33657) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 11849, 24680), (1, 21842, 13751), (1385, 24680, 36)


X(33658) = X(1)X(3)∩X(1483)X(21630)

Barycentrics    a*( 4*a^6-9*(b+c)*a^5-(3*b^2-28*b*c+3*c^2)*a^4+3*(3*b-2*c)*(2*b-3*c)*(b+c)*a^3-2*(3*b^4+3*c^4+(9*b^2-25*b*c+9*c^2)*b*c)*a^2-3*(b^2-c^2)*(b-c)*(3*b^2-7*b*c+3*c^2)*a+5*(b^2-c^2)^2*(b-c)^2) : :
X(33658) = 5*X(1)-X(26285), 3*X(1)-X(26287), X(10525)+7*X(20057)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29246.

X(33658) lies on these lines: {1, 3}, {1483, 21630}, {5901, 6702}, {10525, 20057}, {28204, 32905}

X(33658) = midpoint of X(24680) and X(26087)
X(33658) = reflection of X(33657) in X(1)


X(33659) =  X(5)X(113)∩X(10574)X(24904)

Barycentrics    a^2*((b^2+c^2)*a^12-4*(b^4+c^4)*a^10+5*(b^6+c^6)*a^8-(b+c)*(b^2+c^2)*b^2*c^2*a^7-(11*b^4-18*b^2*c^2+11*c^4)*b^2*c^2*a^6+(b+c)*(b^2+b*c+c^2)*(3*b^2-4*b*c+3*c^2)*b^2*c^2*a^5-(b^2+c^2)*(5*b^6+5*c^6-(10*b^4+10*c^4+(8*b^2-25*b*c+8*c^2)*b*c)*b*c)*(b+c)^2*a^4-(b^2-c^2)*(b-c)*(3*b^4+3*c^4+4*(b^2+b*c+c^2)*b*c)*b^2*c^2*a^3+(4*b^8+4*c^8-(b^4+c^4+2*(b^2+6*b*c+c^2)*b*c)*b^2*c^2)*(b^2-c^2)^2*a^2+(b^3-c^3)*(b^2-c^2)^3*b^2*c^2*a+(b^2-c^2)^3*(b-c)*(b^3+c^3)*(-b^4-c^4-(b^2+3*b*c+c^2)*b*c)) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29250.

X(33659) lies on these lines: {5, 113}, {517, 33661}, {10574, 24904}


X(33660) =  X(5)X(31847)∩X(185)X(526)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29250.

X(33660) lies on these lines: {5, 31847}, {185, 526}, {513, 33662}


X(33661) =  EULER LINE INTERCEPT OF X(517)X(33659)

Barycentrics    2*a^13-2*(b+c)*a^12-(5*b^2+2*b*c+5*c^2)*a^11+(b+c)*(5*b^2-4*b*c+5*c^2)*a^10+(b^4+c^4+4*(b^2+4*b*c+c^2)*b*c)*a^9-(b+c)*(b^4+c^4-(7*b^2-16*b*c+7*c^2)*b*c)*a^8+(6*b^6+6*c^6-(13*b^2+10*b*c+13*c^2)*b^2*c^2)*a^7-(b+c)*(6*b^6+6*c^6-(b^4+c^4+2*(7*b^2-11*b*c+7*c^2)*b*c)*b*c)*a^6-(b^2-c^2)^2*(4*b^4+4*c^4+(4*b^2+13*b*c+4*c^2)*b*c)*a^5+(b^2-c^2)*(b-c)*(4*b^6+4*c^6+(3*b^4+3*c^4+2*(2*b^2+7*b*c+2*c^2)*b*c)*b*c)*a^4-(b^2-c^2)^2*(b^6+c^6-2*(b^4+c^4+(4*b^2+3*b*c+4*c^2)*b*c)*b*c)*a^3+(b^2-c^2)^3*(b-c)^3*(b^2+3*b*c+c^2)*a^2+(b^6-c^6)*(b^2-c^2)^3*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29250.

X(33661) lies on these lines: {2, 3}, {517, 33659}


X(33662) =  EULER LINE INTERCEPT OF X(513)X(33660)

Barycentrics    2*a^13-2*(b+c)*a^12-(5*b^2-6*b*c+5*c^2)*a^11+(b+c)*(5*b^2-4*b*c+5*c^2)*a^10+(b^4+c^4-2*(5*b^2-8*b*c+5*c^2)*b*c)*a^9-(b+c)*(b^4+c^4-(7*b^2-16*b*c+7*c^2)*b*c)*a^8+(6*b^6+6*c^6-(4*b^4+4*c^4+15*(b-c)^2*b*c)*b*c)*a^7-(b^2-c^2)*(b-c)*(6*b^4+6*c^4+11*(b^2+c^2)*b*c)*a^6-(4*b^6+4*c^6-(4*b^4+4*c^4+(11*b^2+2*b*c+11*c^2)*b*c)*b*c)*(b-c)^2*a^5+(b^2-c^2)*(b-c)*(4*b^6+4*c^6+(3*b^2+c^2)*(b^2+3*c^2)*b*c)*a^4-(b^2-c^2)^2*(b^6+c^6+2*(b^4+c^4-(3*b^2-7*b*c+3*c^2)*b*c)*b*c)*a^3+(b^2-c^2)^3*(b-c)*(b^4+c^4+(b-c)^2*b*c)*a^2+(b^4+c^4-(2*b^2-b*c+2*c^2)*b*c)*(b^2-c^2)^4*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29250.

X(33662) lies on these lines: {2, 3}, {513, 33660}


X(33663) =  X(659)X(33660)∩X(2254)X(33662)

Barycentrics    a(2*b*c*a^15-(b+c)^3*a^14+(b^4+c^4-(3*b-c)*(b-3*c)*b*c)*a^13+(b+c)*(4*b^4+4*c^4+(b-c)^2*b*c)*a^12-(4*b^6+4*c^6+(3*b^4+3*c^4+(15*b^2-14*b*c+15*c^2)*b*c)*b*c)*a^11-(b+c)*(5*b^6+5*c^6-(11*b^4+11*c^4-4*(b^2+c^2)*b*c)*b*c)*a^10+(5*b^8+5*c^8+(4*b^6+4*c^6-(5*b^2+21*b*c+5*c^2)*(b-c)^2*b*c)*b*c)*a^9-(b+c)*(14*b^6+14*c^6-(26*b^4+26*c^4-(17*b^2-2*b*c+17*c^2)*b*c)*b*c)*b*c*a^8+(4*b^6+4*c^6-(2*b^4+2*c^4+3*(2*b^2-3*b*c+2*c^2)*b*c)*b*c)*(b+c)^2*b*c*a^7+(b^2-c^2)*(b-c)*(5*b^8+5*c^8+(6*b^6+6*c^6-(13*b^4+13*c^4+3*(b^2+6*b*c+c^2)*b*c)*b*c)*b*c)*a^6-(5*b^10+5*c^10+(b^2+b*c+c^2)*(13*b^6+13*c^6-(4*b^4+4*c^4+7*(b-c)^2*b*c)*b*c)*b*c)*(b-c)^2*a^5-(b^2-c^2)*(b-c)*(4*b^10+4*c^10-(5*b^8+5*c^8+(9*b^6+9*c^6-(b^4+c^4-15*(b^2+c^2)*b*c)*b*c)*b*c)*b*c)*a^4+(b^2-c^2)^2*(4*b^10+4*c^10-(3*b^8+3*c^8-(b^6+c^6-2*(b^4+c^4+(7*b^2-10*b*c+7*c^2)*b*c)*b*c)*b*c)*b*c)*a^3+(b^2-c^2)^3*(b-c)*(b^8+c^8-(3*b^6+3*c^6+4*(b^2-b*c+c^2)*b^2*c^2)*b*c)*a^2-(b^8+c^8-(2*b^2-3*b*c+2*c^2)*(b^4+c^4-(b^2-b*c+c^2)*b*c)*b*c)*(b^2-c^2)^4*a+(b^2-c^2)^5*(b-c)*(b^2+c^2)*b^2*c^2 ) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29250.

X(33663) lies on these lines: {659, 33660}, {2254, 33662}


X(33664) =  X(5)X(3462)∩X(30)X(3481)

Barycentrics    (-a^2 b^2+b^4-a^2 c^2-2 b^2 c^2+c^4) (-a^12+3 a^10 b^2-a^8 b^4-6 a^6 b^6+9 a^4 b^8-5 a^2 b^10+b^12+3 a^10 c^2-5 a^8 b^2 c^2+2 a^6 b^4 c^2-6 a^4 b^6 c^2+11 a^2 b^8 c^2-5 b^10 c^2-3 a^8 c^4+2 a^6 b^2 c^4-2 a^4 b^4 c^4-6 a^2 b^6 c^4+9 b^8 c^4+2 a^6 c^6+2 a^4 b^2 c^6+2 a^2 b^4 c^6-6 b^6 c^6-3 a^4 c^8-5 a^2 b^2 c^8-b^4 c^8+3 a^2 c^10+3 b^2 c^10-c^12) (a^12-3 a^10 b^2+3 a^8 b^4-2 a^6 b^6+3 a^4 b^8-3 a^2 b^10+b^12-3 a^10 c^2+5 a^8 b^2 c^2-2 a^6 b^4 c^2-2 a^4 b^6 c^2+5 a^2 b^8 c^2-3 b^10 c^2+a^8 c^4-2 a^6 b^2 c^4+2 a^4 b^4 c^4-2 a^2 b^6 c^4+b^8 c^4+6 a^6 c^6+6 a^4 b^2 c^6+6 a^2 b^4 c^6+6 b^6 c^6-9 a^4 c^8-11 a^2 b^2 c^8-9 b^4 c^8+5 a^2 c^10+5 b^2 c^10-c^12) : :
Barycentrics    (SA SB+SA SC+2 SB SC) (SA^3 SB^3+SA^3 SB^2 SC+SA^2 SB^3 SC-SA^3 SB SC^2-5 SA^2 SB^2 SC^2-SA SB^3 SC^2-SA^3 SC^3-5 SA^2 SB SC^3-5 SA SB^2 SC^3-SB^3 SC^3) (SA^3 SB^3+SA^3 SB^2 SC+5 SA^2 SB^3 SC-SA^3 SB SC^2+5 SA^2 SB^2 SC^2+5 SA SB^3 SC^2-SA^3 SC^3-SA^2 SB SC^3+SA SB^2 SC^3+SB^3 SC^3) : :
Trilinears    cos(B - C)/(sec A sec(B - C) - sec B sec(C - A) - sec C sec(A - B)) : :

See Aris Pavlakis and Ercole Suppa, Hyacinthos 29253.

X(33664) lies on these lines: {5,3462}, {30,3481}

X(33664) = barycentric product of X(i) and X(j) for these {i,j}: {264,21354}, {324,3463}
X(33664) = barycentric quotient of X(i) and X(j) for these {i,j}: {53,3462}, {3463,97}, {21354,3}
X(33664) = trilinear product X(92)*X(21354)
X(33664) = trilinear quotient X(1087)/X(15780)
X(33664) = polar conjugate of isogonal conjugate of X(21354)
X(33664) = X(4)-cross conjugate of X(5)
X(33664) = circumcircle-inverse of X(34576)
X(33664) = similitude center of tangential and normal triangles of Johnson circumconic

X(33665) =  ISOGONAL CONJUGATE OF X(14885)

Barycentrics    (b^2+c^2) (-a^4-a^2 b^2+b^4-a^2 c^2-b^2 c^2-c^4) (a^4+a^2 b^2+b^4+a^2 c^2+b^2 c^2-c^4) : :
Barycentrics    (2 SA+SB+SC) (SA^2+5 SA SB+3 SB^2+SA SC+5 SB SC+SC^2) (SA^2+SA SB+SB^2+5 SA SC+5 SB SC+3 SC^2) : :

See Aris Pavlakis and Ercole Suppa, Hyacinthos 29253.

Let A' be the point such that triangle A'BC is inversely similar to the symmedial triangle. Define B' and C' cyclically. The lines AA', BB', CC' concur in X(33665); see X(33666). (Randy Hutson, July 29, 2019)

X(33665) lies on these lines: {2,13500}, {5,30218}, {141,384}, {3051,14886}, {4074,7794}, {10007,12143}, {28667,28677}

X(33665) = isogonal conjugate of X(14885)
X(33665) = complement of X(13511)
X(33665) = isotomic conjugate of isogonal conjugate of X(21355)
X(33665) = barycentric product of X(i) and X(j) for these {i,j}: {38,18834}, {76,21355}, {141,1031}, {8024,14370}
X(33665) = barycentric quotient of X(i) and X(j) for these {i,j}: {6,14885}, {38,16556}, {39,10329}, {141,2896}, {1031,83}, {1930,20934}, {3665,17083}, {3917,22138}, {3954,21880}, {14370,251}, {15523,21083}, {16892,21194}, {18834,3112}, {21355,6}
X(33665) = trilinear product of X(i) and X(j) for these {i,j}: {38,1031}, {38,1031}, {39,18834}, {39,18834}, {75,21355}, {75,21355}, {1930,14370}, {1930,14370}
X(33665) = trilinear quotient of X(i) and X(j) for these {i,j}: {1,14885}, {38,10329}, {141,16556}, {1930,2896}, {8024,20934}, {15523,21880}


X(33666) =  X(6)X(148)∩X(755)X(14568)

Barycentrics    1/(a^14 (b^2 - c^2) - 2 a^12 (b^4 - c^4) - 3 a^10 (b^6 - c^6) + 3 a^8 (b^4 - c^4) ((b^2 + c^2)^2 - b^2 c^2) + a^6 (b^2 - c^2) ((b^2 + c^2)^2 - b^2 c^2) (2 b^4 + b^2 c^2 + 2 c^4) - a^4 (b^12 + 3 b^10 c^2 + 3 b^8 c^4 - 3 b^4 c^8 - 3 b^2 c^10 - c^12) - a^2 b^4 c^4 (b^2 - c^2) (2 b^4 + 3 b^2 c^2 + 2 c^4) + b^4 c^4 (b^8 + 3 b^6 c^2 - 3 b^2 c^6 - c^8)) : :

Let A' be the point such that triangle A'BC is directly similar to the symmedial triangle. Define B' and C' cyclically. The lines AA', BB', CC' concur in X(33666); see X(33665). (Randy Hutson, July 29, 2019)

The trilinear polar of X(33666) passes through X(3005).

X(33666) lies on these lines: {6, 148}, {755, 14568}, {2353, 14673}, {11800, 27375}


X(33667) =  REFLECTION OF X(11) IN X(10122)

Barycentrics    a (a+b-c) (a-b+c) (a^3-a^2 b-a b^2+b^3-a^2 c-a b c+b^2 c-a c^2+b c^2+c^3) (a^3 b-a^2 b^2-a b^3+b^4+a^3 c+2 a^2 b c-a^2 c^2-2 b^2 c^2-a c^3+c^4) : :
X(33667) = X[11]-2*X[10122], 3*X[21]-X[12532], 2*X[3035]-X[31938], X[3649]-2*X[5083], X[5441]+X[11571], X[12758]-2*X[15174], 3*X[15670]-2*X[18254]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29258.

X(33667) lies on these lines: {1,399}, {7,11604}, {11,10122}, {21,12532}, {30,11570}, {57,13146}, {79,6583}, {214,5427}, {354,1484}, {442,20118}, {758,1317}, {952,13375}, {2800,10543}, {3035,31938}, {3649,5083}, {5441,11571}, {6917,10044}, {10052,16159}, {10087,16139}, {10427,12832}, {11263,13751}, {12758,15174}, {14151,16140}, {14795,22937}, {14804,22935}, {15670,18254}

X(33667) is the antipode of X(3649) in the hyperbola decribed at X(5083). (Randy Hutson, August 19, 2019)

X(33667) = midpoint of X(i) and X(j) for these {i,j}: {5441,11571}, {17637,17660}
X(33667) = reflection of X(i) in X(j) for these {i,j}: {11,10122}, {3649,5083}, {12758,15174}, {31938,3035}


X(33668) =  COMPLEMENT OF X(13465)

Barycentrics    2 a^6 b-a^5 b^2-5 a^4 b^3+2 a^3 b^4+4 a^2 b^5-a b^6-b^7+2 a^6 c+a^4 b^2 c-a^3 b^3 c-4 a^2 b^4 c+a b^5 c+b^6 c-a^5 c^2+a^4 b c^2-4 a^3 b^2 c^2+a b^4 c^2+3 b^5 c^2-5 a^4 c^3-a^3 b c^3-2 a b^3 c^3-3 b^4 c^3+2 a^3 c^4-4 a^2 b c^4+a b^2 c^4-3 b^3 c^4+4 a^2 c^5+a b c^5+3 b^2 c^5-a c^6+b c^6-c^7 : :
Barycentrics    a b c SA SB+2 a SA SB^2+6 b SA SB^2-2 c SA SB^2+a b c SA SC+2 a b c SB SC+4 b SA SB SC+4 c SA SB SC+2 a SB^2 SC+2 b SB^2 SC-2 c SB^2 SC+2 a SA SC^2-2 b SA SC^2+6 c SA SC^2+2 a SB SC^2-2 b SB SC^2+2 c SB SC^2 : :
X(33668) = 3*X[2]-X[13465], X[3]+X[14450], 2*X[140]-X[191], 3*X[549]-2*X[22937], 5*X[631]-X[31888], 2*X[1125]-X[22936], 5*X[3616]-3*X[28453], 2*X[3647]-3*X[31650], X[3650]-3*X[28465], X[3652]-2*X[10021], 3*X[5886]-X[7701], 2*X[6675]-X[19919], 3*X[10246]-X[15680], 2*X[11277]-X[16139], 2*X[11281]-X[31649]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29258.

X(33668) lies on these lines: {1,30}, {2,13465}, {3,14450}, {5,2771}, {12,11571}, {104,5606}, {140,191}, {442,25005}, {495,14526}, {496,13751}, {549,22937}, {631,31888}, {758,5499}, {946,12267}, {952,2475}, {1071,22805}, {1125,22936}, {1483,13463}, {1484,12005}, {1749,5433}, {3616,28453}, {3647,31650}, {3648,5303}, {3650,28465}, {3651,11849}, {3652,10021}, {3754,11698}, {3845,18243}, {5426,12409}, {5428,17768}, {5563,18244}, {5763,26285}, {5844,16126}, {5886,7701}, {6583,12909}, {6675,19919}, {9955,12009}, {10246,15680}, {10711,18357}, {10916,24475}, {10943,17653}, {11277,16139}, {11281,31649}, {11684,27529}, {12006,31847}, {12433,22938}, {12913,22765}, {13100,16150}, {14988,24987}, {16117,28174}, {25557,26202}

X(33668) = midpoint of X(i) and X(j) for these {i,j}: {3,14450}, {13743,16116}, {16132,16159}
X(33668) = complement of X(13465)
X(33668) = reflection of X(i) in X(j) for these {i,j}: {5,11263}, {191,140}, {3652,10021}, {5690,5499}, {13743,5901}, {16139,11277}, {19919,6675}, {22936,1125}, {31649,11281}
X(33668) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {3652,26725,10021}


X(33669) =  X(65)X(267)∩X(399)X(12702)

Barycentrics    a^2*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 8*a^6*b*c - 14*a^5*b^2*c + 2*a^4*b^3*c + 10*a^3*b^4*c + 2*a^2*b^5*c + 4*a*b^6*c + 4*b^7*c - 4*a^6*c^2 - 14*a^5*b*c^2 - 11*a^4*b^2*c^2 + 8*a^3*b^3*c^2 + 9*a^2*b^4*c^2 + 6*a*b^5*c^2 + 6*b^6*c^2 + 2*a^4*b*c^3 + 8*a^3*b^2*c^3 + 4*a^2*b^3*c^3 - 10*a*b^4*c^3 - 4*b^5*c^3 + 6*a^4*c^4 + 10*a^3*b*c^4 + 9*a^2*b^2*c^4 - 10*a*b^3*c^4 - 14*b^4*c^4 + 2*a^2*b*c^5 + 6*a*b^2*c^5 - 4*b^3*c^5 - 4*a^2*c^6 + 4*a*b*c^6 + 6*b^2*c^6 + 4*b*c^7 + c^8) : :

X(33669) lies on these lines: {65, 267}, {399, 12702}, {3579, 16553}


X(33670) =  X(35)X(1255)∩X(65)X(1014)

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

X(33670) lies on these lines: {35, 1255}, {65, 1014}, {267, 846}, {484, 1126}, {2940, 3678}, {3219, 3579}, {5951, 8701}


X(33671) =  X(35)X(33635)∩X(65)X(1126)

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

X(33671) lies on these lines: {35, 33635}, {65, 1126}


X(33672) =  ISOTOMIC CONJUGATE OF X(3345)

Barycentrics    b*c*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^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(33672) lies on the cubic K183 and these lines: {8, 10366}, {69, 189}, {75, 225}, {253, 322}, {344, 27508}, {3718, 8806}, {5224, 18736}, {5232, 26591}, {7013, 7020}, {14829, 19814}, {16284, 20932}, {18743, 27413}, {20220, 21270}, {20445, 21582}

X(33672) = isotomic conjugate of X(3345)
X(33672) = isotomic conjugate of the isogonal conjugate of X(1490)
X(33672) = X(i)-Ceva conjugate of X(j) for these (i,j): {3718, 75}, {14615, 322}
X(33672) = X(i)-isoconjugate of X(j) for these (i,j): {6, 7152}, {31, 3345}, {56, 7037}, {184, 7149}, {603, 7007}, {1034, 1397}, {2194, 8811}, {2206, 8806}, {2208, 3342}
X(33672) = barycentric product X(i)*X(j) for these {i,j}: {76, 1490}, {304, 3176}, {312, 5932}, {349, 13614}, {561, 3197}, {1035, 28659}, {4554, 14302}
X(33672) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7152}, {2, 3345}, {9, 7037}, {92, 7149}, {207, 608}, {226, 8811}, {281, 7007}, {312, 1034}, {321, 8806}, {329, 3342}, {1035, 604}, {1490, 6}, {3176, 19}, {3197, 31}, {3341, 1436}, {5932, 57}, {8063, 6129}, {8885, 1474}, {13138, 8064}, {13614, 284}, {14302, 650}
X(33672) = {X(307),X(318)}-harmonic conjugate of X(75)


X(33673) =  X(3)X(6359)∩X(7)X(354)

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

X(33673) lies on these lines: {3, 6359}, {7, 354}, {8, 10377}, {20, 1097}, {29, 34}, {69, 1034}, {75, 280}, {92, 18652}, {223, 20921}, {269, 3673}, {279, 17863}, {307, 31627}, {312, 18629}, {314, 5931}, {322, 326}, {658, 7013}, {934, 17134}, {1014, 3188}, {1119, 17170}, {1323, 17861}, {1439, 10446}, {1441, 3160}, {1446, 3945}, {1847, 18650}, {2951, 24014}, {3718, 4554}, {4398, 22464}, {5088, 7053}, {5930, 14615}, {6356, 17181}, {7177, 18655}, {7183, 8822}, {7264, 7271}, {17077, 17080}, {18623, 18750}, {20946, 28753}, {28741, 30829}

Let A1B1C1 and A2B2C2 be the 1st and 2nd Conway triangles, resp. Let A'1 be the trilinear product B1*C1, and define B'1, C'1 cyclically. Let A'2 be the trilinear product B2*C2, and define B'2, C'2 cyclically. The lines A'1A'2, B'1B'2, C'1C'2 concur in X(33673). (Randy Hutson, August 19, 2019)

X(33673) = isotomic conjugate of the isogonal conjugate of X(1394)
X(33673) = X(i)-Ceva conjugate of X(j) for these (i,j): {314, 7}, {7182, 85}
X(33673) = X(i)-cross conjugate of X(j) for these (i,j): {20, 18750}, {5930, 18623}
X(33673) = X(i)-isoconjugate of X(j) for these (i,j): {6, 30457}, {8, 33581}, {9, 2155}, {33, 19614}, {41, 2184}, {55, 64}, {253, 2175}, {281, 14642}, {607, 1073}, {1253, 8809}, {1857, 14379}, {1918, 5931}, {2212, 19611}, {6056, 6526}, {6059, 15394}
X(33673) = cevapoint of X(i) and X(j) for these (i,j): {20, 18623}, {347, 5932}
X(33673) = barycentric product X(i)*X(j) for these {i,j}: {7, 18750}, {20, 85}, {57, 14615}, {75, 18623}, {76, 1394}, {77, 15466}, {154, 20567}, {274, 5930}, {305, 3213}, {310, 30456}, {348, 1895}, {610, 6063}, {1088, 27382}, {1249, 7182}, {4554, 21172}, {4569, 14331}, {4573, 17898}, {4625, 6587}, {4635, 14308}, {7183, 14249}
X(33673) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 30457}, {7, 2184}, {20, 9}, {56, 2155}, {57, 64}, {77, 1073}, {85, 253}, {154, 41}, {204, 607}, {222, 19614}, {273, 459}, {274, 5931}, {279, 8809}, {348, 19611}, {603, 14642}, {604, 33581}, {610, 55}, {1097, 27382}, {1249, 33}, {1394, 6}, {1895, 281}, {3079, 7156}, {3172, 2212}, {3198, 1334}, {3213, 25}, {5930, 37}, {6587, 4041}, {7070, 220}, {7125, 14379}, {7156, 7071}, {7183, 15394}, {7338, 610}, {7365, 10375}, {8057, 8611}, {8804, 210}, {14308, 4171}, {14331, 3900}, {14615, 312}, {15466, 318}, {15905, 212}, {17898, 3700}, {18623, 1}, {18750, 8}, {21172, 650}, {27382, 200}, {30456, 42}
X(33673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {77, 273, 85}, {347, 1440, 348}, {497, 7197, 7}


X(33674) =  X(105)X(385)∩X(238)X(666)

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

X(33674) lies on the cubic K770 and these lines: {105, 385}, {238, 666}, {239, 335}, {350, 14942}, {740, 2481}, {6654, 20162}, {18785, 24727}

X(33674) = X(1)-Ceva conjugate of X(14942)
X(33674) = X(672)-isoconjugate of X(2111)
X(33674) = barycentric product X(i)*X(j) for these {i,j}: {673, 17794}, {2110, 18031}, {2481, 24578}
X(33674) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 2111}, {2110, 672}, {8849, 18206}, {17794, 3912}, {20694, 3930}, {20762, 1818}, {24578, 518}


X(33675) =  X(291)X(1738)∩X(518)X(2481)

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

X(33675) lies on these lines: {291, 1738}, {518, 2481}, {3685, 14197}, {3912, 14943}

X(33675) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2481}, {20795, 18589}
X(33675) = X(2)-Ceva conjugate of X(2481)
X(33675) = crosssum of PU(97)
X(33675) = barycentric quotient X(20795) / X(20752)


X(33676) =  X(105)X(8684)∩X(239)X(335)

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

X(33676) lies on the cubic K768 and these lines: {105, 8684}, {239, 335}, {291, 1738}, {666, 1757}, {726, 2481}, {813, 20605}, {1916, 5992}, {2550, 22116}, {3508, 18785}, {3685, 3693}, {3717, 3975}, {4562, 32850}, {4876, 5853}, {5263, 5701}, {6185, 17738}, {14197, 14200}

X(33676) = reflection of X(10030) in X(1738)
X(33676) = X(i)-cross conjugate of X(j) for these (i,j): {8, 14942}, {3061, 18031}
X(33676) = X(i)-isoconjugate of X(j) for these (i,j): {34, 20778}, {56, 8299}, {238, 1458}, {241, 1914}, {518, 1428}, {604, 17755}, {659, 2283}, {672, 1429}, {1025, 8632}, {1284, 3286}, {1447, 2223}, {1876, 7193}, {2210, 9436}, {9454, 10030}, {9455, 18033}, {12835, 22116}
X(33676) = cevapoint of X(i) and X(j) for these (i,j): {8, 4518}, {2310, 28132}
X(33676) = trilinear pole of line {885, 3716}
X(33676) = barycentric product X(i)*X(j) for these {i,j}: {294, 334}, {335, 14942}, {673, 4518}, {885, 4562}, {1024, 4583}, {2195, 18895}, {2481, 4876}, {6559, 7233}, {7077, 18031}
X(33676) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 17755}, {9, 8299}, {105, 1429}, {219, 20778}, {291, 241}, {292, 1458}, {294, 238}, {335, 9436}, {660, 1025}, {673, 1447}, {813, 2283}, {884, 8632}, {885, 812}, {1024, 659}, {1438, 1428}, {2195, 1914}, {2311, 3286}, {2481, 10030}, {3252, 1362}, {3685, 27919}, {4518, 3912}, {4562, 883}, {4876, 518}, {6559, 3685}, {7077, 672}, {13576, 16609}, {14942, 239}, {18031, 18033}, {18265, 9454}, {18785, 1284}, {28071, 3684}, {28132, 3716}


X(33677) =  X(2)X(20935)∩X(7)X(8)

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

X(33677) = lies on these lines: {2, 20935}, {7, 8}, {76, 3886}, {120, 325}, {200, 6063}, {344, 6376}, {346, 17786}, {350, 14942}, {664, 1818}, {668, 3717}, {1229, 17788}, {1233, 3996}, {1376, 7196}, {1654, 25001}, {1975, 9305}, {2481, 5853}, {3912, 14943}, {3935, 23989}, {4130, 4391}, {4417, 4766}, {4437, 18037}, {4554, 6745}, {5218, 30988}, {5701, 17263}, {9443, 20906}, {10005, 25278}, {14189, 28058}, {14829, 24592}, {17300, 20905}, {18057, 19815}, {18156, 20946}, {20823, 24499}, {25568, 30545}, {27304, 31997}, {30036, 30062}, {30827, 32023}

X(33677) = Euler-Gergonne-Soddy-circle-inverse of X(14135)
X(33677) = isotomic conjugate of X(9442)
X(33677) = isotomic conjugate of the isogonal conjugate of X(9441)
X(33677) = X(3912)-Ceva conjugate of X(350)
X(33677) = X(i)-isoconjugate of X(j) for these (i,j): {31, 9442}, {604, 14943}
X(33677) = cevapoint of X(10025) and X(28058)
X(33677) = barycentric product X(i)*X(j) for these {i,j}: {75, 10025}, {76, 9441}, {85, 28058}, {312, 14189}
X(33677) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9442}, {8, 14943}, {9441, 6}, {10025, 1}, {14189, 57}, {28058, 9}


X(33678) =  X(335)X(20363)∩X(726)X(3226)

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

X(33678) lies on these lines: {335, 20363}, {726, 3226}, {3253, 24349}

X(33678) = X(31)-complementary conjugate of X(3226)
X(33678) = X(2)-Ceva conjugate of X(3226)


X(33679) =  X(8)X(2113)∩X(239)X(20332)

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

X(33679) lies on the cubic K767 and these lines: {8, 2113}, {239, 20332}, {291, 350}, {740, 3226}, {3253, 3923}, {3978, 6650}

X(33679) = X(2109)-isoconjugate of X(3009)
X(33679) = barycentric quotient X(i)/X(j) for these {i,j}: {2108, 3009}, {20332, 2109}, {20797, 20777}, {27920, 17475}


X(33680) =  X(1)X(3253)∩X(291)X(350)

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

X(33680) lies on these lines: {1, 3253}, {291, 350}, {335, 20363}, {518, 3226}, {694, 6542}

X(33680) = X(i)-isoconjugate of X(j) for these (i,j): {87, 20663}, {2053, 8850}, {2162, 17475}, {7121, 17793}
X(33680) = barycentric quotient X(i)/X(j) for these {i,j}: {43, 17475}, {192, 17793}, {1423, 8850}, {2176, 20663}, {20691, 20681}, {20760, 20750}


X(33681) =  X(1)X(87)∩X(2)X(16557)

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

X(33681) lies on these lines: {1, 87}, {2, 16557}, {9, 21379}, {239, 20332}, {2162, 8026}, {3229, 6651}, {3360, 16827}, {3501, 17350}, {4063, 4785}, {6196, 20971}, {6376, 24343}, {10025, 11689}, {10436, 26143}, {19579, 20671}

X(33681) = X(1575)-Ceva conjugate of X(239)
X(33681) = crosssum of X(1575) and X(17459)


X(33682) =  MIDPOINT OF X(1) AND X(894)

Barycentrics    2*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(33682) = 5 X[3616] - X[6646],7 X[3622] + X[31300],7 X[3624] - 5 X[17326],X[17254] - 3 X[25055]

X(33682) lies on the cubic K1113 and these lines: {1, 87}, {2, 2308}, {5, 29287}, {6, 10}, {8, 28650}, {31, 19684}, {37, 4672}, {42, 19717}, {44, 3842}, {55, 19722}, {57, 29650}, {58, 86}, {63, 29644}, {81, 3741}, {142, 5138}, {171, 4279}, {226, 1397}, {239, 4991}, {386, 1740}, {516, 572}, {519, 4649}, {524, 3775}, {527, 551}, {594, 17772}, {597, 3826}, {612, 4090}, {740, 1100}, {742, 1386}, {748, 25501}, {752, 4026}, {870, 21443}, {902, 19741}, {940, 3840}, {946, 13323}, {978, 25528}, {984, 3758}, {1193, 18792}, {1203, 25526}, {1215, 3745}, {1385, 29369}, {1428, 30097}, {1449, 4709}, {1654, 19856}, {1698, 17349}, {1738, 20179}, {1757, 16830}, {1961, 27064}, {1980, 23803}, {2209, 5264}, {2295, 21760}, {2796, 4366}, {3052, 19747}, {3120, 29833}, {3244, 4133}, {3286, 5267}, {3487, 24669}, {3589, 3836}, {3616, 6646}, {3622, 31300}, {3624, 17298}, {3634, 16477}, {3636, 16484}, {3661, 20145}, {3662, 29646}, {3666, 4697}, {3683, 10180}, {3696, 16666}, {3720, 4368}, {3739, 4974}, {3755, 5114}, {3771, 5712}, {3773, 17369}, {3791, 31993}, {3817, 13478}, {3821, 14621}, {3846, 6703}, {3912, 20132}, {3944, 29841}, {3971, 5311}, {3980, 5256}, {4011, 5287}, {4021, 28526}, {4027, 5988}, {4038, 32942}, {4298, 7175}, {4307, 4660}, {4310, 4747}, {4360, 28522}, {4363, 32921}, {4418, 4970}, {4432, 5625}, {4527, 17388}, {4645, 29633}, {4651, 19743}, {4655, 4657}, {4676, 17394}, {4685, 19738}, {4722, 4981}, {4732, 16668}, {4733, 4969}, {4759, 16826}, {4871, 32944}, {5248, 19762}, {5249, 23812}, {5259, 28619}, {5269, 29670}, {5294, 29653}, {5695, 16884}, {5759, 10186}, {6327, 29647}, {6541, 17355}, {6679, 17056}, {6686, 17122}, {7277, 17771}, {7290, 24331}, {9347, 32931}, {9791, 29586}, {10436, 16475}, {10459, 23579}, {11599, 14534}, {14996, 30942}, {15254, 28639}, {15668, 16457}, {15988, 24563}, {16466, 28365}, {16704, 30970}, {16707, 21415}, {16738, 19863}, {17017, 24165}, {17019, 32930}, {17045, 17768}, {17140, 29819}, {17165, 29816}, {17227, 25539}, {17245, 31289}, {17246, 17767}, {17254, 25055}, {17289, 32846}, {17300, 29637}, {17302, 32857}, {17321, 24695}, {17353, 20159}, {17368, 29674}, {17378, 33087}, {17380, 33149}, {17381, 32784}, {17449, 29823}, {17600, 32939}, {17766, 20147}, {17778, 32783}, {19740, 21747}, {19786, 33097}, {19808, 32861}, {19854, 27317}, {19864, 27145}, {20131, 29571}, {20134, 27255}, {20142, 24603}, {20155, 29600}, {20158, 29576}, {20182, 32934}, {20888, 30940}, {21241, 29631}, {21352, 23578}, {23301, 23570}, {23660, 24512}, {24248, 26626}, {24723, 28508}, {26098, 29635}, {26825, 26965}, {26860, 29824}, {27186, 29852}, {27273, 30103}, {28512, 33076}, {29636, 31019}, {29648, 33069}, {29829, 33104}, {29834, 33148}, {29837, 33106}, {29842, 33144}, {29845, 33107}, {29847, 31053}, {32780, 33073}

X(33682) = midpoint of X(i) and X(j) for these {i,j}: {1, 894}, {4649, 5263}
X(33682) = reflection of X(i) in X(j) for these {i,j}: {10, 5750}, {4357, 1125}
X(33682) = complement of X(33082)
X(33682) = crosspoint of X(86) and X(14621)
X(33682) = crosssum of X(42) and X(2276)
X(33682) = crossdifference of every pair of points on line {834, 4079}
X(33682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 87, 5145}, {1, 3923, 3993}, {81, 32772, 3741}, {86, 238, 1125}, {940, 25496, 3840}, {1386, 4670, 24325}, {4418, 17011, 4970}, {4432, 5625, 15569}, {5311, 26223, 3971}, {10436, 16475, 16825}, {16830, 17120, 1757}, {23812, 29654, 5249}, {29631, 33112, 21241}


X(33683) =  X(6)X(598)∩X(194)X(524)

Barycentrics    (a^2 - 2*b^2 - 2*c^2)*(8*a^4 + a^2*b^2 + 2*b^4 + a^2*c^2 - 5*b^2*c^2 + 2*c^4) : :
X(33683) = 3 X[6] - 2 X[598],9 X[6] - 8 X[9731],3 X[598] - 4 X[9731],3 X[599] - 4 X[15810]

X(33683) lies on the cubic K1113 and these lines: {6, 598}, {194, 524}, {382, 576}, {542, 32447}, {574, 599}, {3849, 7798}, {4027, 8592}, {5038, 7617}, {7870, 11285}, {8176, 11646}, {9755, 9774}, {10484, 11163}, {13330, 32479}, {15533, 31859}


X(33684) =  X(2)X(3167)∩X(6)X(2996)

Barycentrics    (3*a^2 - b^2 - c^2)*(7*a^4 - 6*a^2*b^2 + 3*b^4 - 6*a^2*c^2 - 10*b^2*c^2 + 3*c^4) : :
X(33684) = 4 X[6] - X[2996],X[193] + 2 X[6337],2 X[5052] + X[32477],4 X[10008] - X[20080]

X(33684) lies on the cubic K1113 and these lines: {2, 3167}, {6, 2996}, {193, 439}, {194, 5052}, {1353, 32973}, {5033, 7793}, {6776, 32982}, {16834, 28526}

X(33684) = reflection of X(7612) in X(5050)


X(33685) =  X(194)X(1003)∩X(732)X(5085)

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

X(33685) lies on the cubic K1113 and these lines: {194, 1003}, {732, 5085}


X(33686) =  X(83)X(194)∩X(3098)X(9751)

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

X(33686) lies on the cubic K1113 and these lines: {83, 194}, {3098, 9751}, {3329, 10007}, {6329, 9478}, {6704, 7779}, {7878, 12206}, {14492, 29012}


X(33687) =  X(2)X(8587)∩X(187)X(194)

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

X(33687) lies on the cubic K1113 and these lines: {2, 8587}, {187, 194}, {3832, 22803}, {5008, 32479}


X(33688) =  X(10)X(213)∩X(42)X(22024)

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

X(33688) lies on the cubic K1113 and these lines: {10, 213}, {42, 22024}, {43, 4418}, {194, 386}, {730, 20970}, {2092, 3029}, {2239, 6685}, {5282, 19587}


X(33689) =  X(194)X(574)∩X(385)X(8586)

Barycentrics    (a^4 - 2*a^2*b^2 - 2*a^2*c^2 - 3*b^2*c^2)*(5*a^4 - 2*a^2*b^2 + 2*b^4 - 2*a^2*c^2 - 5*b^2*c^2 + 2*c^4) : :
X(33689) = X[8786] - 3 X[8859]

X(33689) lies on the cubic K1113 and these lines: {194, 574}, {385, 8586}, {671, 14712}, {5965, 7608}, {8786, 8787}, {9873, 17578}, {9979, 12077}, {10484, 15534}


X(33690) =  (name pending)

Barycentrics    (5*a^4 - a^2*b^2 - a^2*c^2 - 6*b^2*c^2)*(35*a^4 + 4*a^2*b^2 + 5*b^4 + 4*a^2*c^2 - 26*b^2*c^2 + 5*c^4) : :

X(33690) lies on the cubic K1113 and these lines: {194, 1384}


X(33691) =  X(194)X(1691)∩X(3398)X(14561)

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

X(33691) lies on the cubic K1113 and these lines: {194, 1691}, {3398, 14561}, {10000, 24256}


X(33692) =  X(194)X(3053)∩X(5033)X(8667)

Barycentrics    (3*a^4 - a^2*b^2 - a^2*c^2 - 4*b^2*c^2)*(15*a^4 + 2*a^2*b^2 + 3*b^4 + 2*a^2*c^2 - 10*b^2*c^2 + 3*c^4) : :

X(33692) lies on the cubic K1113 and these lines: {194, 3053}, {5033, 8667}, {5050, 9756}, {5182, 8556}


X(33693) =  REFLECTION OF X(10000) IN X(39)

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

X(33693) lies on the cubic K1113 and these lines: {6, 1916}, {39, 10000}, {194, 315}, {3094, 3314}, {31859, 32476}

X(33693) = reflection of X(10000) in X(39)


X(33694) =  X(39)X(98)∩X(99)X(5008)

Barycentrics    2*a^8 + 3*a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 + 3*a^6*c^2 - 12*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 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 - 2*b^2*c^6 : :
X(33694) = X[98] - 5 X[32467]

X(33694) lies on these lines: {39, 98}, {99, 5008}, {115, 5066}, {148, 598}, {620, 5215}, {1569, 5007}, {2782, 5041}, {4027, 32450}, {5107, 19924}, {7765, 12830}, {18800, 20583}


X(33695) =  X(5)X(83)∩X(39)X(112)

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

X(33695) lies on these lines: {5, 83}, {39, 112}, {185, 575}, {9479, 32467}, {11643, 14908}, {13335, 22467}

X(33695) = reflection of X(827) and X(14675)
X(33695) = focus of a parabola related to cubic K1113; see K1113.


X(33696) =  X(1)X(3845)∩X(8)X(4532)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29263.

Let IAIBIC be the excentral triangle. Let LA be the trilinear polar of I wrt BCIA, and define LB and LC cyclically. Let A' = LB∩LC, B' = LC∩LA, C' = LA∩LB. Let A" be the reflection of A' in BC, and define B" and C" cyclically. The lines AA", BB", CC" concur in X(33696). (Randy Hutson, August 19, 2019)

X(33696) lies on the Feuerbach hyperbola and these lines: {1, 3845}, {8, 4532}, {3583, 13606}


X(33697) =  X(1)X(3830)∩X(3)X(7989)

Barycentrics    6*a^4-(b+c)*a^3-2*(b^2-c*b+c^2)*a^2+(b^2-c^2)*(b-c)*a-4*(b^2-c^2)^2 : :
X(33697) = X(1)-3*X(3830), 5*X(3)-7*X(7989), 3*X(3)-5*X(18492), 9*X(4)-5*X(3616), 7*X(4)-3*X(5731), 5*X(4)-3*X(5886), 13*X(4)-9*X(9779), 3*X(4)-2*X(9955), 3*X(4)-X(18481), 9*X(1385)-10*X(3616), 7*X(1385)-6*X(5731), 5*X(1385)-6*X(5886), 13*X(1385)-18*X(9779), 3*X(1385)-4*X(9955), 3*X(1385)-2*X(18481), 5*X(3616)-6*X(9955), 5*X(3616)-3*X(18481), 5*X(5731)-7*X(5886), 9*X(5731)-14*X(9955), 9*X(5731)-7*X(18481), 13*X(5886)-15*X(9779), 9*X(5886)-10*X(9955)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29263.

X(33697) lies on these lines: {1, 3830}, {3, 7989}, {4, 1385}, {5, 17502}, {8, 15682}, {10, 30}, {20, 9956}, {40, 5073}, {65, 16118}, {145, 3543}, {165, 17800}, {226, 15174}, {355, 3146}, {376, 19877}, {381, 3624}, {382, 517}, {388, 31795}, {515, 1483}, {516, 4746}, {519, 28645}, {546, 4297}, {548, 10175}, {549, 31253}, {550, 11231}, {551, 12101}, {942, 12943}, {944, 17578}, {946, 3853}, {1125, 3845}, {1319, 18514}, {1539, 11699}, {1657, 5587}, {1698, 3534}, {1699, 5076}, {2646, 18513}, {2771, 4018}, {3149, 23961}, {3529, 26446}, {3576, 3843}, {3583, 24928}, {3585, 5441}, {3586, 5045}, {3617, 15640}, {3634, 8703}, {3636, 15687}, {3648, 5086}, {3649, 10572}, {3656, 20057}, {3817, 3861}, {3822, 16160}, {3828, 19710}, {3850, 10165}, {3851, 7987}, {3857, 10171}, {3860, 19883}, {3922, 13145}, {4301, 28224}, {4316, 5442}, {4663, 11645}, {4668, 12702}, {4701, 28194}, {4743, 29040}, {5049, 9657}, {5059, 5818}, {5066, 19862}, {5122, 10826}, {5126, 10896}, {5251, 16117}, {5493, 28182}, {5586, 18541}, {5690, 28150}, {5698, 31672}, {5722, 31776}, {5901, 12102}, {5919, 26088}, {6583, 12680}, {6684, 15704}, {6851, 18516}, {7756, 31430}, {7967, 10248}, {9579, 31794}, {9613, 9668}, {9626, 14130}, {9778, 11541}, {9780, 11001}, {9957, 12953}, {10164, 12103}, {10172, 15712}, {11112, 25011}, {11113, 24564}, {11362, 28178}, {12262, 18383}, {12512, 31447}, {13369, 16616}, {13491, 31760}, {15685, 19875}, {15693, 19872}, {15695, 19876}, {15696, 31423}, {17609, 26089}, {18482, 25557}, {18526, 31162}, {18527, 18990}, {19541, 32612}, {22799, 22935}

X(33697) = midpoint of X(i) and X(j) for these {i,j}: {40, 5073}, {355, 3146}, {382, 5691}, {9589, 12645}
X(33697) = reflection of X(i) in X(j) for these (i,j): (20, 9956), (550, 19925), (551, 12101), (946, 3853), (1385, 4), (1657, 31663), (3579, 18480), (4297, 546), (5901, 12102), (11278, 12699), (11699, 1539), (12262, 18383), (12680, 6583), (13369, 16616), (13491, 31760), (15704, 6684), (18480, 31673), (18481, 9955), (19710, 3828), (22793, 3627), (22935, 22799), (24680, 22793), (31730, 18357)
X(33697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 18481, 9955), (9955, 18481, 1385)


X(33698) =  X(98)X(15687)∩X(262)X(14269)

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

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29263.

X(33698) lies on the Kiepert hyperbola and these lines: {98, 15687}, {262, 14269}, {381, 11669}, {382, 7607}, {546, 7608}, {550, 10185}, {671, 3629}, {2996, 23334}, {5466, 32478}, {8352, 10302}, {10159, 33229}, {11668, 15681}, {33604, 33625}, {33605, 33623}

X(33698) = isotomic conjugate of the anticomplement of X(20583)


X(33699) =  COMPLEMENT OF X(15685)

Barycentrics    16*a^4-5*(b^2+c^2)*a^2-11*(b^2-c^2)^2 : :
X(33699) = 11*X(2)-9*X(3), 5*X(2)-9*X(4), 8*X(2)-9*X(5), 17*X(2)-9*X(20), 19*X(2)-18*X(140), 13*X(2)-9*X(376), 7*X(2)-9*X(381), X(2)+9*X(382), 13*X(2)-18*X(546), 17*X(2)-18*X(547), 25*X(2)-18*X(548), 10*X(2)-9*X(549), 14*X(2)-9*X(550), 23*X(2)-9*X(1657), 7*X(2)+9*X(3146), 29*X(2)-9*X(3529), 5*X(2)-3*X(3534), X(2)-9*X(3543), 2*X(2)-9*X(3627), X(2)-3*X(3830)

As a point on the Euler line, X(33699) has Shinagawa coefficients (-5, 27).

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29263.

X(33699) lies on these lines: {2, 3}, {302, 33610}, {303, 33611}, {395, 12817}, {396, 12816}, {519, 28645}, {1483, 31162}, {3654, 28178}, {3656, 28186}, {4654, 15935}, {4669, 28198}, {4745, 18480}, {4995, 18513}, {5298, 18514}, {5349, 16268}, {5350, 16267}, {5663, 21969}, {5690, 28202}, {5874, 13691}, {5875, 13810}, {7776, 32896}, {8584, 11645}, {10283, 28190}, {10386, 11237}, {10723, 14692}, {11648, 14075}, {12279, 16881}, {12290, 14449}, {12953, 15170}, {13391, 32062}, {13451, 15072}, {13607, 22793}, {13623, 14487}, {14537, 15048}, {14848, 14927}, {14915, 21849}, {15534, 31670}, {19116, 22615}, {19117, 22644}, {19924, 22165}, {22791, 28208}

X(33699) = midpoint of X(i) and X(j) for these {i,j}: {4, 15684}, {376, 5073}, {381, 3146}, {382, 3543}, {3534, 15640}, {3830, 15682}
X(33699) = reflection of X(i) in X(j) for these (i,j): (2, 12101), (3, 14893), (5, 15687), (20, 547), (376, 546), (381, 3853), (547, 12102), (549, 4), (550, 381), (1483, 31162), (3529, 15691), (3534, 5066), (3627, 3543), (3845, 3830), (8703, 3845), (11001, 12100), (12103, 11737), (15072, 13451), (15681, 140), (15683, 548), (15685, 15690), (15686, 5), (15687, 3627), (15690, 3860), (15691, 3850), (15704, 549), (19710, 2)
X(33699) = complement of X(15685)
X(33699) = anticomplement of X(15690)
X(33699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 15640, 3534), (3830, 15640, 5066), (15640, 15682, 15684)


X(33700) =  (name pending)

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

X(33700) lies on this line: {2, 33675}

X(33700) = X(518)-cross conjugate of X(6184)


X(33701) =  X(1)X(33674)∩X(2)X(3252)

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

X(33701) lies on these lines: on lines {1, 33674}, {2, 3252}, {9, 2111}, {6184, 17755}

X(33701) = X(518)-cross conjugate of X(17755)


X(33702) =  X(3)X(31361)∩X(4)X(8567)

Barycentrics    (a^2+b^2-c^2) (a^2-b^2+c^2) (5 a^4-10 a^2 b^2+5 b^4+2 a^2 c^2+2 b^2 c^2-7 c^4) (3 a^4-2 a^2 b^2-b^4-2 a^2 c^2+2 b^2 c^2-c^4) (5 a^4+2 a^2 b^2-7 b^4-10 a^2 c^2+2 b^2 c^2+5 c^4) : :
Barycentrics    (384 R^4+16 R^2 SB+16 R^2 SC-SB SC-192 R^2 SW-4 SB SW-4 SC SW+24 SW^2)S^2 -1152 R^4 SB SC+528 R^2 SB SC SW-60 SB SC SW^2 : :
X(33702) = 3*X[376]-2*X[16251]

See Tran Quang Hung and Ercole Suppa, Hyacinthos 29265.

X(33702) lies on these lines: lies on these lines: {3,31361}, {4,8567}, {30,253}, {376,16251}, {1294,11001}, {3079,10152}, {3346,3529}, {5925,22049}, {11541,15319}

X(33702) = barycentric quotient X(1249)/X(3543)
X(33702) = trilinear quotient X(1895)/X(3543)

X(33703) =  ANTICOMPLEMENT OF X(1657)

Barycentrics    9 a^4-4 a^2 b^2-5 b^4-4 a^2 c^2+10 b^2 c^2-5 c^4 : :
Barycentrics    2 S^2 - 7 SB SC : :
X(33703) = 15*X[2]-14*X[3], 4*X[3]-5*X[4], 7*X[40]-8*X[4691], 2*X[52]-X[12279], 3*X[146]-2*X[23236], 9*X[165]-10*X[31399], 7*X[944]-8*X[3635], 10*X[946]-9*X[30392], 5*X[962]-4*X[11278], 4*X[1216]-5*X[11439], 3*X[3060]-2*X[10575], 25*X[3616]-24*X[31662], 6*X[3630]-7*X[15069], 6*X[4297]-7*X[9624], 5*X[4668]-7*X[5691], 16*X[5097]-15*X[14912], 6*X[5102]-5*X[6776], 4*X[5446]-3*X[15072], 9*X[5485]-8*X[7751], 2*X[5562]-3*X[11455], 3*X[5656]-2*X[17845], 3*X[5657]-4*X[31673], 3*X[5667]-2*X[23241], 3*X[5731]-4*X[22793], 10*X[5734]-9*X[7967], 15*X[5818]-14*X[9588], 6*X[5886]-7*X[10248], 3*X[5890]-4*X[13598], 2*X[5894]-3*X[18405], 3*X[5918]-4*X[16616], 3*X[6031]-4*X[31824], 5*X[8567]-6*X[23324], 3*X[9778]-4*X[18480], 9*X[9779]-8*X[13624], 21*X[9780]-20*X[31447], 6*X[9812]-5*X[10595], X[9862]-2*X[10723], 3*X[10167]-4*X[31822], 5*X[10574]-4*X[14641], 2*X[10625]-3*X[15305], 2*X[10721]-X[12383], 2*X[10722]-X[13172], 2*X[10724]-X[12248], 2*X[10728]-X[13199], 2*X[10733]-X[12244], 2*X[10735]-X[12253], 9*X[11002]-8*X[13630], 3*X[11206]-4*X[22802], 2*X[11381]-X[11412], 5*X[11444]-6*X[16194], 3*X[11459]-4*X[13474], 17*X[11465]-16*X[17704], 8*X[11793]-9*X[16261], 4*X[12121]-5*X[20125], 4*X[12512]-5*X[18492], 6*X[14855]-7*X[15043], 14*X[15057]-15*X[15081], 5*X[15058]-4*X[15644], 2*X[18525]-X[20070], 3*X[20127]-4*X[20379], 2*X[20427]-3*X[32064], 3*X[21168]-4*X[31672], 3*X[23039]-4*X[32137]

As a point on the Euler line, X(30703) has Shinagawa coefficients (2, -7).

See Tran Quang Hung and Ercole Suppa, Hyacinthos 29265.

The perspeconic of the inner and outer Grebe triangles is a circle, here named the Grebe circle. X(33703) = inverse-in-Grebe-circle of X(186). (Randy Hutson, August 19, 2019)

Let A'B'C' be the mid-triangle of the tangential and intangents triangles. Let LA be the reflection of line B'C' in the external angle bisector of A, and define LB, LC cyclically. Let A" = LB∩LC, and define B", C" cyclically. Triangle A"B"C" is homothetic to ABC at X(2) and to the Euler triangle at X(3850). X(33703) = X(20)-of-A"B"C". (Randy Hutson, August 19, 2019)

X(33703) lies on these lines: {1,28172}, {2,3}, {8,28146}, {40,4691}, {52,12279}, {55,31410}, {68,11738}, {69,29317}, {74,15749}, {99,32823}, {145,28186}, {146,23236}, {155,12112}, {165,31399}, {262,18844}, {315,32822}, {316,32818}, {325,32876}, {355,28154}, {371,23269}, {372,23275}, {388,4309}, {390,9655}, {393,18849}, {497,4317}, {511,12290}, {515,3633}, {516,3625}, {517,20053}, {574,31417}, {578,8718}, {944,3635}, {946,30392}, {950,4114}, {958,31420}, {962,11278}, {1056,6284}, {1058,7354}, {1075,15005}, {1093,18847}, {1151,23253}, {1152,23263}, {1204,18918}, {1216,11439}, {1285,5254}, {1478,4330}, {1479,4325}, {1503,6144}, {1587,6431}, {1588,6432}, {1620,15752}, {1788,4333}, {1870,9643}, {1975,32875}, {2549,5041}, {2777,12317}, {3060,10575}, {3085,9656}, {3086,9671}, {3183,6761}, {3488,9579}, {3585,8164}, {3600,9668}, {3616,31662}, {3619,7910}, {3621,28212}, {3630,15069}, {3632,28232}, {4045,18841}, {4293,12953}, {4294,12943}, {4297,9624}, {4299,5225}, {4302,5229}, {4304,5714}, {4316,7288}, {4324,5218}, {4338,10572}, {4668,5691}, {5008,5319}, {5013,31407}, {5097,14912}, {5102,6776}, {5261,31480}, {5270,10385}, {5343,22238}, {5344,22236}, {5446,15072}, {5475,31450}, {5485,7751}, {5562,11455}, {5656,17845}, {5657,31673}, {5667,23241}, {5731,22793}, {5734,7967}, {5818,9588}, {5886,10248}, {5889,14915}, {5890,13598}, {5894,18405}, {5918,16616}, {6000,14531}, {6031,31824}, {6225,11271}, {6337,7814}, {6429,9541}, {6430,13939}, {6437,23249}, {6438,23259}, {6459,23267}, {6460,23273}, {6484,31412}, {6560,7582}, {6561,7581}, {6759,9705}, {7689,15107}, {7736,7756}, {7737,7765}, {7738,7747}, {7750,32826}, {7759,32479}, {7761,18840}, {7796,32006}, {8567,23324}, {8884,18851}, {8981,9692}, {9539,32047}, {9542,10137}, {9543,13903}, {9607,14482}, {9706,13352}, {9778,18480}, {9779,13624}, {9780,31447}, {9812,10595}, {9862,10723}, {9936,17702}, {10138,13993}, {10167,31822}, {10574,14641}, {10580,31776}, {10588,18513}, {10589,18514}, {10590,15338}, {10591,15326}, {10625,15305}, {10721,12383}, {10722,13172}, {10724,12248}, {10728,13199}, {10733,12244}, {10735,12253}, {11002,13630}, {11037,31795}, {11206,22802}, {11270,32110}, {11381,11412}, {11431,12241}, {11444,16194}, {11459,13474}, {11465,17704}, {11793,16261}, {12121,20125}, {12289,29012}, {12512,18492}, {12645,28216}, {12702,28182}, {13346,14157}, {13391,18439}, {14483,15740}, {14855,15043}, {15057,15081}, {15058,15644}, {15602,31457}, {16263,18853}, {18525,20070}, {18540,26878}, {20127,20379}, {20427,32064}, {21168,31672}, {23039,32137}, {31404,31492}, {32815,32877}, {32819,32878}, {32827,32889}

X(33703) = reflection of X(i) in X(j) for these {i,j}: {4,3146}, {3146,5073}, {11001,3543}, {12383,10721}, {13199,10728}, {15161,10736}
X(33703) = anticomplement of X(1657)
X(33703) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {2,20,548}, {2,1657,17538}, {2,3627,4}, {2,10304,15718}, {2,14093,3524}, {2,17538,21735}, {2,33271,33247}, {3,4,3545}, {3,26,13620}, {3,382,3853}, {3,1656,11812}, {3,1657,15686}, {3,3533,15719}, {3,3543,4}, {3,3545,3533}, {3,3832,5067}, {3,3845,5056}, {3,3850,2}, {3,3851,15723}, {3,3853,3832}, {3,5056,15702}, {3,5059,11001}, {3,5067,631}, {3,11539,3523}, {3,15690,3522}, {3,15719,10299}, {4,20,631}, {4,376,3090}, {4,631,3855}, {4,1657,21735}, {4,3146,15682}, {4,3524,3091}, {4,3525,381}, {4,3528,5}, {4,3529,376}, {4,3544,3839}, {4,5067,3832}, {4,5071,546}, {4,6899,6965}, {4,6916,6900}, {4,11001,3}, {4,13619,3147}, {4,15704,15698}, {4,17538,2}, {4,19708,3544}, {5,20,3528}, {5,382,17578}, {5,3528,631}, {5,15696,15717}, {5,17578,4}, {5,17800,20}, {20,382,4}, {20,548,17538}, {20,631,376}, {20,3091,21734}, {20,3146,382}, {20,3543,3832}, {20,3832,3}, {20,3853,5067}, {20,3861,3524}, {20,7486,3522}, {20,15717,15696}, {20,17578,5}, {20,21734,550}, {23,12084,21844}, {140,3839,3544}, {140,5076,3839}, {376,3090,10299}, {376,3533,3}, {376,3545,15719}, {376,3855,631}, {381,3522,3525}, {381,3530,7486}, {381,15690,15708}, {381,15704,3522}, {382,1657,3843}, {382,3526,3830}, {382,3529,3855}, {382,3843,3627}, {382,3853,3543}, {382,5059,5067}, {382,15685,3856}, {382,17800,5}, {384,33192,33238}, {384,33238,33190}, {439,33228,32959}, {546,3523,5071}, {546,3534,3523}, {547,550,3}, {547,3853,3861}, {547,15686,14093}, {548,1657,20}, {548,3627,3843}, {548,3843,2}, {548,3853,3850}, {548,12812,3530}, {548,23046,3526}, {550,3091,3524}, {550,3526,21734}, {550,3627,23046}, {550,3830,3091}, {550,3861,3526}, {550,12108,14093}, {550,23046,12108}, {631,3529,20}, {631,3545,5067}, {631,3855,3090}, {631,5067,3533}, {631,15698,3530}, {1003,32982,32951}, {1593,12082,7512}, {1656,12103,10304}, {1656,15685,12103}, {1657,3627,2}, {1657,3830,12108}, {1657,3843,548}, {1657,5072,15689}, {1657,5076,15706}, {1657,15684,3627}, {1657,15718,12103}, {2041,2042,3146}, {2043,2044,15692}, {3090,10299,15709}, {3090,15719,3533}, {3091,3522,15713}, {3091,3830,4}, {3091,15683,550}, {3091,21734,3526}, {3146,5059,3543}, {3146,11541,3529}, {3146,15640,5073}, {3153,31725,4}, {3520,7387,7556}, {3522,3525,15698}, {3522,7486,3530}, {3522,15708,3}, {3524,3526,631}, {3525,3530,631}, {3526,3830,3861}, {3526,3861,3091}, {3526,21734,3524}, {3529,3543,3533}, {3529,15682,4}, {3530,7486,3525}, {3533,3545,3090}, {3534,5071,15710}, {3534,15710,376}, {3543,3832,3853}, {3543,5059,3}, {3543,11001,3545}, {3543,15683,547}, {3544,19708,140}, {3545,3832,3855}, {3545,11001,376}, {3545,15682,3543}, {3545,15710,11539}, {3552,16041,33189}, {3552,33279,16041}, {3627,15686,3850}, {3627,15704,12812}, {3627,15712,14893}, {3628,14269,3854}, {3830,14093,23046}, {3830,15683,3524}, {3832,3853,4}, {3832,5059,20}, {3832,5067,3545}, {3839,5076,4}, {3839,15681,19708}, {3843,3850,3832}, {3843,15684,382}, {3843,17538,631}, {3845,15702,3545}, {3850,12108,547}, {3850,15686,3}, {3850,21735,3533}, {3851,8703,10303}, {3853,11001,631}, {3853,16239,3845}, {3854,15692,3628}, {3858,5054,15022}, {3861,23046,3843}, {5025,33193,33239}, {5025,33239,33191}, {5055,15697,15715}, {5056,16239,5067}, {5059,11001,3529}, {5059,15708,15704}, {5067,15702,16239}, {5072,15689,15712}, {5072,15712,2}, {5073,11541,15682}, {5076,15681,140}, {6655,14033,32956}, {6655,33280,14033}, {6658,33017,14001}, {7391,20063,7493}, {7580,21669,6875}, {7819,33210,33232}, {7833,14068,32968}, {7841,32981,14069}, {8352,33235,32972}, {8356,32979,32957}, {8357,11159,33198}, {8357,33198,33230}, {8369,33200,32953}, {8370,33023,32960}, {8597,33257,14063}, {8703,12102,3851}, {9541,23251,13886}, {9541,31454,9693}, {9693,13886,31454}, {9812,18481,10595}, {9855,14062,32964}, {11114,31295,443}, {11361,32997,16043}, {11413,18534,3518}, {12103,15687,1656}, {13586,32996,32969}, {14035,32986,16045}, {14035,33256,32986}, {14039,32974,33194}, {14041,33244,32970}, {14042,32965,32983}, {14044,33268,2}, {14062,32964,32984}, {14063,32985,32955}, {14063,33257,32985}, {14066,33267,2}, {14093,23046,2}, {14269,19710,15692}, {14784,14785,3534}, {14892,15718,2}, {14893,15689,2}, {14893,15712,5072}, {14927,31670,14912}, {15644,32062,15058}, {15682,21735,3627}, {15683,21734,20}, {15684,15686,3543}, {15685,15687,10304}, {15691,19709,15705}, {15696,15717,3528}, {15704,15713,550}, {15722,19708,15698}, {16044,33253,33215}, {16924,33264,33226}, {17538,21735,376}, {17578,17800,3528}, {18586,18587,12101}, {19687,32974,14039}, {32966,33254,33216}, {32973,33229,33285}, {32973,33285,33195}, {32995,33243,33273}, {33006,33014,32977}, {33007,33019,14064}, {33008,33018,32975}, {33016,33260,32978}, {33184,33201,32952}

X(33704) =  X(6)X(249)∩X(187)X(6660)

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

X(33704) lies on these lines: {6, 249}, {187, 6660}, {512, 9217}, {1691, 2393}, {2079, 9431}, {3111, 10329}, {3124, 9218}

X(33704) = midpoint of X(9217) and X(20998)
X(33704) = reflection of X(9217) in the Brocard axis
X(33704) = tangential-isogonal conjugate of X(99)
X(33704) = X(i)-Ceva conjugate of X(j) for these (i,j): {3124, 6}, {9218, 512}
X(33704) = crossdifference of every pair of points on line {10190, 11053}
X(33704) = barycentric product X(110)*X(13187)
X(33704) = barycentric quotient X(13187)/X(850)


X(33705) =  X(3)X(538)∩X(3734)X(32524)

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

X(33705) lies on the cubic K1114 and these lines: {3, 538}, {3734, 32524}, {7772, 9490}

X(33705) = Thomson-isogonal conjugate of X(33706)


X(33706) =  X(2)X(51)∩X(30)X(76)

Barycentrics    4*a^6*b^2 - 2*a^4*b^4 - 2*a^2*b^6 + 4*a^6*c^2 + 3*a^4*b^2*c^2 - 6*a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 - 6*a^2*b^2*c^4 - 2*b^4*c^4 - 2*a^2*c^6 + b^2*c^6 : :
X(33706) = 4 X[2] - 3 X[262],X[2] - 3 X[6194],5 X[2] - 6 X[15819],2 X[2] - 3 X[22712],2 X[39] - 3 X[3524],X[76] + 2 X[9821],X[76] - 4 X[32521],X[194] - 3 X[10304],X[262] - 4 X[6194],5 X[262] - 8 X[15819],2 X[3534] - 3 X[22676],3 X[3545] - 4 X[3934],3 X[3839] - 5 X[31276],2 X[3845] - 3 X[7697],2 X[4669] - 3 X[22697],6 X[5054] - 5 X[7786],3 X[5055] - 2 X[14881],4 X[5188] - X[11257],2 X[5188] + X[12251],5 X[6194] - 2 X[15819],8 X[6683] - 9 X[15709],3 X[7709] - 5 X[19708],4 X[7767] - X[9873],4 X[8703] - X[11055],X[9821] + 2 X[32521],X[11001] + 2 X[14711],3 X[11171] - 4 X[12100],X[11257] + 2 X[12251],4 X[11272] - 5 X[15694],4 X[13334] - 5 X[15692],5 X[14093] - X[32520],5 X[15693] - 3 X[32447],7 X[15698] - 6 X[21163],9 X[15710] - 4 X[32450],4 X[15819] - 5 X[22712],5 X[19709] - 3 X[22728]

X(33706) lies on thesse lines: {2, 51}, {3, 6179}, {4, 7854}, {30, 76}, {39, 3524}, {98, 1350}, {141, 9993}, {194, 10304}, {376, 538}, {381, 7883}, {385, 3098}, {524, 9764}, {549, 3095}, {842, 6035}, {1916, 6055}, {1992, 13354}, {2782, 3534}, {3094, 5306}, {3104, 16963}, {3105, 16962}, {3543, 6248}, {3545, 3934}, {3655, 7976}, {3839, 31276}, {3845, 7697}, {3972, 9301}, {4669, 22697}, {4995, 12837}, {5050, 9751}, {5054, 7786}, {5055, 14881}, {5092, 7766}, {5171, 13586}, {5298, 12836}, {5976, 6054}, {6033, 7850}, {6683, 15709}, {7470, 7751}, {7709, 19708}, {7834, 10357}, {7865, 18806}, {7894, 12054}, {8556, 13860}, {8597, 22679}, {8703, 11055}, {8782, 11177}, {9300, 13330}, {9737, 33273}, {9755, 31884}, {10033, 19924}, {11001, 14711}, {11171, 12100}, {11179, 32451}, {11180, 14994}, {11272, 15694}, {11286, 12110}, {12263, 31162}, {13085, 30270}, {13108, 15681}, {13334, 15692}, {14093, 32520}, {14492, 24256}, {15693, 32447}, {15698, 21163}, {15710, 32450}, {16986, 19130}, {16990, 31670}, {19709, 22728}

X(33706) = midpoint of X(i) and X(j) for these {i,j}: {376, 12251}, {8782, 11177}, {13108, 15681}
X(33706) = reflection of X(i) in X(j) for these {i,j}: {4, 9466}, {262, 22712}, {376, 5188}, {1916, 6055}, {1992, 13354}, {3095, 549}, {3543, 6248}, {6054, 5976}, {7757, 3}, {7976, 3655}, {11180, 14994}, {11257, 376}, {22712, 6194}, {31162, 12263}, {32451, 11179}
X(33706) = Thomson-isogonal conjugate of X(33705)
X(33706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5188, 12251, 11257}, {9821, 32521, 76}


X(33707) =  X(524)X(3098)∩X(538)X(8161)

Barycentrics    3*a^8 + 22*a^6*b^2 - 17*a^4*b^4 - 8*a^2*b^6 + 22*a^6*c^2 - 12*a^4*b^2*c^2 - 24*a^2*b^4*c^2 - 2*b^6*c^2 - 17*a^4*c^4 - 24*a^2*b^2*c^4 + 4*b^4*c^4 - 8*a^2*c^6 - 2*b^2*c^6 - Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2]*(14*a^6 + 7*a^4*b^2 - 20*a^2*b^4 - b^6 + 7*a^4*c^2 - 24*a^2*b^2*c^2 + b^4*c^2 - 20*a^2*c^4 + b^2*c^4 - c^6) : :

X(33707) lies on the cubic K1114 and these lines: {524, 3098}, {538, 8161}, {1671, 7757}

X(33707) = {X(3098),X(8703)}-harmonic conjugate of X(33708)
X(33707) = Thomson-isogonal conjugate of X(1670)


X(33708) =  X(524)X(3098)∩X(538)X(8160)

Barycentrics    3*a^8 + 22*a^6*b^2 - 17*a^4*b^4 - 8*a^2*b^6 + 22*a^6*c^2 - 12*a^4*b^2*c^2 - 24*a^2*b^4*c^2 - 2*b^6*c^2 - 17*a^4*c^4 - 24*a^2*b^2*c^4 + 4*b^4*c^4 - 8*a^2*c^6 - 2*b^2*c^6 + Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2]*(14*a^6 + 7*a^4*b^2 - 20*a^2*b^4 - b^6 + 7*a^4*c^2 - 24*a^2*b^2*c^2 + b^4*c^2 - 20*a^2*c^4 + b^2*c^4 - c^6) : :

X(33708) lies on the cubic K1114 and these lines: {524, 3098}, {538, 8160}, {1670, 7757}

X(33708) = Thomson-isogonal conjugate of X(1671)
X(33708) = {X(3098),X(8703)}-harmonic conjugate of X(33707)


X(33709) =  X(2)X(5541)∩X(10)X(1320)

Barycentrics    2*a^4 - a^3*b - 5*a^2*b^2 + a*b^3 + 3*b^4 - a^3*c + 8*a^2*b*c - 5*a^2*c^2 - 6*b^2*c^2 + a*c^3 + 3*c^4 : :
X(33709) = X[1] - 9 X[32558],9 X[2] - X[5541],15 X[2] + X[9802],3 X[2] + X[21630],3 X[10] + X[1320],X[10] + 3 X[16173],X[10] - 5 X[31272],3 X[11] + X[214],7 X[11] + X[10609],9 X[11] - X[12690],X[11] + 3 X[32557],X[80] + 3 X[551],5 X[80] + 3 X[10031],X[100] - 5 X[19862],X[104] + 3 X[3817],X[119] - 3 X[10171],X[149] + 7 X[3624],X[153] - 9 X[7988],X[214] - 3 X[1125],7 X[214] - 3 X[10609],3 X[214] + X[12690],X[214] - 9 X[32557],5 X[551] - X[10031],3 X[946] + X[12515],7 X[1125] - X[10609],9 X[1125] + X[12690],X[1125] - 3 X[32557],X[1145] - 3 X[3828],X[1320] - 9 X[16173],X[1320] + 15 X[31272],3 X[1387] + X[3036],X[1484] + 3 X[11230],X[3036] - 3 X[6702],X[3065] + 3 X[11263],7 X[3090] + X[6264],X[3218] - 9 X[3582],X[3218] + 3 X[11813],3 X[3582] + X[11813],15 X[3616] + X[20085],5 X[3616] - X[33337],7 X[3622] + X[9897],3 X[3898] + X[17636],3 X[4669] + X[26726],5 X[5541] + 3 X[9802],X[5,541] + 3 X[21630],11 X[5550] - 3 X[15015],3 X[5883] + X[17638],3 X[5886] + X[10265],X[6224] - 9 X[25055],5 X[8227] - X[21635],7 X[9624] + X[12247],7 X[9780] + X[12653],X[9802] - 5 X[21630],3 X[10164] + X[14217],3 X[10165] + X[10738],3 X[10175] + X[12737],9 X[10609] + 7 X[12690],X[10609] - 21 X[32557],X[10707] + 3 X[19883],X[11715] + 3 X[23513],X[12512] - 3 X[21154],X[12690] + 27 X[32557],3 X[16173] + 5 X[31272],X[19925] - 3 X[23513],X[20085] + 3 X[33337]

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29270.

X(33709) lies on these lines: {1, 32558}, {2, 5541}, {10, 1320}, {11, 214}, {80, 551}, {100, 19862}, {104, 3817}, {119, 10171}, {149, 3624}, {153, 7988}, {516, 6713}, {519, 1387}, {946, 12515}, {952, 3636}, {1145, 3828}, {1484, 11230}, {1749, 3218}, {2771, 12009}, {2802, 3634}, {2829, 12571}, {3035, 19878}, {3065, 10266}, {3090, 6264}, {3306, 10199}, {3616, 20085}, {3622, 9897}, {3635, 15863}, {3884, 6797}, {3898, 17636}, {4669, 26726}, {4691, 5854}, {4701, 25416}, {4997, 21087}, {5533, 13411}, {5550, 15015}, {5883, 17638}, {5886, 10265}, {6224, 25055}, {6681, 7743}, {6715, 25351}, {8227, 21635}, {9624, 12247}, {9780, 12653}, {10164, 14217}, {10165, 10738}, {10175, 12737}, {10200, 11024}, {10707, 19883}, {11715, 19925}, {12053, 20107}, {12512, 21154}, {12619, 13464}, {14028, 24222}, {17719, 23869}

X(33709) = midpoint of X(i) and X(j) for these {i,j}: {11, 1125}, {1387, 6702}, {3635, 15863}, {3884, 6797}, {4701, 25416}, {6681, 7743}, {6713, 16174}, {11715, 19925}, {12619, 13464}
X(33709) = reflection of X(i) in X(j) for these {i,j}: {3035, 19878}, {3634, 6667}
X(33709) = X(i)-complementary conjugate of X(j) for these (i,j): {3065, 121}, {19302, 16594}
X(33709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 32557, 1125}, {11715, 23513, 19925}, {16173, 31272, 10}


X(33710) =  X(1)X(1501)∩X(2)X(3)

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

X(33710) lies on these lines: {1, 1501}, {2, 3}, {1724, 20859}, {5248, 8628}


X(33711) =  X(1)X(9233)∩X(2)X(3)

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

X(33711) lies on these lines: {1, 9233}, {2, 3}


X(33712) =  (name pending)

Barycentrics    a^13*b - a^11*b^3 - a^5*b^9 + a^3*b^11 - a^13*c + a^9*b^4*c + a^9*b^3*c^2 - a*b^11*c^2 + a^11*c^3 - a^9*b^2*c^3 - a^9*b*c^4 + a*b^9*c^4 + a^5*c^9 - a*b^4*c^9 - a^3*c^11 + a*b^2*c^11 : :

X(33712) lies on these lines: {2, 3}


X(33713) =  (name pending)

Barycentrics    a^14*b - a^12*b^3 - a^5*b^10 + a^3*b^12 - a^14*c + a^10*b^4*c + a^10*b^3*c^2 - a*b^12*c^2 + a^12*c^3 - a^10*b^2*c^3 - a^10*b*c^4 + a*b^10*c^4 + a^5*c^10 - a*b^4*c^10 - a^3*c^12 + a*b^2*c^12 : :

X(33713) lies on these lines: {2, 3}


X(33714) =  X(2)X(3)∩X(6)X(560)

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

X(33714) lies on these lines: {2, 3}, {6, 560}, {55, 16681}, {2200, 26893}, {2352, 16974}, {10477, 20769}, {16689, 21010}


X(33715) =  X(2)X(3)∩X(6)X(1917)

Barycentrics    a^11*b^2 - a^9*b^4 - a^6*b^7 + a^4*b^9 - a^11*c^2 + 2*a^7*b^4*c^2 - a^2*b^9*c^2 + a^9*c^4 - 2*a^7*b^2*c^4 + a^2*b^7*c^4 + a^6*c^7 - a^2*b^4*c^7 - a^4*c^9 + a^2*b^2*c^9 : :

X(33715) lies on these lines: {2, 3}, {6, 1917}


X(33716) =  (name pending)

Barycentrics    a^13*b^2 - a^11*b^4 - a^6*b^9 + a^4*b^11 - a^13*c^2 + 2*a^9*b^4*c^2 - a^2*b^11*c^2 + a^11*c^4 - 2*a^9*b^2*c^4 + a^2*b^9*c^4 + a^6*c^9 - a^2*b^4*c^9 - a^4*c^11 + a^2*b^2*c^11 : :

X(33716) lies on these lines: {2, 3}


X(33717) =  X(2)X(3)∩X(194)X(5938)

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

X(33717) lies on these lines: {2, 3}, {194, 5938}, {2353, 7754}, {6179, 7669}, {7823, 11641}


X(33718) =  X(2)X(3)∩X(31)X(32)

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

X(33718) lies on these lines: {2, 3}, {31, 32}, {55, 2295}, {160, 5124}, {172, 2352}, {193, 23079}, {198, 2110}, {584, 15624}, {604, 22389}, {980, 10458}, {1400, 2309}, {1843, 18591}, {2509, 23228}, {3053, 21779}, {3941, 4275}, {8849, 24621}, {16693, 21010}, {19757, 19758}, {19800, 19840}, {20966, 22380}, {22449, 25940}


X(33719) =  X(2)X(3)∩X(31)X(1501)

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

X(33719) lies on these lines: {2, 3}, {31, 1501}


X(33720) =  X(2)X(3)∩X(31)X(1917)

Barycentrics    a^11*b^3 - a^9*b^5 - a^7*b^7 + a^5*b^9 + a^7*b^5*c^2 - a^3*b^9*c^2 - a^11*c^3 + a^7*b^4*c^3 - a^7*b^3*c^4 + a^3*b^7*c^4 + a^9*c^5 - a^7*b^2*c^5 + a^7*c^7 - a^3*b^4*c^7 - a^5*c^9 + a^3*b^2*c^9 : :

X(33720) lies on these lines: {2, 3}, {31, 1917}


X(33721) =  X(2)X(3)∩X(31)X(19559)

Barycentrics    a^13*b^3 - a^11*b^5 - a^7*b^9 + a^5*b^11 + a^9*b^5*c^2 - a^3*b^11*c^2 - a^13*c^3 + a^9*b^4*c^3 - a^9*b^3*c^4 + a^3*b^9*c^4 + a^11*c^5 - a^9*b^2*c^5 + a^7*c^9 - a^3*b^4*c^9 - a^5*c^11 + a^3*b^2*c^11 : :

X(33721) lies on these lines: {2, 3}, {31, 19559}


X(33722) =  X(2)X(3)∩X(32)X(560)

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

X(33722) lies on these lines: {2, 3}, {32, 560}, {193, 23176}, {2271, 23212}, {5021, 20775}


X(33723) =  X(2)X(3)∩X(32)X(1917)

Barycentrics    a^11*b^4 - a^9*b^6 - a^8*b^7 + a^6*b^9 + a^7*b^6*c^2 - a^4*b^9*c^2 - a^11*c^4 + a^4*b^7*c^4 + a^9*c^6 - a^7*b^2*c^6 + a^8*c^7 - a^4*b^4*c^7 - a^6*c^9 + a^4*b^2*c^9 : :

X(33723) lies on these lines: {2, 3}, {32, 1917}


X(33724) =  X(2)X(3)∩X(560)X(1501)

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

X(33724) lies on these lines: {2, 3}, {560, 1501}


X(33725) =  X(2)X(3)∩X(560)X(1917)

Barycentrics    a^11*b^5 - 2*a^9*b^7 + a^7*b^9 + a^7*b^7*c^2 - a^5*b^9*c^2 - a^7*b^5*c^4 + a^5*b^7*c^4 - a^11*c^5 + a^7*b^4*c^5 + 2*a^9*c^7 - a^7*b^2*c^7 - a^5*b^4*c^7 - a^7*c^9 + a^5*b^2*c^9 : :

X(33725) lies on these lines: {2, 3}, {560, 1917}


X(33726) =  (name pending)

Barycentrics    a^14*b^5 - a^12*b^7 - a^9*b^10 + a^7*b^12 + a^10*b^7*c^2 - a^5*b^12*c^2 - a^10*b^5*c^4 + a^5*b^10*c^4 - a^14*c^5 + a^10*b^4*c^5 + a^12*c^7 - a^10*b^2*c^7 + a^9*c^10 - a^5*b^4*c^10 - a^7*c^12 + a^5*b^2*c^12 : :

X(33726) lies on these lines: {2, 3}


X(33727) =  X(2)X(3)∩X(1501)X(1917)

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

X(33727) lies on these lines: {2, 3}, {1501, 1917}


X(33728) =  X(2)X(3)∩X(32)X(23209)

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

X(33728) lies on these lines: {2, 3}, {32, 23209}, {160, 10329}, {574, 23210}, {1501, 9233}


X(33729) =  X(2)X(3)∩X(75)X(700)

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

X(33729) lies on these lines: {2, 3}, {75, 700}, {869, 7270}, {19800, 23537}


X(33730) =  X(2)X(3)∩X(38)X(75)

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

X(33730) lies on these lines: {2, 3}, {38, 75}, {42, 7270}, {58, 25453}, {81, 4645}, {86, 32773}, {274, 23682}, {314, 3914}, {333, 4429}, {982, 19805}, {1043, 33171}, {2239, 29850}, {2363, 29631}, {2887, 3736}, {3662, 5208}, {3720, 19786}, {3741, 19787}, {3786, 27184}, {3840, 19801}, {3925, 27164}, {4388, 27644}, {4653, 29642}, {4847, 16750}, {10453, 19785}, {10458, 25957}, {17027, 19834}, {17156, 33297}, {19791, 31027}, {19796, 31136}, {19803, 30942}, {19808, 33115}, {19815, 30821}, {28375, 32947}, {29667, 30599}, {33088, 33296}


X(33731) =  X(2)X(3)∩X(32)X(75)

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

X(33731) lies on these lines: {2, 3}, {32, 75}, {5266, 19791}, {5337, 19792}, {7270, 30149}, {17030, 19841}, {19761, 19838}, {19844, 20172}


X(33732) =  X(2)X(3)∩X(75)X(560)

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

X(33732) lies on these lines: {2, 3}, {75, 560}


X(33733) =  X(2)X(3)∩X(75)X(1501)

Barycentrics    a^11*b - a^7*b^5 - a^11*c + a^9*b^2*c + a^4*b^7*c - a^2*b^9*c - a^9*b*c^2 + a^7*b^3*c^2 - a^7*b^2*c^3 + b^9*c^3 + a^7*c^5 - b^7*c^5 - a^4*b*c^7 + b^5*c^7 + a^2*b*c^9 - b^3*c^9 : :

X(33733) lies on these lines: {2, 3}, {75, 1501}


X(33734) =  X(2)X(3)∩X(6)X(16890)

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

X(33734) lies on these lines: {2, 3}, {6, 16890}, {76, 19562}, {83, 1501}, {315, 3051}, {626, 3117}, {1613, 7784}, {3229, 7853}, {3978, 7790}, {5012, 10349}, {5254, 20023}, {7761, 8623}, {7803, 20965}


X(33735) =  X(2)X(3)∩X(76)X(1928)

Barycentrics    a^9*b^7*c^2 - a^5*b^11*c^2 - a^7*b^7*c^4 + a^5*b^9*c^4 - a^6*b^7*c^5 + a^2*b^11*c^5 - a^9*b^2*c^7 + a^7*b^4*c^7 + a^6*b^5*c^7 - a^2*b^9*c^7 - a^5*b^4*c^9 + a^2*b^7*c^9 + a^5*b^2*c^11 - a^2*b^5*c^11 : :

X(33735) lies on these lines: {2, 3}, {76, 1928}


X(33736) =  X(2)X(3)∩X(6)X(21287)

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

X(33736) lies on these lines: {2, 3}, {6, 21287}, {63, 24995}, {76, 321}, {81, 315}, {83, 18096}, {190, 2345}, {194, 31089}, {239, 5016}, {306, 13161}, {316, 5006}, {335, 4812}, {626, 980}, {940, 7784}, {1211, 5254}, {2895, 7754}, {2997, 26176}, {3096, 33172}, {3187, 5015}, {3662, 17863}, {3673, 17184}, {3767, 26243}, {4256, 30851}, {4261, 21245}, {5262, 19834}, {5286, 5739}, {5317, 17907}, {5337, 7761}, {5716, 26561}, {7748, 24271}, {7763, 30760}, {7803, 32911}, {7879, 32863}, {9308, 18685}, {16706, 18744}, {17192, 24204}, {17316, 18134}, {19719, 26131}, {20556, 32773}, {29616, 31017}


X(33737) =  X(2)X(3)∩X(31)X(76)

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

X(33737) lies on these lines: {2, 3}, {31, 76}


X(33738) =  X(2)X(3)∩X(76)X(560)

Barycentrics    a^11*b^2 - a^7*b^6 - a^11*c^2 + a^7*b^4*c^2 + a^4*b^7*c^2 - a^2*b^9*c^2 - a^7*b^2*c^4 + b^9*c^4 + a^7*c^6 - b^7*c^6 - a^4*b^2*c^7 + b^6*c^7 + a^2*b^2*c^9 - b^4*c^9 : :

X(33738) lies on these lines: {2, 3}, {76, 560}


X(33739) =  X(2)X(3)∩X(32)X(4159)

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

X(33739) lies on these lines: {2, 3}, {32, 4159}, {76, 1501}, {83, 20859}, {315, 16893}, {1369, 10343}, {3060, 10349}, {4048, 20023}, {14602, 18806}


X(33740) =  X(2)X(3)∩X(32)X(561)

Barycentrics    a^11*b^3 - a^7*b^7 - a^9*b^3*c^2 + a^7*b^5*c^2 - a^11*c^3 + a^9*b^2*c^3 + a^4*b^7*c^3 - a^2*b^9*c^3 - a^7*b^2*c^5 + b^9*c^5 + a^7*c^7 - a^4*b^3*c^7 + a^2*b^3*c^9 - b^5*c^9 : :

X(33740) lies on these lines: {2, 3}, {32, 561}


X(33741) =  X(2)X(3)∩X(560)X(561)

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

X(33741) lies on these lines: {2, 3}, {560, 561}


X(33742) =  X(2)X(3)∩X(561)X(1501)

Barycentrics    a^13*b^3 - a^9*b^7 - a^11*b^3*c^2 + a^9*b^5*c^2 - a^13*c^3 + a^11*b^2*c^3 + a^4*b^9*c^3 - a^2*b^11*c^3 - a^9*b^2*c^5 + b^11*c^5 + a^9*c^7 - b^9*c^7 - a^4*b^3*c^9 + b^7*c^9 + a^2*b^3*c^11 - b^5*c^11 : :

X(33742) lies on these lines: {2, 3}, {561, 1501}


X(33743) =  X(2)X(3)∩X(10)X(1502)

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

X(33743) lies on these lines: {2, 3}, {10, 1502}


X(33744) =  X(2)X(3)∩X(10)X(561)

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

X(33744) lies on these lines: {2, 3}, {10, 561}, {1185, 1330}


X(33745) =  X(2)X(3)∩X(10)X(32)

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

X(33745) lies on these lines: {2, 3}, {10, 32}, {37, 3923}, {171, 29674}, {942, 24549}, {980, 25526}, {1104, 16825}, {2198, 5282}, {2295, 3695}, {3416, 4275}, {4362, 5266}, {5247, 5814}, {5294, 5320}, {5337, 10479}, {5717, 29671}, {19701, 19758}


X(33746) =  X(2)X(3)∩X(10)X(560)

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

X(33746) lies on these lines: {2, 3}, {10, 560}, {32, 5015}


X(33747) =  X(2)X(3)∩X(10)X(1501)

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

X(33747) lies on these lines: {2, 3}, {10, 1501}


X(33748) =  X(2)X(3167)∩X(4)X(18845)

Barycentrics    11*a^6 - 15*a^4*b^2 + 5*a^2*b^4 - b^6 - 15*a^4*c^2 - 18*a^2*b^2*c^2 + b^4*c^2 + 5*a^2*c^4 + b^2*c^4 - c^6 : :
X(33748) = 4 X[69] - 13 X[10303],10 X[631] - X[20080],8 X[1353] + X[20080],8 X[5085] - 5 X[15692],2 X[6467] + 7 X[15043],2 X[11160] - 11 X[15721]

X(33748) lies on these lines: {2, 3167}, {4, 18845}, {6, 20}, {69, 10303}, {182, 193}, {376, 5093}, {511, 5032}, {524, 15708}, {575, 3091}, {631, 1353}, {698, 11148}, {1351, 3522}, {1352, 7486}, {1503, 3839}, {1587, 22646}, {1692, 5304}, {1992, 5085}, {3398, 32973}, {3525, 11898}, {3543, 11179}, {3618, 5056}, {3629, 10541}, {3832, 18583}, {4232, 11003}, {5012, 10565}, {5052, 32522}, {5059, 21850}, {5068, 18440}, {5422, 7398}, {5462, 12283}, {5622, 25321}, {5999, 14930}, {6467, 15043}, {7544, 18935}, {8584, 31884}, {11160, 15721}, {11433, 13394}, {12017, 15717}, {14913, 15028}, {15520, 15697}, {15534, 21167}, {15988, 17580}, {17809, 18928}, {18911, 30769}, {22234, 31670}

X(33748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 193, 3523}, {631, 1353, 20080}, {3618, 5921, 5056}, {3618, 8550, 5921}, {5050, 14912, 2}


X(33749) =  X(3)X(15534)∩X(4)X(22234)

Barycentrics    6*a^6 - 8*a^4*b^2 + 3*a^2*b^4 - b^6 - 8*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(33749) = 5 X[5] - 9 X[597],9 X[69] - 25 X[631],9 X[182] - 5 X[631],X[550] + 3 X[8584],9 X[1992] + 7 X[3528],9 X[3098] - 13 X[21734],11 X[5070] - 9 X[24206],5 X[10168] - 3 X[21358],3 X[10169] - X[18383],7 X[14869] - 3 X[22165],3 X[15533] - 11 X[15720],9 X[20423] - X[33703],4 X[25555] - 3 X[25565]

X(33749) lies on these lines: {3, 15534}, {4, 22234}, {5, 542}, {6, 382}, {20, 576}, {30, 22330}, {54, 69}, {114, 16984}, {184, 32068}, {193, 17508}, {384, 18800}, {389, 11649}, {397, 31710}, {398, 31709}, {511, 548}, {524, 3530}, {550, 8584}, {567, 16003}, {858, 13366}, {1352, 7486}, {1353, 5092}, {1503, 3861}, {1658, 8546}, {1992, 3528}, {2854, 12006}, {3098, 21734}, {3398, 14981}, {3520, 5095}, {3526, 10168}, {3564, 16239}, {3589, 15806}, {3629, 14810}, {3832, 6776}, {3843, 5476}, {3853, 9731}, {3859, 18583}, {4325, 19369}, {4330, 8540}, {5012, 11225}, {5038, 5477}, {5050, 5070}, {5067, 11178}, {5097, 29317}, {5182, 33225}, {5643, 9143}, {6055, 10486}, {6143, 32234}, {7519, 15004}, {7749, 10485}, {7794, 12151}, {8593, 16044}, {8705, 16881}, {9706, 15462}, {9976, 15037}, {10169, 18383}, {11003, 32223}, {11402, 15121}, {11477, 15696}, {11482, 17800}, {11579, 13434}, {13488, 15471}, {14130, 32305}, {14869, 22165}, {15018, 24981}, {15032, 15063}, {15062, 25321}, {15533, 15720}, {15602, 33554}, {19662, 33249}, {20423, 33703}, {22462, 32254}, {25738, 32396}

X(33749) = {X(575),X(18553)}-harmonic conjugate of X(597)


X(33750) =  X(2)X(6030)∩X(3)X(69)

Barycentrics    (a^2 - b^2 - c^2)*(11*a^4 + 8*a^2*b^2 + b^4 + 8*a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(33750) = X[2] - 4 X[17508],10 X[3] - X[69],8 X[3] + X[6776],4 X[3] - X[10519],19 X[3] - X[11898],2 X[3] + X[25406],2 X[6] + 7 X[3528],X[20] + 8 X[5092],X[20] + 2 X[14561],4 X[69] + 5 X[6776],2 X[69] - 5 X[10519],19 X[69] - 10 X[11898],X[69] + 5 X[25406],8 X[140] + X[14927],4 X[141] - 13 X[10299],4 X[182] + 5 X[3522],X[193] + 8 X[14810],8 X[206] + X[12250],5 X[376] + 4 X[597],X[376] + 2 X[5085],2 X[376] + X[14853],4 X[548] + 5 X[12017],4 X[550] + 5 X[3618],2 X[597] - 5 X[5085],8 X[597] - 5 X[14853],2 X[599] - 11 X[15715],5 X[631] - 2 X[10516],2 X[1350] - 11 X[21735],5 X[1350] + 4 X[32455],2 X[1352] - 11 X[15717],4 X[3098] - 13 X[21734],35 X[3523] - 8 X[18553],5 X[3524] - 2 X[21358],X[3529] + 8 X[3589],16 X[3530] - 7 X[3619],4 X[3818] - 13 X[10303],X[5032] + 5 X[10304],X[5050] + 2 X[8703],X[5059] + 8 X[19130],4 X[5085] - X[14853],4 X[5092] - X[14561],X[5093] + 5 X[14093],4 X[5476] + 5 X[15697],4 X[5480] + 5 X[17538],X[5596] + 8 X[15578],X[5656] - 4 X[23041],X[6776] + 2 X[10519],19 X[6776] + 8 X[11898],X[6776] - 4 X[25406],8 X[10168] + X[15683],19 X[10519] - 4 X[11898],X[10519] + 2 X[25406],X[11180] - 10 X[15692],2 X[11898] + 19 X[25406],5 X[14912] - 2 X[15534],X[14912] + 5 X[19708],X[14912] + 2 X[31884],2 X[15534] + 25 X[19708],X[15534] + 5 X[31884],5 X[15696] + 4 X[18583],7 X[15698] - 4 X[21167],10 X[15712] - X[18440],4 X[17504] - X[21356],5 X[19708] - 2 X[31884],55 X[21735] + 8 X[32455]

X(33750) lies on these lines: {2, 6030}, {3, 69}, {6, 3528}, {20, 5092}, {140, 14927}, {141, 10299}, {182, 3522}, {193, 14810}, {206, 12250}, {376, 597}, {511, 5032}, {524, 15710}, {542, 15705}, {548, 12017}, {550, 3618}, {599, 15715}, {631, 10516}, {1350, 21735}, {1352, 15717}, {1503, 3524}, {3098, 21734}, {3523, 18553}, {3529, 3589}, {3530, 3619}, {3818, 10303}, {3839, 29323}, {5050, 8703}, {5059, 19130}, {5093, 14093}, {5476, 15697}, {5480, 17538}, {5596, 15578}, {5656, 23041}, {7386, 13394}, {7605, 20062}, {10168, 15683}, {10984, 11821}, {11180, 15692}, {11645, 15708}, {14826, 15246}, {14912, 15534}, {15696, 18583}, {15698, 21167}, {15712, 18440}, {17504, 21356}

X(33750) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 25406, 10519}, {376, 5085, 14853}, {10519, 25406, 6776}, {14912, 19708, 31884}


X(33751) =  X(3)X(2916)∩X(20)X(17508)

Barycentrics    6*a^6 - 5*a^2*b^4 - b^6 - 8*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 + b^2*c^4 - c^6 : :
X(33751) = 13 X[3] - 5 X[3763],5 X[3] - X[3818],11 X[3] - 3 X[10516],3 X[3] - X[24206],X[20] + 3 X[17508],X[182] + 3 X[376],7 X[182] - 3 X[20423],7 X[376] + X[20423],9 X[548] + X[12007],13 X[548] + X[32455],3 X[550] + X[5480],2 X[550] + X[25555],X[1350] - 9 X[15688],X[1351] + 15 X[15695],X[1352] - 9 X[10304],X[3098] - 5 X[3522],3 X[3098] + X[6776],13 X[3098] - X[20080],15 X[3522] + X[6776],65 X[3522] - X[20080],25 X[3763] - 13 X[3818],55 X[3763] - 39 X[10516],15 X[3763] - 13 X[24206],11 X[3818] - 15 X[10516],3 X[3818] - 5 X[24206],3 X[5085] + 5 X[15696],3 X[5092] - X[5480],X[5476] + 3 X[15689],2 X[5480] - 3 X[25555],13 X[6776] + 3 X[20080],3 X[8703] - X[14810],13 X[8703] - X[22165],9 X[10516] - 11 X[24206],3 X[11178] + X[14927],X[11178] - 5 X[19708],X[11898] - 9 X[31884],13 X[12007] - 9 X[32455],3 X[14561] + 5 X[17538],13 X[14810] - 3 X[22165],X[14927] + 15 X[19708],3 X[15690] + X[18583],3 X[17504] - X[25561],3 X[17508] - X[19130],X[18553] - 3 X[21167]

X(33751) lies on these lines: {3, 2916}, {20, 17508}, {30, 25565}, {125, 6636}, {140, 29323}, {182, 376}, {511, 548}, {542, 8703}, {550, 5092}, {1204, 3098}, {1350, 15688}, {1351, 15695}, {1352, 10304}, {3534, 10168}, {3589, 12103}, {5085, 15696}, {5116, 6781}, {5476, 15689}, {7492, 32223}, {10691, 15448}, {11178, 14927}, {11898, 31884}, {14561, 17538}, {15578, 18400}, {15690, 18583}, {17504, 25561}, {18553, 21167}, {20190, 29181}

X(33751) = midpoint of X(i) and X(j) for these {i,j}: {20, 19130}, {550, 5092}, {3534, 10168}, {3589, 12103}
X(33751) = reflection of X(25555) in X(5092)
X(33751) = {X(20),X(17508)}-harmonic conjugate of X(19130)


X(33752) =  X(5)X(523)∩X(32)X(2485)

Barycentrics    a^2*(b - c)*(b + c)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^4 - b^4 + b^2*c^2 - c^4) : :
X(33752) = X[684] + 3 X[17994],X[879] - 3 X[14561]

X(33752) lies on these lines: {5, 523}, {32, 2485}, {110, 14998}, {114, 132}, {182, 512}, {381, 23878}, {511, 23350}, {520, 576}, {525, 5480}, {526, 11622}, {647, 1995}, {690, 32271}, {804, 22505}, {850, 5169}, {879, 14561}, {2433, 3066}, {2489, 8743}, {2492, 6593}, {2514, 23099}, {2793, 21731}, {2881, 25644}, {3005, 8371}, {3267, 7752}, {4230, 14966}, {5094, 30476}, {5099, 18311}, {5968, 8430}, {6132, 11616}, {7533, 31296}, {7624, 30209}, {7630, 9737}, {8673, 19139}, {9178, 11637}

X(33752) = reflection of X(i) in X(j) for these {i,j}: {11616, 6132}, {18312, 5} X(33752) = reflection of X(18312) in the Euler line
X(33752) = X(3)-of-X(3)X(4)X(6)
X(33752) = X(i)-isoconjugate of X(j) for these (i,j): {293, 935}, {1910, 17708}, {2157, 2966} X(33752) = crosspoint of X(4230) and X(5968)
X(33752) = crosssum of X(879) and X(5967)
X(33752) = crossdifference of every pair of points on line {50, 67}
X(33752) = barycentric product X(i)*X(j) for these {i,j}: {23, 2799}, {297, 9517}, {316, 3569}, {325, 2492}, {511, 9979}, {5968, 18311}, {6333, 8744}, {7664, 8430}, {16230, 22151}
X(33752) = X(3)X(4)X(6)-isogonal conjugate of X(879)
X(33752) = barycentric quotient X(i)/X(j) for these {i,j}: {23, 2966}, {232, 935}, {511, 17708}, {2491, 3455}, {2492, 98}, {2799, 18019}, {3569, 67}, {8430, 10415}, {8744, 685}, {9517, 287}, {9979, 290}, {10561, 9154}, {17994, 8791}, {18374, 2715}, {22151, 17932}


X(33753) =  X(4)X(33695)∩X(5)X(24975)

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

X(33753) lies on these lines: {4, 33695}, {5, 24975}, {24, 39}, {382, 3398}, {575, 7530}, {1576, 11623}, {1598, 23347}, {12084, 13335}, {15562, 20975}

X(33753) = X(6)-of-X(3)X(4)X(6)
X(33753) = X(3)X(4)X(6)-isogonal conjugate of X(14561)


X(33754) =  X(30)X(511)∩X(879)X(14561)

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

X(33754) lies one these lines: {30, 511}, {879, 14561}, {10516, 18312}

X(33754) = X(30)-of-X(3)X(4)X(6)


X(33755) =  X(6)X(694)∩X(99)X(511)

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

X(33755) lies on the cubic K1115 and these lines: {6, 694}, {99, 511}, {182, 21444}, {183, 6786}, {287, 6467}, {373, 3329}, {805, 8289}, {2871, 17710}, {4027, 17970}, {5039, 9427}, {6784, 11174}, {9467, 19120}, {9772, 14510}, {9976, 13210}, {11152, 14509}


X(33756) =  X(3)X(5106)∩X(6)X(32524)

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

X(33756) lies on the cubic K1115 and these lines: {3, 5106}, {6, 32524}, {32, 33705}, {39, 729}, {99, 187}, {574, 9468}, {3511, 5210}, {5024, 9431}, {8588, 21444}


X(33757) =  X(6)X(99)∩X(887)X(21006)

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

X(33757) lies on the cubic K1115 and these lines: {6, 99}, {887, 21006}, {3225, 22253}, {5106, 13586}

X(33757) = {X(99),X(729)}-harmonic conjugate of X(7757)


X(33758) =  X(3)X(76)∩X(7735)X(9468)

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

X(33758) lies on the cubic K1115 and these lines: {3, 76}, {7735, 9468}


X(33759) =  (name pending)

Barycentrics    -2*a^12*b^4 + a^10*b^6 - 2*a^8*b^8 + 3*a^6*b^10 + 4*a^12*b^2*c^2 - a^10*b^4*c^2 + 7*a^8*b^6*c^2 + 15*a^6*b^8*c^2 - 7*a^4*b^10*c^2 - 2*a^12*c^4 - a^10*b^2*c^4 + 8*a^8*b^4*c^4 + 45*a^6*b^6*c^4 - 10*a^4*b^8*c^4 + 5*a^2*b^10*c^4 + a^10*c^6 + 7*a^8*b^2*c^6 + 45*a^6*b^4*c^6 - 29*a^4*b^6*c^6 - 5*a^2*b^8*c^6 - b^10*c^6 - 2*a^8*c^8 + 15*a^6*b^2*c^8 - 10*a^4*b^4*c^8 - 5*a^2*b^6*c^8 + 2*b^8*c^8 + 3*a^6*c^10 - 7*a^4*b^2*c^10 + 5*a^2*b^4*c^10 - b^6*c^10 : :

X(33759) lies on the cubic K1115 and this line: {3, 194}

leftri

Perspectors T1(X(i), X(j)) involving triangles inscribed in a circumconic: X(33760)-X(33780)

rightri

Centers X(33760)-X(33780) were contributed by Clark Kimberling and Peter Moses, August 4, 2019.

Suppose that P = p : q : r and U = u : v : w (barycentrics) are points. Define M(P,U) = p/(v - w) : q/(w - u) : r/(u - v), so that M(P,U) lies on the circumconic p/x + q/y + r/z = 0.

Let T1 be the anticevian triangle of P, given by vertices
A' = -p : q : r
B' = p : - q : r
C' = p : q : -r

Let T2 be the anticevian triangle of U, given by vertices
A" = -u : v : w
B" = u : - v : w
C" = u : v : -w

Let M(P,T2) denote the triangle with vertices M(P,A"), M(P,B"), M(P,C"). The triangles T1 and M(T2) are perspective, and their perspector is given by

T1(P,U) = p*(u^2 + uv + uw - vw) : q*(v^2 + vw + vu - wu) : r*(w^2 + wu + wv - uv)

The appearance of (i,j,k) in the following list means that T1(X(i),X(j)) = X(k).

(1,1,32911), (1,2,1), (1,4,1748), (1,6,33760), (1,7,1445), (1,8,63), (1,9,7676), (1,10,33761), (1,30,2349), (1,31,33762), (1,32,33763), (1,63,411), (1,69,1760), (1,75,17277), (1,76,33764), (1,85,33765), (1,86,33766), (1,92,412), (1,144,2951), (1,145,23511)

(2,1,4360), (2,2,2), (2,4,317), (2,6,7760), (2,7,6604), (2,8,69), (2,9,32024), (2,10,32025), (2,20,6527), (2,30,1494), (2,31,33767), (2,32,33768), (2,37,32026), (2,69,315), (2,75,17143), (2,76,33769), (2,86,33770), (2,141,32027), (2,144,30695), (2,145,4452)

(6,1,595), (6,2,6), (6,3,1614), (6,4,24), (6,6,1627), (6,7,1617), (6,8,3), (6,10,33771), (6,20,1498), (6,30,74), (6,31,33772), (6,32,33773), (6,63,1630), (6,69,22), (6,75,1621), (6,76,1078), (6,86,33774), (6,100,1618), (6,144,1615), (6,145,1616), (6,148,33704)

(75,1,18140), (75,2,75), (75,6,18064), (75,7,21609), (75,8,304), (75,10,33775), (75,31,33776), (75,32,33777), (75,69,20641), (75,75,18152), (75,76, 33778), (75,86,33779), (75,145,33780)


X(33760) =  Perspector T1(X(1),X(6))

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

X(33760) lies on these lines: {19, 162}, {31, 75}, {47, 4008}, {58, 5263}, {100, 2220}, {171, 17289}, {238, 3821}, {560, 662}, {595, 32922}, {748, 17370}, {750, 17371}, {799, 18058}, {896, 17446}, {1580, 1964}, {1582, 2234}, {1631, 24598}, {1707, 1760}, {1724, 4429}, {1733, 2964}, {1923, 1966}, {2345, 4275}, {3573, 16685}, {4000, 17127}, {4118, 17799}, {5247, 32850}, {11677, 24597}, {16568, 17872}, {17871, 20915}, {23868, 24530}


X(33761) =  Perspector T1(X(1),X(10))

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

X(33761) lies on these lines: {1, 4127}, {2, 45}, {9, 5256}, {10, 32936}, {21, 3453}, {37, 81}, {38, 3315}, {44, 17011}, {63, 3731}, {100, 756}, {192, 5278}, {238, 3989}, {239, 32026}, {306, 31143}, {321, 5235}, {333, 3995}, {344, 33172}, {651, 16577}, {894, 5333}, {896, 1961}, {940, 16675}, {968, 3681}, {984, 1621}, {1001, 7226}, {1125, 32940}, {1211, 32849}, {1214, 29007}, {1215, 4756}, {1376, 9330}, {1654, 3969}, {1707, 9347}, {1748, 17916}, {1757, 1962}, {1931, 21816}, {1999, 4921}, {2292, 5260}, {2895, 17332}, {3187, 4664}, {3240, 3715}, {3293, 32635}, {3305, 4850}, {3578, 6542}, {3663, 26724}, {3666, 16814}, {3670, 17536}, {3683, 3920}, {3685, 4981}, {3695, 26064}, {3826, 33102}, {3842, 4418}, {3925, 33100}, {3929, 5287}, {3932, 33083}, {3971, 32917}, {3993, 32864}, {4026, 33166}, {4078, 33078}, {4096, 4767}, {4259, 26911}, {4357, 33157}, {4359, 17260}, {4360, 19742}, {4392, 4423}, {4425, 33115}, {4640, 5297}, {4643, 32858}, {4648, 20078}, {4655, 29854}, {4656, 31204}, {4671, 5737}, {4679, 29680}, {4683, 29653}, {4703, 29643}, {4854, 33139}, {4972, 9791}, {5220, 17018}, {5296, 19822}, {5302, 17016}, {5311, 7262}, {5718, 26792}, {5743, 33168}, {6211, 11203}, {6536, 32780}, {6646, 18139}, {6763, 27784}, {7191, 15254}, {9342, 17596}, {10436, 25734}, {10707, 29690}, {14829, 31035}, {14996, 16677}, {15523, 24697}, {15650, 19767}, {16826, 32090}, {16861, 30117}, {16885, 20182}, {16948, 31445}, {17054, 17570}, {17056, 17484}, {17125, 17591}, {17147, 17277}, {17184, 17258}, {17243, 32863}, {17245, 26842}, {17246, 33150}, {17247, 32774}, {17257, 17776}, {17262, 19732}, {17276, 27186}, {17318, 19723}, {17333, 32859}, {17334, 17483}, {17336, 26223}, {17346, 20017}, {17350, 19684}, {17390, 20086}, {17534, 24046}, {18136, 29396}, {20602, 28594}, {21061, 25058}, {21368, 21811}, {24703, 29664}, {26037, 32934}, {26580, 30831}, {26738, 28609}, {29661, 33101}, {29682, 33096}, {31247, 32779}

X(33760) = isogonal conjugate of isotomic conjugate of X(18064)


X(33762) =  Perspector T1(X(1),X(31))

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

X(33762) lies on these lines: {32, 76}, {1492, 1917}, {1932, 3510}, {1933, 6196}, {7031, 17738}


X(33763) =  Perspector T1(X(1),X(32))

Barycentrics    a*(a^8 + a^4*b^4 + a^4*c^4 - b^4*c^4) : :

X(33763) lies on this line: {560, 561}


X(33764) =  Perspector T1(X(1),X(76))

Barycentrics    b*c*(-a^4 + a^2*b^2 + a^2*c^2 + b^2*c^2) : :

X(33764) lies on these lines: {31, 75}, {38, 1966}, {63, 561}, {76, 32933}, {190, 18152}, {304, 2167}, {310, 32939}, {334, 33067}, {350, 32936}, {874, 17135}, {896, 1965}, {1150, 6382}, {1580, 1930}, {1748, 1969}, {1909, 32940}, {1920, 3218}, {1921, 3219}, {1978, 14829}, {4361, 23538}, {4436, 23371}, {4438, 30632}, {5278, 10009}, {7018, 33119}, {14213, 20944}, {17147, 30940}, {17149, 18075}, {18059, 32913}, {30631, 33115}


X(33765) =  Perspector T1(X(1),X(85))

Barycentrics    (a + b - c)^2*(a - b + c)^2*(a^2 - a*b - a*c - b*c) : :

X(33765) lies on these lines: {7, 55}, {57, 658}, {63, 85}, {81, 279}, {82, 3668}, {86, 8021}, {190, 21609}, {348, 9776}, {354, 14189}, {552, 4637}, {664, 3873}, {1155, 9446}, {1996, 5435}, {2094, 17079}, {3188, 11020}, {3306, 31627}, {4554, 18045}, {4860, 31526}, {5088, 10167}, {6063, 14829}, {6604, 17784}, {7176, 20358}, {9441, 10481}, {20059, 23618}


X(33766) =  Perspector T1(X(1),X(86))

Barycentrics    a*(a + b)*(a + c)*(a^2 + 3*a*b + 3*a*c + b*c) : :

X(33766) lies on these lines: {6, 662}, {37, 81}, {44, 1963}, {58, 1918}, {86, 4416}, {333, 28653}, {593, 2220}, {741, 872}, {799, 18046}, {897, 13610}, {940, 24944}, {1100, 1931}, {1468, 18042}, {1509, 17277}, {2185, 4275}, {3759, 17103}, {4420, 4663}, {16668, 16702}, {16704, 28604}, {17120, 19623}, {17289, 17731}, {17315, 32004}, {18722, 20360}, {20090, 25536}, {31248, 32014}


X(33767) =  Perspector T1(X(2),X(31))

Barycentrics    a^6 + a^3*b^3 + a^3*c^3 - b^3*c^3 : :

X(33767) lies on these lines: {31, 561}, {171, 30631}, {1501, 4586}, {1915, 19565}, {17127, 20345}


X(33768) =  Perspector T1(X(2),X(32))

Barycentrics    a^8 + a^4*b^4 + a^4*c^4 - b^4*c^4 : :

X(33768) lies on these lines: {32, 710}, {141, 10347}, {4577, 8264}, {8265, 16985}


X(33769) =  Perspector T1(X(2),X(76))

Barycentrics    b^2*c^2*(-a^4 + a^2*b^2 + a^2*c^2 + b^2*c^2) : :

X(33769) lies on these lines: {2, 31613}, {6, 76}, {69, 290}, {95, 183}, {99, 8266}, {141, 3978}, {264, 12167}, {317, 18022}, {319, 18891}, {350, 18170}, {385, 1627}, {524, 9230}, {599, 6374}, {1978, 17295}, {2998, 3228}, {3631, 30736}, {3760, 18194}, {4445, 6382}, {4577, 19121}, {6383, 7232}, {6664, 14970}, {8264, 20081}, {8920, 15069}, {9464, 31128}, {14603, 14994}, {18137, 27853}, {20148, 20913}, {24437, 24732}

X(33769) = isotomic conjugate of X(27375)


X(33770) =  Perspector T1(X(2),X(86))

Barycentrics    (a + b)*(a + c)*(a^2 + 3*a*b + 3*a*c + b*c) : :

X(33770) lies on these lines: {1, 99}, {10, 86}, {81, 213}, {83, 20132}, {190, 24051}, {261, 17394}, {315, 3945}, {551, 6626}, {595, 757}, {648, 17911}, {671, 6625}, {873, 17143}, {940, 1078}, {1125, 17731}, {1931, 29580}, {2106, 20963}, {2668, 4038}, {3636, 6629}, {4340, 7802}, {5209, 25303}, {5712, 7752}, {6537, 20536}, {6542, 8025}, {7256, 9347}, {7760, 17379}, {7809, 20337}, {17300, 32027}, {18166, 21788}, {26805, 27189}, {28619, 30966}


X(33771) =  Perspector T1(X(6),X(10))

Barycentrics    a^2*(a^2 - a*b - 2*b^2 - a*c - 3*b*c - 2*c^2) : :

X(33771) lies on these lines: {1, 88}, {6, 24047}, {8, 16347}, {10, 1043}, {21, 3293}, {31, 5312}, {35, 42}, {43, 5248}, {55, 386}, {72, 4689}, {73, 3256}, {101, 1500}, {103, 6577}, {109, 2594}, {171, 4658}, {284, 3453}, {387, 5281}, {484, 2650}, {580, 32613}, {581, 11248}, {692, 17104}, {785, 28509}, {846, 3678}, {899, 5259}, {902, 1203}, {991, 10310}, {995, 1616}, {1001, 17749}, {1078, 4360}, {1125, 3750}, {1193, 3746}, {1468, 5010}, {1621, 3216}, {1724, 3240}, {1757, 3647}, {1758, 12432}, {1834, 17734}, {2271, 3730}, {2276, 4251}, {2646, 15955}, {2901, 7081}, {3017, 4995}, {3214, 5251}, {3570, 32026}, {3584, 21935}, {3621, 16499}, {3679, 10448}, {3684, 25092}, {3699, 4075}, {3743, 5293}, {3811, 17594}, {3841, 29640}, {3874, 17596}, {3881, 3979}, {3914, 24160}, {3915, 5313}, {3931, 30115}, {3953, 3957}, {3996, 19270}, {4015, 5524}, {4026, 24931}, {4253, 31448}, {4257, 5217}, {4300, 5537}, {4414, 5904}, {4421, 5711}, {4646, 24929}, {4849, 31445}, {4894, 29849}, {4972, 25645}, {5030, 20963}, {5132, 23374}, {5218, 5292}, {5230, 31452}, {5260, 31855}, {5264, 19767}, {5396, 11849}, {5492, 12738}, {5687, 19765}, {5730, 17461}, {6690, 24880}, {6788, 12433}, {9310, 9331}, {9327, 21008}, {10902, 13329}, {10955, 18340}, {11263, 24715}, {11285, 20162}, {13405, 23537}, {16484, 19862}, {16783, 17756}, {17592, 30142}, {17715, 30148}, {17735, 20970}, {19863, 32945}, {19864, 32943}, {20108, 32942}, {21070, 26244}, {24440, 30143}, {25526, 29822}, {28527, 29014}

X(33771) = isogonal conjugate of isotomic conjugate of X(32025)


X(33772) =  Perspector T1(X(6),X(31))

Barycentrics    a^2*(a^6 + a^3*b^3 + a^3*c^3 - b^3*c^3) : :

X(33772) lies on these lines: {75, 560}, {753, 7087}, {825, 9233}, {2210, 24478}, {7122, 24575}


X(33773) =  Perspector T1(X(6),X(32))

Barycentrics    a^2*(a^8 + a^4*b^4 + a^4*c^4 - b^4*c^4) : :

X(33773) lies on these lines: {76, 1501}, {755, 2353}, {1691, 7828}, {1915, 7832}, {2715, 32540}

X(33773) = Vu tangential transform of X(32)


X(33774) =  Perspector T1(X(6),X(86))

Barycentrics    a^2*(a + b)*(a + c)*(a^2 + 3*a*b + 3*a*c + b*c) : :

X(33774) lies on these lines: {21, 17019}, {22, 4252}, {31, 110}, {35, 42}, {81, 4640}, {99, 17150}, {111, 2248}, {757, 1621}, {1326, 2308}, {1333, 2205}, {1931, 3920}, {2363, 5297}, {3187, 11104}, {5012, 5019}, {5170, 9218}, {7109, 18268}, {7341, 16878}, {15107, 20461}, {20069, 31059}


X(33775) =  Perspector T1(X(75),X(10))

Barycentrics    b*c*(-a^2 + a*b + 2*b^2 + a*c + 3*b*c + 2*c^2) : :

X(33775) lies on these lines: {75, 3624}, {76, 1978}, {274, 321}, {304, 29573}, {312, 17308}, {668, 1089}, {1655, 7230}, {1909, 4066}, {3159, 30966}, {3802, 16825}, {4037, 32026}, {4125, 25280}, {4568, 24044}, {4647, 20947}, {7769, 33168}, {18145, 20911}, {22036, 31027}


X(33776) =  Perspector T1(X(75),X(31))

Barycentrics    b*c*(-a^6 - a^3*b^3 - a^3*c^3 + b^3*c^3) : :

X(33776) lies on these lines: {6, 706}, {560, 789}, {561, 26222}, {1580, 24732}, {1582, 19567}, {3759, 20446}, {18048, 18140}


X(33777) =  Perspector T1(X(75),X(32))

Barycentrics    b*c*(-a^8 - a^4*b^4 - a^4*c^4 + b^4*c^4) : :

X(33777) lies on these lines: {31, 1928}, {1917, 4593}

X(33778) =  Perspector T1(X(75),X(76))

Barycentrics    b^3*c^3*(-a^4 + a^2*b^2 + a^2*c^2 + b^2*c^2) : :

X(33778) lies on thesse lines: {1, 561}, {304, 1928}, {1102, 3403}, {1920, 27020}, {1921, 26959}, {1923, 1966}, {1925, 14210}, {1926, 1930}


X(33779) =  Perspector T1(X(75),X(86))

Barycentrics    b*(a + b)*c*(a + c)*(a^2 + 3*a*b + 3*a*c + b*c) : :

X(33779) lies on these lines: {2, 799}, {42, 86}, {99, 5284}, {274, 321}, {310, 25507}, {748, 17103}, {756, 18827}, {899, 2668}, {1434, 28387}, {1509, 32911}, {2664, 17175}, {2669, 3720}, {16709, 20947}, {18064, 31997}


X(33780) =  Perspector T1(X(75),X(145))

Barycentrics    b*c*(a^2 + 2*a*b + b^2 + 2*a*c - 6*b*c + c^2) : :

X(33780) lies on these lines: {10, 75}, {85, 5226}, {279, 1997}, {304, 18145}, {312, 26563}, {350, 16284}, {668, 17158}, {1088, 18153}, {1446, 20946}, {1847, 6335}, {2899, 7195}, {3760, 4673}, {4358, 21605}, {4452, 6552}, {4737, 7264}, {18140, 20925}, {18151, 21588}, {18156, 18159}, {18739, 18751}

leftri

Perspectors T2(X(i), X(j)) involving triangles inscribed in a circumconic: X(33781)-X(33789)

rightri

Centers X(33781)-X(33789) were contributed by Clark Kimberling and Peter Moses, August 4, 2019

Suppose that P = p : q : r and U = u : v : w are points Define M(U) = p/(v - w) : q/(w - u) : r/(u - v), so that M(U) lies on the circumconic p/x + q/y + r/z = 0

Let T1 be the triangle with vertices
A' = -p : q : r
B' = p : - q : r
C' = p : q : -r

Let T2 be the triangle with vertices
A" = 0 : y : z
B" = x : 0 : z
C" = x : y : 0

The triangles T1 and M(T2) are perspective, and their perspector is given by

T2(P,X) = p*(x^2 y^2 + x^2 z^2 - y^2 z^2) : q*(y^2 z^2 + y^2 x^2 - z^2 x^2) : r*(z^2 x^2 + z^2 y^2 - x^2 y2)

The appearance of (i,j,k) in the following list means that T2(X(i),X(j)) = X(k)

(1,1,1740), (1,2,1), (1,4,33781), (1,6,33782), (1,7,23511), (1,8,2951), (1,75,63), (1,76,1760), (1,83,33783), (1,85,1445), (1,86,32911), (1,87,33784), (1,92,6515), (1,99,99)

(2,1,194), (2,2,2), (2,4,6293), (2,6,8264), (2,7,4452), (2,8,30695), (2,66,33785), (2,69,6527), (2,75,69), (2,76,315), (2,83,7760), (2,85,6604), (2,86,4360), (2,87,32033), (2,92,6515), (2,99,99)

(6,1,1613), (6,2,6), (6,4,1611), (6,6,33786), (6,7,1616), (6,8,1615), (6,69,1498), (6,75,3), (6,76,22), (6,83,1627), (6,85,1617), (6,86,595), (6,92,1609), (6,95,1614), (6,99,110)

(75,1,17149), (75,2,75), (75,4,33787), (75,6,33788), (75,7,33789), (75,75,304), (75,83,18064), (75,85,21609), (75,86,18140), (75,99,799)


X(33781) =  Perspector T2(X(1),X(4))

Barycentrics    a*(a^4 + 2*a^2*b^2 + b^4 + 2*a^2*c^2 - 6*b^2*c^2 + c^4) : :

X(33781) lies on these lines: {1, 75}, {4, 1716}, {19, 1707}, {63, 17872}, {77, 25570}, {238, 12717}, {240, 1712}, {610, 1580}, {1711, 1713}, {1742, 30503}, {1760, 16570}, {2324, 2664}, {2345, 5268}, {2640, 18594}, {2643, 18713}, {3008, 21629}, {3068, 8941}, {3069, 8945}, {3186, 7093}, {4000, 5272}, {5227, 24445}, {16778, 23381}, {17871, 21406}, {17890, 20883}, {25571, 25930}


X(33782) =  Perspector T2(X(1),X(6))

Barycentrics    a*(a^4*b^4 + a^4*c^4 - b^4*c^4) : :

X(33782) lies on these lines: {1, 561}, {31, 1582}, {43, 1185}, {748, 14823}, {1580, 2172}, {3510, 16998}, {16690, 23371}


X(33783) =  Perspector T2(X(1),X(31))

Barycentrics    a (a^6 b^6+a^6 c^6-b^6 c^6) : :

X(33783) lies on these lines:


X(33784) =  Perspector T2(X(1),X(87))

Barycentrics    a*(a*b - a*c - b*c)*(a*b - a*c + b*c)*(a^2*b^2 - 2*a*b^2*c + a^2*c^2 - 2*a*b*c^2 + b^2*c^2) : :

X(33784) lies on these lines: {1, 8026}, {6, 43}, {330, 3009}, {748, 932}, {1215, 24661}, {2053, 14823}, {3223, 20332}, {4393, 23493}, {4598, 16569}, {6384, 17793}, {7121, 32911}, {15966, 17277}


X(33785) =  Perspector T2(X(2),X(66))

Barycentrics    a^8 + 2*a^4*b^4 + b^8 + 2*a^4*c^4 - 6*b^4*c^4 + c^8 : :

X(33785) lies on these lines: {2, 308}, {66, 20065}, {3164, 19577}, {5596, 16985}


X(33786) =  Perspector T2(X(6),X(6))

Barycentrics    a^2*(a^4*b^4 + a^4*c^4 - b^4*c^4) : :

X(33786) lies on these lines: {6, 76}, {32, 1613}, {99, 3360}, {182, 6310}, {194, 32748}, {206, 1691}, {384, 18899}, {394, 10350}, {805, 32541}, {1078, 21001}, {1207, 7808}, {1975, 10341}, {3051, 7787}, {3053, 9431}, {3231, 7793}, {5017, 10790}, {6179, 9427}, {7766, 9490}, {8619, 21776}, {11490, 21792}

X(33786) = isogonal conjugate of isotomic conjugate of X(8264)
X(33786) = vertex conjugate of PU(159)


X(33787) =  Perspector T2(X(75),X(4))

Barycentrics    b*c*(a^4 + 2*a^2*b^2 + b^4 + 2*a^2*c^2 - 6*b^2*c^2 + c^4) : :

X(33787) lies on these lines: {38, 75}, {92, 18056}, {304, 18068}, {1966, 18750}, {18075, 20641}


X(33788) =  Perspector T2(X(75),X(6))

Barycentrics    b*c*(-(a^4*b^4) - a^4*c^4 + b^4*c^4) : :

X(33788) lies on these lines: {1, 1965}, {75, 1928}, {1760, 1966}, {1917, 4593}, {1925, 3116}, {2227, 18837}, {5283, 6376}, {6384, 26959}, {18046, 18148}


X(33789) =  Perspector T2(X(75),X(87))

Barycentrics    b c (a b-a c+b c) (-a b+a c+b c) (a^2 b^2-2 a b^2 c+a^2 c^2-2 a b c^2+b^2 c^2) : :

X(33789) lies on these lines:

leftri

Perspectors T3(X(i), X(j)) involving triangles inscribed in a circumconic: X(33790)-X(33809)

rightri

Centers X(33790)-X(33809) were contributed by Clark Kimberling and Peter Moses, August 4, 2019

Suppose that P = p : q : r and U = u : v : w are points Define M(U) = p/(v - w) : q/(w - u) : r/(u - v), so that M(U) lies on the circumconic p/x + q/y + r/z = 0

Let T1 be the triangle with vertices
A' = -p : q : r
B' = p : - q : r
C' = p : q : -r

Let T2 be the triangle with vertices
A" = 0 : z : -y
B" = -z : 0 : x
C" = y : -x : 0

The triangles T1 and M(T2) are perspective, and their perspector is given by

T3(P,X) = p*(y^2 + z^2 - x^2) : q*(z^2 + x^2 - y^2) : r*(x^2 + y^2 - z^2)

The appearance of (i,j,k) in the following list means that T3(X(i),X(j)) = X(k).

(1,1,63), (1,2,1), (1,3,1748), (1,6,1760), (1,7,2951), (1,8,23511), (1,9,1445), (1,10,32911), (1,30,2349), (1,31,33790), (1,32,32791), (1,37,17277), (1,39,33792), (1,63,920), (1,65,23512), (1,69,33793), (1,75,1740), (1,76,33794), (1,142,7676), (1,145,33795)

(2,1,69), (2,2,2), (2,3,317), (2,4,6527), (2,6,315), (2,7,30695), (2,8,4452), (2,9,6604), (2,10,4360), (2,30,1494), (2,31,33796), (2,32,33797), (2,37,17143), (2,39,33798), (2,44,32032), (2,63,6515), (2,69,6392), (2,75,194), (2,76,8264), (2,115,33799), (2,141,7760), (2,142,32024), (2,145,33800)

(6,1,3), (6,2,6), (6,3,24), (6,4,1498), (6,5,1614), (6,6,22), (6,7,1615), (6,8,1616), (6,9,1617), (6,11,1618), (6,13,24303), (6,15,1605), (6,16,1606), (6,19,1619), (6,20,1620), (6,30,74), (6,31,33801), (6,32,22802), (6,37,1621), (6,39,1078), (6,40,1622), (6,42,23374), (6,44,1623), (6,54,1601), (6,55,1602), (6,56,1603), (6,57,1604), (6,61,1607), (6,62,1608), (6,63,1609), (6,65,1610), (6,69,1611), (6,72,1612), (6,75,1613), (6,76,33803), (6,79,33669), (6,99,33704), (6,110,30715), (6,141,1627), (6,145,33804)

(75,1,304), (75,2,75), (75,6,20641), (75,8,33805), (75,9,21609), (75,10,18140), (75,31,33806), (75,32,33807), (75,37,18152), (75,38,18053), (75,69,33808), (75,75,17149), (75,76,338089), (75,141,18064)

Note that X(k) for k = 1601, 1602,...,1623 occur in the above list; see the preamble just before X(1601).


X(33790) =  Perspector T3(X(1),X(31))

Barycentrics    a*(a^6 - b^6 - c^6) : :

X(33790) lies on these lines:s {1, 1917}, {63, 16545}, {76, 1759}, {163, 18717}, {1102, 18596}, {1760, 3403}, {9247, 18715}


X(33791) =  Perspector T3(X(1),X(32))

Barycentrics    a*(a^8 - b^8 - c^8) : :

X(33791) lies on these lines: {1, 33712}, {561, 1760}, {4599, 16544}, {16568, 17871}


X(33792) =  Perspector T3(X(1),X(42))

Barycentrics    a (a^4 b^2-a^2 b^4+2 a^4 b c-2 a b^4 c+a^4 c^2-b^4 c^2-a^2 c^4-2 a b c^4-b^2 c^4) : :

X(33792) lies on these lines:


X(33793) =  Perspector T3(X(1),X(38))

Barycentrics    a (a^4 b^2-a^2 b^4+a^4 c^2+2 a^2 b^2 c^2+b^4 c^2-a^2 c^4+b^2 c^4) : :

X(33793) lies on these lines:


X(33794) =  Perspector T3(X(1),X(45))

Barycentrics    a (a^4-4 a^3 b+4 a b^3-b^4-4 a^3 c+8 a^2 b c-8 a b^2 c+4 b^3 c-8 a b c^2-8 b^2 c^2+4 a c^3+4 b c^3-c^4) : :

X(33794) lies on these lines:


X(33795) =  Perspector T3(X(1),X(145))

Barycentrics    a*(7*a^2 - 2*a*b - 9*b^2 - 2*a*c + 14*b*c - 9*c^2) : :

X(33795) lies on these lines: {1, 3}, {2, 4902}, {516, 21267}, {2999, 23958}, {3218, 23511}, {3306, 33761}, {3664, 31326}, {3817, 22166}, {3928, 3973}, {4862, 5435}, {10563, 12513}


X(33796) =  Perspector T3(X(2),X(31))

Barycentrics    a^6 - b^6 - c^6 : :

X(33796) lies on these lines: {2, 1501}, {69, 1369}, {141, 16949}, {315, 2387}, {316, 3060}, {561, 6327}, {1370, 4176}, {2979, 16275}, {4048, 16893}, {4121, 29012}, {5422, 7773}, {6515, 32006}, {8024, 11550}, {21243, 26233}, {23293, 33651}, {30877, 32664}

X(33796) = anticomplement of X(1501)


X(33797) =  Perspector T3(X(2),X(32))

Barycentrics    a^8 - b^8 - c^8 : :

X(33797) lies on these lines: {2, 9233}, {66, 315}, {290, 18124}, {4577, 5596}


X(33798) =  Perspector T3(X(2),X(38))

Barycentrics    a^4 b^2-a^2 b^4+a^4 c^2+2 a^2 b^2 c^2+b^4 c^2-a^2 c^4+b^2 c^4 : :

X(33798) lies on these lines:


X(33799) =  Perspector T3(X(2),X(115))

Barycentrics    (a - b)*(a + b)*(a - c)*(a + c)*(a^4 - a^2*b^2 + 2*b^4 - a^2*c^2 - 3*b^2*c^2 + 2*c^4) : :

X(33799) lies on these lines: {99, 523}, {148, 23991}, {688, 14509}, {1272, 5641}, {2966, 4577}, {6368, 17932}, {8591, 18823}, {11123, 31632}, {14061, 31644}, {17930, 28175}, {18020, 30716}, {20094, 23992}

X(33799) = isotomic conjugate of X(36955)


X(33800) =  Perspector T3(X(2),X(145))

Barycentrics    7*a^2 - 2*a*b - 9*b^2 - 2*a*c + 14*b*c - 9*c^2 : :

X(33800) lies on these lines: {2, 7}, {8, 4902}, {69, 20052}, {75, 25296}, {145, 4862}, {320, 4452}, {3621, 4373}, {3622, 4888}, {3623, 3663}, {4346, 4360}, {4454, 7232}, {4488, 30833}, {4678, 31995}, {4747, 17235}, {4869, 7238}, {4896, 30712}, {11682, 19604}, {20049, 32105}, {20080, 32029}


X(33801) =  Perspector T3(X(6),X(31))

Barycentrics    a^2*(a^6 - b^6 - c^6) : :

X(33801) lies on these lines: {3, 2916}, {6, 6660}, {22, 157}, {23, 7806}, {75, 1631}, {159, 1634}, {206, 3001}, {1576, 12220}, {1609, 9909}, {1624, 26283}, {2930, 22152}, {6636, 16986}, {7784, 10828}, {9019, 14575}, {16682, 23378}, {19127, 23635}, {23374, 23852}


X(33802) =  Perspector T3(X(6),X(32))

Barycentrics    a^2*(a^8 - b^8 - c^8) : :

X(33802) lies on these lines: {3, 3096}, {6, 33717}, {22, 76}, {23, 3767}, {25, 7828}, {26, 98}, {157, 1078}, {827, 20993}, {1352, 7512}, {1975, 5938}, {1995, 7942}, {3148, 7786}, {6636, 7795}, {7485, 7930}, {9909, 14568}


X(33803) =  Perspector T3(X(6),X(115))

Barycentrics    a^2 (a^2-b^2) (a^2-c^2) (a^4-a^2 b^2+2 b^4-a^2 c^2-3 b^2 c^2+2 c^4) : :

X(33803) lies on these lines:

X(33803) = isogonal conjugate of X(36955)
X(33803) = isogonal conjugate of X(99) wrt its cevian triangle
X(33803) = anticomplement of X(35605)
X(33803) = crosssum of X(i) and X(j) for these {i,j}: {523, 10190}, {1649, 33919}
X(33803) = crossdifference of every pair of points on line X(1648)X(33906)
X(33803) = Vu tangential transform of X(99)


X(33804) =  Perspector T3(X(6),X(145))

Barycentrics    a^2*(7*a^2 - 2*a*b - 9*b^2 - 2*a*c + 14*b*c - 9*c^2) : :

X(33804) lies on these lines: {6, 41}, {36, 1616}, {44, 7963}, {3052, 32577}, {3445, 5204}, {5126, 17054}, {7280, 16486}, {15803, 15854}


X(33805) =  Perspector T3(X(75),X(30))

Barycentrics    b c (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) : :

X(33805) lies on these lines:

X(33805) = isogonal conjugate of X(9406)
X(33805) = isotomic conjugate of X(2173)


X(33806) =  Perspector T3(X(75),X(31))

Barycentrics    b*c*(-a^6 + b^6 + c^6) : :

X(33806) lies on these lines: {75, 560}, {92, 18053}, {304, 18715}, {1502, 20444}, {10010, 20649}, {18041, 20944}, {18051, 20641}


X(33807) =  Perspector T3(X(75),X(32))

Barycentrics    b*c*(-a^8 + b^8 + c^8) : :

X(33807) lies on these lines: {75, 1917}, {1928, 20641}, {4593, 20931}, {21593, 33764}


X(33808) =  Perspector T3(X(75),X(63))

Barycentrics    b c (-a^6+3 a^4 b^2-3 a^2 b^4+b^6+3 a^4 c^2+2 a^2 b^2 c^2-b^4 c^2-3 a^2 c^4-b^2 c^4+c^6) : :

X(33808) lies on these lines:


X(33809) =  Perspector T3(X(75),X(115))

Barycentrics    b c (a^2-b^2) (a^2-c^2) (a^4-a^2 b^2+2 b^4-a^2 c^2-3 b^2 c^2+2 c^4) : :

X(33809) lies on these lines:


X(33810) = REFLECTION OF X(40) IN X(23845)

Barycentrics    a*((b+c)*a^8-(b^2+6*b*c+c^2)*a^7-(b+c)*(3*b^2-7*b*c+3*c^2)*a^6+(3*b^4+3*c^4+2*(5*b^2-7*b*c+5*c^2)*b*c)*a^5+(b^3+c^3)*(b-3*c)*(3*b-c)*a^4-(3*b^4+3*c^4+2*(4*b^2+b*c+4*c^2)*b*c)*(b-c)^2*a^3-(b^3+c^3)*(b-c)^4*a^2+(b^2-c^2)^3*(b-c)*b*c+(b^2-c^2)^2*(b^4+c^4-2*(b^2-3*b*c+c^2)*b*c)*a) : :
Trilinears    (8*sin(A/2)-6*sin(3*A/2)+sin(5*A/2))*cos((B-C)/2)+(2*cos(A)-cos(2*A)-3)*cos(B-C)+sin(A/2)*cos(3*(B-C)/2)+8*cos(A)-3*cos(2*A)-3 : :

X(33810) lies on the excentral-hexyl ellipse, the Stammler hyperbola, and these lines: {1,104}, {3,25934}, {4,3216}, {6,1012}, {40,23361}, {101,610}, {102,1633}, {294,30500}, {517,23169}, {900,6326}, {946,1450}, {1086,1537}, {1618,2716}, {1715,28348}, {1721,1740}, {2654,6705}, {2829,4551}, {2917,20833}, {2948,5538}, {3560,15805}, {3576,8053}, {5292,6847}, {6260,22072}, {6914,17194}, {12332,23703}, {13743,15047}

X(33810) = reflection of X(40) in X(23845)
X(33810) = X(23181)-of-hexyl-triangle


X(33811) = X(1)X(15622) ∩ X(2)X(33536)

Barycentrics    a*((b+c)*a^7-4*b*c*a^6-(b+c)*(3*b^2-7*b*c+3*c^2)*a^5+3*(b-c)^2*b*c*a^4+(b^2-c^2)*(b-c)*(3*b^2-4*b*c+3*c^2)*a^3+2*(b^2+4*b*c+c^2)*(b-c)^2*b*c*a^2-(b^2-c^2)*(b-c)*(b^4+c^4-(b^2-8*b*c+c^2)*b*c)*a-(b^2-c^2)^2*(b-c)^2*b*c) : :
Trilinears    (2*sin(A/2)-2*sin(3*A/2)+sin(5*A/2))*cos((B-C)/2)+(cos(2*A)+3)*cos(B-C)-sin(A/2)*cos(3*(B-C)/2)-2*cos(A)-cos(2*A)-1 : :
X(33811) = 3*X(165)-2*X(23845)

X(33811) lies on the excentral-hexyl ellipse and these lines: {1,15622}, {2,33536}, {3,25934}, {20,16528}, {33,57}, {40,78}, {64,1715}, {84,412}, {165,3185}, {474,33537}, {900,1768}, {1006,33538}, {1020,15252}, {1054,2821}, {1204,28077}, {1350,1764}, {1730,19541}, {2807,4551}, {5535,33535}, {5709,16389}, {6911,11472}, {6985,12163}, {6996,29481}, {10860,12717}, {11381,27622}, {13257,21362}, {16117,33542}

X(33811) = X(23181)-of-excentral triangle


X(33812) =  X(1)X(149)∩X(10)X(7972)

Barycentrics    (b + c-2 a) (3 a^3-a^2 b-3 a b^2+b^3-a^2 c+5 a b c-b^2 c-3 a c^2-b c^2+c^3) : :
X(33812) = 5*X[1]-X[149], X[10]+X[7972], X[11]-2*X[3636], X[80]-3*X[551], X[100]+X[3244], X[145]+3*X[15015], X[944]+X[21635], X[1483]+X[22935], 2*X[3035]-X[3626], 2*X[3036]-3*X[3828], 3*X[3241]+X[5541], 5*X[3616]-X[9897], 5*X[3623]-X[12653], 2*X[3634]-X[15863], X[3878]+X[17660], 3*X[3898]-X[17638], X[4297]+X[10698], X[4301]+X[12119], 3*X[5731]+X[13253], X[5882]+X[6265], 3*X[5883]-X[17636], X[6326]+3*X[7967], 3*X[10165]-X[19914], 3*X[10246]-X[10265], 2*X[11729]-X[19925], X[13199]+3*X[16200], 7*X[15808]-5*X[31272], 7*X[20057]+X[20095]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29274.

X(33812) lies on these lines: {1,149}, {10,7972}, {11,3636}, {80,551}, {100,3244}, {119,28236}, {142,12737}, {145,15015}, {214,519}, {515,12611}, {516,25485}, {942,2802}, {944,21635}, {952,1125}, {1320,5425}, {1385,32905}, {1483,22935}, {1484,3822}, {1537,28164}, {2771,3884}, {2800,13369}, {2932,25439}, {3035,3626}, {3036,3828}, {3241,5541}, {3616,9897}, {3623,12653}, {3634,15863}, {3825,11698}, {3878,17660}, {3898,17638}, {4297,10698}, {4301,12119}, {5248,12773}, {5731,13253}, {5882,6265}, {5883,17636}, {6264,30147}, {6326,7967}, {10074,14798}, {10165,19914}, {10246,10265}, {11715,24299}, {11729,19925}, {13199,16200}, {15808,31272}, {20057,20095}, {24466,28228}

X(33812) = midpoint of X(i) and X(j) for these {i,j}: {1,33337}, {10,7972}, {100,3244}, {214,1317}, {551,10031}, {944,21635}, {1483,22935}, {3878,17660}, {4301,12119}, {5882,6265}, {6224,21630}
X(33812) = reflection of X(i) in X(j) for these {i,j}: {11,3636}, {3626,3035}, {3635,12735}, {15863,3634}, {19925,11729}
X(33812) = barycentric quotient of X(44)/X(1343)
X(33812) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {1,6224,21630}, {214,11274,1317}, {21630,33337,6224}


X(33813) =  COMPLEMENT OF X(6321)

Barycentrics    2 a^8-5 a^6 b^2+5 a^4 b^4-2 a^2 b^6-5 a^6 c^2+4 a^4 b^2 c^2-a^2 b^4 c^2+b^6 c^2+5 a^4 c^4-a^2 b^2 c^4-2 b^4 c^4-2 a^2 c^6+b^2 c^6 : :
Barycentrics    7 S^4 + (-9 SB SC+2 SB SW+2 SC SW-3 SW^2)S^2 + SB SC SW^2 : :
X(33813) = 3*X[2]-X[6321], X[4]-3*X[15561], X[5]-2*X[620], X[20]+X[6033], X[115]-2*X[140], X[147]+3*X[376], X[148]-5*X[631], 3*X[381]-X[10723], 2*X[547]-3*X[9167], 2*X[548]+X[14981], 5*X[632]-4*X[6722], X[671]-3*X[5054], X[1350]+X[12177], X[1351]-3*X[5182], 5*X[1656]-3*X[14639], X[1657]+X[10722], 5*X[3522]-X[9862], 7*X[3523]-3*X[14651], 3*X[3524]+X[8591], 7*X[3526]-5*X[14061], X[3534]+X[6054], 3*X[3576]+X[13174], X[3627]-4*X[20399], 4*X[3628]-3*X[23514], X[3655]+X[9881], X[3830]-3*X[23234], 3*X[5050]-X[10754], 2*X[5461]-3*X[11539], X[5984]-9*X[10304], X[6055]-2*X[12100], 2*X[6699]-X[15535], 3*X[7709]+X[8782], X[7970]+X[12702], X[7983]-3*X[10246], X[8586]-3*X[22525], X[8596]-9*X[15708], 3*X[9166]-X[12355], X[9864]+X[18481], 4*X[10124]-3*X[14971], 3*X[10165]-X[11599], X[11005]+X[12121], X[11177]-5*X[19708], 2*X[11623]-5*X[15712], X[11710]-2*X[13624], 2*X[11724]-X[22791], X[12243]-5*X[15692], X[12383]+X[15545], X[13178]-3*X[26446], X[13179]-3*X[26451], 7*X[14869]-4*X[20398], 3*X[15035]-X[18332], 5*X[15051]-X[22265], X[15342]-3*X[32609], 3*X[15699]-4*X[22247], X[21636]+X[31730]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29274.

X(33813) is the nine-point center of the mid-triangle of the antipedal triangles of X(13) and X(14). (Randy Hutson, August 19, 2019)

X(33813) lies on these lines: {1,15452}, {2,6321}, {3,76}, {4,15561}, {5,620}, {20,6033}, {24,5186}, {30,114}, {35,3023}, {36,3027}, {55,10089}, {56,10086}, {115,140}, {147,376}, {148,631}, {182,5969}, {187,1569}, {378,12131}, {381,10723}, {384,11272}, {498,13182}, {499,13183}, {511,5026}, {517,11711}, {542,8703}, {543,549}, {547,9167}, {548,14981}, {550,2794}, {574,2023}, {632,6722}, {671,5054}, {690,1511}, {804,11616}, {1003,10352}, {1350,12177}, {1351,5182}, {1353,14645}, {1656,14639}, {1657,10722}, {1916,8350}, {2080,4027}, {2452,4558}, {2795,5428}, {2967,4235}, {3095,3552}, {3398,7783}, {3522,9862}, {3523,14651}, {3524,8591}, {3526,14061}, {3534,6054}, {3576,13174}, {3582,12354}, {3584,18969}, {3587,24469}, {3627,20399}, {3628,23514}, {3655,9881}, {3734,9734}, {3830,23234}, {3972,32447}, {4226,9155}, {4299,12184}, {4302,12185}, {5050,10754}, {5149,9737}, {5204,10069}, {5217,10053}, {5461,11539}, {5965,14148}, {5984,10304}, {5985,17549}, {5987,6636}, {6055,12100}, {6179,32520}, {6194,8289}, {6319,26341}, {6320,26348}, {6390,32458}, {6642,13175}, {6699,15535}, {7417,31128}, {7502,14655}, {7709,8782}, {7757,11842}, {7863,32152}, {7970,12702}, {7983,10246}, {8290,11676}, {8586,22525}, {8589,15819}, {8596,15708}, {9166,12355}, {9864,18481}, {10124,14971}, {10165,11599}, {10267,13173}, {10269,22514}, {10734,16281}, {11005,12121}, {11156,11288}, {11177,19708}, {11623,15712}, {11710,13624}, {11724,22791}, {12054,12176}, {12243,15692}, {12251,33014}, {12383,15545}, {13178,26446}, {13179,26451}, {13180,26492}, {13181,26487}, {13189,16203}, {13190,16202}, {13335,32448}, {13479,22143}, {13496,18570}, {13860,22681}, {14033,14494}, {14570,22085}, {14869,20398}, {15035,18332}, {15051,22265}, {15342,32609}, {15357,32423}, {15699,22247}, {21636,31730}, {24472,24929}

X(33813) = midpoint of X(i) and X(j) for these {i,j}: {3,99}, {20,6033}, {98,13188}, {115,10992}, {376,8724}, {381,12117}, {1350,12177}, {1657,10722}, {1916,19910}, {3534,6054}, {3655,9881}, {5984,14692}, {6055,15300}, {6321,13172}, {7970,12702}, {8591,11632}, {9864,18481}, {11005,12121}, {12188,23235}, {12383,15545}, {21636,31730}
X(33813) = reflection of X(i) in X(j) for these {i,j}: {5,620}, {115,140}, {6055,12100}, {9880,547}, {11710,13624}, {12042,3}, {15535,6699}, {22505,114}, {22515,5}, {22791,11724}
X(33813) = complement of X(6321)
X(33813) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {2,13172,6321}, {3,1975,10104}, {3,13188,98}, {98,99,13188}, {99,21166,3}, {114,22505,22566}, {187,1569,12829}, {1656,14639,15092}, {3523,20094,14651}, {3524,8591,11632}, {9167,9880,547}, {11171,19910,1916}, {12121,14850,11005}, {12355,15694,9166}, {14692,14830,5984}, {23514,31274,3628}, {32481,32482,13108}


X(33814) =  COMPLEMENT OF X(10738)

Barycentrics    a (2 a^6-2 a^5 b-4 a^4 b^2+4 a^3 b^3+2 a^2 b^4-2 a b^5-2 a^5 c+4 a^4 b c+2 a^3 b^2 c-5 a^2 b^3 c+b^5 c-4 a^4 c^2+2 a^3 b c^2+2 a b^3 c^2+4 a^3 c^3-5 a^2 b c^3+2 a b^2 c^3-2 b^3 c^3+2 a^2 c^4-2 a c^5+b c^5) : :
Barycentrics    5 R S^3 - (4 a R^2-4 b R^2-2 a SB+2 b SB+c SB-2 a SC+b SC+2 c SC+b SW)S^2 -3 R S SB SC-b SB SC^2 + c SB SC^2 + b SB SC SW : :
X(33814) = 3*X[2]-X[10738], X[5]-2*X[3035], X[20]+X[10742], X[40]+X[6265], X[149]-5*X[631], X[153]+3*X[376], 3*X[165]+X[6326], X[355]+X[12119], 3*X[381]-X[10724], X[1320]-3*X[10246], X[1657]+X[10728], X[1768]+X[12738], 5*X[3522]-X[12248], 7*X[3523]+X[20095], 7*X[3526]-5*X[31272], 4*X[3530]+X[6154], X[3534]+X[10711], 3*X[3576]+X[5541], X[3627]-4*X[20400], 4*X[3628]-3*X[23513], 3*X[5050]-X[10755], 3*X[5054]-X[10707], X[5528]+3*X[21153], X[5531]+7*X[16192], 3*X[5660]-X[16128], 3*X[5886]-X[14217], X[6246]-2*X[9956], X[6264]-5*X[7987], 2*X[6702]-3*X[11231], X[6909]+X[18524], 3*X[10164]-X[10265], 3*X[10165]-X[21630], X[10767]-3*X[14643], X[10768]-3*X[15561], X[10778]-3*X[15061], 3*X[11171]-X[32454], 3*X[11230]-2*X[16174], X[11362]+X[33337], X[11715]-2*X[13624], X[12751]+X[18481], X[13268]-3*X[26451], 3*X[13587]-X[22765], 5*X[15712]-2*X[20418], X[21635]+X[31730]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29274.

X(33814) lies on these lines: {1,24302}, {2,10738}, {3,8}, {5,3035}, {10,26086}, {11,35}, {20,10742}, {24,1862}, {30,119}, {36,1317}, {40,6265}, {46,12739}, {55,1387}, {56,10087}, {80,5010}, {149,631}, {153,376}, {165,6326}, {182,9024}, {214,517}, {355,12119}, {378,12138}, {381,10724}, {404,5901}, {498,13273}, {499,13274}, {516,12611}, {519,23961}, {528,549}, {550,2829}, {632,5248}, {758,10225}, {971,6594}, {993,3036}, {1006,12690}, {1155,11570}, {1320,10246}, {1376,6914}, {1385,2802}, {1482,4188}, {1483,5854}, {1511,8674}, {1537,6905}, {1657,10728}, {1737,12743}, {1768,12738}, {2080,13194}, {2771,9943}, {2783,12042}, {2800,3579}, {2805,14650}, {3149,12775}, {3522,12248}, {3523,20095}, {3526,31272} ,{3530,6154}, {3534,10711}, {3576,5541}, {3627,20400}, {3628,23513}, {3651,13257}, {3871,25416}, {3880,18857}, {4189,12747}, {4242,21664}, {4299,12763}, {4302,12764}, {4421,10269}, {4640,18254}, {5050,10755}, {5054,10707}, {5119,12740}, {5172,12832}, {5204,10074}, {5217,10058}, {5259,16239}, {5267,15863}, {5428,6684}, {5432,8068}, {5433,5533}, {5440,14988}, {5499,31659}, {5528,21153}, {5531,16192}, {5537,28212}, {5660,16128}, {5762,10427} ,{5790,6950}, {5843,6068}, {5856,31657}, {5886,14217}, {6147,10044}, {6221,19082}, {6246,9956}, {6264,7987}, {6398,19081}, {6551,29348}, {6642,13222}, {6702,11231}, {6906,18357}, {6909,18524}, {6924,11248}, {6942,10698}, {6970,8166}, {7280,7972}, {7427,31073}, {10039,18976}, {10073,24914}, {10164,10265}, {10165,21630}, {10267,13205}, {10679,16371}, {10680,19537}, {10767,14643}, {10768,15561}, {10778,15061}, {10956,18990}, {11171,32454}, {11230,16174}, {11362,33337}, {11495,12332}, {11715,13624}, {12054,12199}, {12100,15931}, {12736,24929}, {12751,18481}, {13235,26316}, {13268,26451}, {13269,26341}, {13270,26348}, {13271,26492}, {13272,26487}, {13278,16203}, {13279,16202}, {13587,22765}, {15325,32760}, {15712,20418}, {19919,31835}, {21635,31730}, {31789,32554}

X(33814) = midpoint of X(i) and X(j) for these {i,j}: {3,100}, {11,10993}, {20,10742}, {40,6265}, {104,12331}, {119,24466}, {355,12119}, {550,11698}, {1657,10728}, {1768,12738}, {3534,10711}, {3579,22935}, {5541,12737}, {6224,19914}, {6326,12515}, {6909,18524}, {10698,12702}, {10738,13199}, {11362,33337}, {12751,18481}, {21635,31730}, {22560,25438}
X(33814) = reflection of X(i) in X(j) for these {i,j}: {5,3035}, {11,140}, {1484,6713}, {6246,9956}, {11715,13624}, {12619,6684}, {19907,214}, {22791,11729}, {22799,119}, {22938,5}
X(33814) = complement of X(10738)
X(33814) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {2,13199,10738}, {3,5687,32153}, {3,12331,104}, {40,15015,6265}, {55,10090,1387}, {56,10087,12735}, {100,104,12331}, {100,2932,9945}, {100,4996,1145}, {100,17100,10609}, {165,6326,12515}, {404,11849,5901}, {549,1484,6713}, {3576,5541,12737}, {4421,22560,25438}, {5010,26446,7508}, {5657,6224,19914}, {6174,24466,119}, {6924,11248,22791}, {8715,32612,1483}, {23513,31235,3628}, {25440,26285,5}


X(33815) =  X(1)X(1392)∩X(2)X(4084)

Barycentrics    a (2 a^2 b-2 b^3+2 a^2 c+2 a b c+3 b^2 c+3 b c^2-2 c^3) : :
X(33815) = 3*X[2]+X[4084], 7*X[10]-3*X[3681], 5*X[65]+3*X[392], X[72]-3*X[3828], 3*X[354]-X[3635], 9*X[551]-5*X[3890], X[960]-3*X[3833], 5*X[1698]-X[4067], X[3244]-5*X[18398], X[3555]+7*X[3922], 5*X[3617]+3*X[3894], X[3625]+3*X[3873], X[3626]-3*X[3753], 5*X[3698]-3*X[4745], 3*X[3740]-X[4127], 3*X[3742]-X[3884], X[3869]+3*X[4744], 3*X[3877]-7*X[15808], 3*X[3892]+X[10914], 3*X[3899]-11*X[5550], X[3901]+3*X[4134], X[4018]+3*X[10176], X[4297]-5*X[15016], 3*X[4430]+5*X[4668], X[5694]-3*X[10172], X[5784]+3*X[30329], X[5884]+X[19925], X[5887]-3*X[10171]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29274.

X(33815) lies on these lines: {1,1392}, {2,4084}, {8,17146}, {10,3681}, {46,30143}, {57,30147}, {65,392}, {72,3828}, {354,3635}, {404,5425}, {515,5885}, {516,31870}, {517,3530}, {518,3918}, {519,942}, {535,24470}, {551,3890}, {758,3634}, {960,3833}, {993,5221}, {1159,25524}, {1193,24168}, {1698,4067}, {1737,11263}, {1739,2650}, {2802,5045}, {3035,16137}, {3244,18398}, {3306,30144}, {3333,22837}, {3336,5267}, {3339,31424}, {3555,3922}, {3617,3894}, {3625,3873}, {3626,3753}, {3649,3814}, {3698,4745}, {3740,4127}, {3742,3884}, {3869,4744}, {3877,15808}, {3892,10914}, {3899,5550}, {3901,4134}, {3997,20271}, {4018,10176}, {4297,15016}, {4298,18838}, {4430,4668}, {4867,17531}, {4880,5260}, {5046,11552}, {5270,26842}, {5290,18419}, {5438,11529}, {5542,10915}, {5690,25557}, {5694,10172}, {5708,8666}, {5784,30329}, {5884,19925}, {5887,10171}, {6001,12571}, {6583,28234}, {6738,10122}, {7686,28164}, {8715,15934}, {9943,28158}, {10129,15079}, {11375,20107}, {11551,24982}, {12005,28236}, {13145,28194}, {17049,28512}, {18395,31019}, {20104,24914}, {28228,31788}

X(33815) = midpoint of X(i) and X(j) for these {i,j}: {65,1125}, {942,3754}, {960,4757}, {3555,4701}, {3626,3874}, {3812,31794}, {3881,5836}, {4745,24473}, {5045,10107}, {5884,19925}
X(33815) = reflection of X(i) in X(j) for these {i,j}: {960,19878}, {3634,3812}, {4691,3918}
X(33815) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {65,5439,3878}, {65,5883,1125}, {942,5836,3881}, {960,3833,19878}, {3753,3874,3626}, {3754,3881,5836}, {3833,4757,960}, {3878,5439,1125}, {3878,5883,5439}, {3901,9780,4134}, {4744,19862,3869}, {12736,13750,6738}

leftri

4th degree polynomial centers on the Euler line: X(33816)-X(33841)

rightri

Centers X(33816)-X(33841) were contributed by Peter Moses, August 5, 2019


X(33816) =  X(2)X(3)∩X(8)X(20142)

Barycentrics    a^4 + a^3*b + a*b^3 + a^3*c + b^3*c + b^2*c^2 + a*c^3 + b*c^3 : :

As a point on the Euler line, X(33816) has Shinagawa coefficients ((E+F)2-S2+2(E+F)$bc$-abc$a$,2S2).

X(33816) lies on these lines: {2, 3}, {8, 20142}, {35, 27324}, {76, 25497}, {86, 1655}, {274, 24275}, {315, 16991}, {385, 27040}, {894, 21808}, {1089, 30168}, {1468, 31028}, {2292, 6651}, {3314, 26099}, {3329, 27109}, {3767, 17003}, {3797, 5262}, {4366, 26965}, {4766, 30175}, {5247, 31027}, {5251, 27274}, {6645, 27097}, {7783, 27162}, {7823, 26085}, {7839, 26770}, {7893, 17007}, {14621, 29966}, {17000, 26035}, {17128, 26978}, {17379, 27523}, {21024, 33295}, {24514, 24549}, {25992, 26582}, {26779, 31020}, {26801, 32942}, {28082, 31317}


X(33817) =  X(2)X(3)∩X(6)X(32004)

Barycentrics    a^4 + a^3*b + a*b^3 + a^3*c - a^2*b*c - a*b^2*c + b^3*c - a*b*c^2 + b^2*c^2 + a*c^3 + b*c^3 : :

As a point on the Euler line, X(33817) has Shinagawa coefficients ((E+F)2-S2+2(E+F)$bc$-2abc$a$,2S2).

X(33817) lies on these lines: {2, 3}, {6, 32004}, {86, 27269}, {986, 6651}, {1468, 30967}, {3992, 30141}, {4366, 27299}, {4766, 30174}, {5247, 31028}, {5248, 27324}, {7839, 27523}, {10449, 20142}, {14621, 29968}, {16974, 20947}, {16998, 27040}, {18140, 25497}, {25992, 26590}


X(33818) =  X(2)X(3)∩X(86)X(7864)

Barycentrics    a^4 + a^3*b - a^2*b^2 + a*b^3 - b^4 + a^3*c + a^2*b*c + a*b^2*c + b^3*c - a^2*c^2 + a*b*c^2 + b^2*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33818) has Shinagawa coefficients ((E+F)2+S2-2(E+F)$bc$,-4S2).

X(33818) lies on these lines: {2, 3}, {86, 7864}, {1654, 7929}, {3096, 24275}, {3336, 30150}, {5224, 7928}, {7784, 31090}, {7823, 17277}, {7904, 26244}, {9598, 17302}, {17128, 17234}, {17245, 32819}, {17300, 20081}, {17349, 20088}, {26101, 26806}


X(33819) =  X(2)X(3)∩X(6)X(27109)

Barycentrics    a^4 + a^3*b - a^2*b^2 + a*b^3 + a^3*c + b^3*c - a^2*c^2 + a*c^3 + b*c^3 : :

As a point on the Euler line, X(33819) has Shinagawa coefficients (2S2-2(E+F)$bc$+abc$a$,-2S2).

X(33819) lies on these lines: {2, 3}, {6, 27109}, {31, 29960}, {35, 30107}, {36, 30110}, {39, 25497}, {41, 17353}, {46, 26562}, {55, 26965}, {56, 27097}, {100, 27299}, {171, 29966}, {172, 17279}, {183, 27040}, {325, 26099}, {672, 24549}, {748, 29991}, {750, 29968}, {894, 25082}, {956, 26759}, {976, 17755}, {996, 29699}, {997, 26689}, {1468, 3912}, {1931, 33172}, {1975, 26978}, {2896, 16991}, {2975, 27248}, {3286, 27185}, {3670, 30105}, {3891, 30168}, {3915, 30038}, {4257, 29473}, {4385, 26247}, {4423, 27148}, {5013, 27162}, {5021, 30941}, {5248, 16818}, {5255, 30036}, {5264, 30109}, {5902, 30131}, {5903, 30128}, {7750, 26085}, {7754, 26770}, {7767, 17007}, {7797, 17003}, {14974, 17152}, {15668, 16705}, {16819, 23407}, {16968, 20911}, {16992, 26035}, {17030, 24552}, {17103, 17234}, {17126, 29986}, {18600, 31859}, {24631, 28082}, {26686, 28734}, {27256, 27335}, {27368, 27474}


X(33820) =  X(2)X(3)∩X(148)X(26978)

Barycentrics    a^4 + a^3*b - a^2*b^2 + a*b^3 - b^4 + a^3*c + b^3*c - a^2*c^2 + b^2*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33820) has Shinagawa coefficients ((E+F)2+S2-2(E+F)$bc$+abc$a$,-4S2).

X(33820) lies on these lines: {2, 3}, {148, 26978}, {194, 26099}, {2896, 27040}, {7779, 26770}, {7784, 16991}, {7785, 27109}, {7790, 25497}, {7851, 17003}, {7898, 26085}, {7929, 17007}, {17350, 21285}


X(33821) =  X(1)X(17755)∩X(2)X(3)

Barycentrics    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 + a*c^3 + b*c^3 : :

As a point on the Euler line, X(33821) has Shinagawa coefficients (S2)-(E+F)$bc$+abc$a$,-S2).

X(33821) lies on these lines: {1, 17755}, {2, 3}, {9, 24549}, {31, 29966}, {55, 27299}, {86, 5283}, {171, 29968}, {218, 26685}, {238, 29960}, {304, 16968}, {332, 27623}, {595, 30109}, {758, 30131}, {894, 16601}, {958, 27248}, {993, 30110}, {1220, 27255}, {1621, 26965}, {2975, 27097}, {3701, 26247}, {3878, 30128}, {3912, 5247}, {3915, 30036}, {4426, 17279}, {4511, 26689}, {5021, 30962}, {5120, 26106}, {5248, 30107}, {5255, 30030}, {5259, 16818}, {5263, 16819}, {7754, 27523}, {9534, 20154}, {14828, 17499}, {14974, 21281}, {17030, 32942}, {17123, 29991}, {17127, 29986}, {17206, 30945}, {17735, 20255}, {24047, 24170}, {27060, 28771}, {30168, 32926}


X(33822) =  X(2)X(3)∩X(191)X(30150)

Barycentrics    a^4 + a^3*b - a^2*b^2 + a*b^3 - b^4 + a^3*c - a^2*b*c - a*b^2*c + b^3*c - a^2*c^2 - a*b*c^2 + b^2*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33822) has Shinagawa coefficients ((E+F)2+S2-2(E+F)$bc$+2abc$a$,-4S2).

X(33822) lies on these lines: {2, 3}, {191, 30150}, {484, 30156}, {1655, 26099}, {4648, 6625}, {5134, 24190}, {7779, 27523}, {26145, 27109}


X(33823) =  X(2)X(3)∩X(145)X(6653)

Barycentrics    a^4 - a^2*b^2 - b^4 + a^2*b*c + a*b^2*c - a^2*c^2 + a*b*c^2 + b^2*c^2 - c^4 : :

As a point on the Euler line, X(33823) has Shinagawa coefficients ((E+F)2+S2-abc$a$,-4S2).

X(33823) lies on these lines: {2, 3}, {145, 6653}, {148, 18135}, {274, 7761}, {330, 20553}, {668, 9651}, {1478, 26752}, {1655, 2549}, {3585, 27091}, {4418, 30177}, {5254, 16997}, {5276, 7864}, {5277, 7790}, {5283, 7847}, {7354, 26582}, {7748, 18140}, {7750, 16998}, {7898, 27318}, {9597, 21226}, {9665, 27195}, {11263, 30135}, {12943, 26687}, {26079, 27109}


X(33824) =  X(2)X(3)∩X(8)X(25270)

Barycentrics    a^4 - a^2*b^2 - b^4 - a^2*b*c - a*b^2*c - a^2*c^2 - a*b*c^2 + b^2*c^2 - c^4 : :

As a point on the Euler line, X(33824) has Shinagawa coefficients ((E+F)2+S2+abc$a$,-4S2).

X(33824) lies on these lines: {2, 3}, {8, 25270}, {274, 7748}, {315, 1655}, {316, 5283}, {1479, 26801}, {2896, 18135}, {3583, 17030}, {3585, 27255}, {3617, 6653}, {3797, 5016}, {5254, 16998}, {5276, 7823}, {5277, 7802}, {6284, 26558}, {6646, 21285}, {7750, 16997}, {7761, 18140}, {7842, 16589}, {7854, 18145}, {7898, 27269}, {7936, 18146}, {9598, 17759}, {9664, 17143}, {11813, 30140}, {12953, 20172}, {26145, 27162}, {30177, 32930}


X(33825) =  X(2)X(3)∩X(80)X(30156)

Barycentrics    a^4 - a^3*b - a*b^3 - a^3*c + a^2*b*c + a*b^2*c - b^3*c + a*b*c^2 + b^2*c^2 - a*c^3 - b*c^3 : :

As a point on the Euler line, X(33825) has Shinagawa coefficients ((E+F)2-S2-2(E+F)$bc$+2abc$a$,2S2).

X(33825) lies on these lines: {2, 3}, {80, 30156}, {101, 24190}, {169, 7187}, {239, 3976}, {2271, 17300}, {5697, 16820}, {6626, 17259}, {6645, 27299}, {16827, 24586}, {16997, 26978}, {17033, 24602}, {17206, 17349}, {17234, 18755}, {17277, 27318}, {24591, 27002}, {24596, 26801}, {26007, 26561}, {27008, 28749}


X(33826) =  X(2)X(3)∩X(41)X(3662)

Barycentrics    a^4 - a^3*b - a*b^3 - a^3*c - b^3*c + b^2*c^2 - a*c^3 - b*c^3 : :

As a point on the Euler line, X(33826) has Shinagawa coefficients ((E+F)2-S2-2(E+F)$bc$+abc$a$,2S2).

X(33826) lies on these lines: {2, 3}, {41, 3662}, {172, 16706}, {257, 9317}, {385, 26978}, {673, 26801}, {1468, 17367}, {1580, 24169}, {3314, 26085}, {3329, 27162}, {3589, 17103}, {3616, 20137}, {3884, 16820}, {3934, 29479}, {3972, 25497}, {4366, 27097}, {4680, 30169}, {5278, 24621}, {6645, 26965}, {7783, 27109}, {7795, 16991}, {7823, 26099}, {7839, 18600}, {16788, 24190}, {16999, 26100}, {17033, 24586}, {17034, 29473}, {17128, 27040}, {17169, 20147}, {18266, 33123}, {26007, 26558}


X(33827) =  X(2)X(3)∩X(41)X(31004)

Barycentrics    a^4 - a^3*b - a*b^3 - a^3*c - a^2*b*c - a*b^2*c - b^3*c - a*b*c^2 + b^2*c^2 - a*c^3 - b*c^3 : :

As a point on the Euler line, X(33827) has Shinagawa coefficients ((E+F)2-S2+2(E+F)$bc$,2S2).

X(33827) lies on these lines: {2, 3}, {41, 31004}, {86, 7787}, {194, 17277}, {218, 6646}, {257, 24249}, {1975, 17259}, {2896, 17234}, {4352, 7839}, {4366, 27248}, {4426, 16706}, {4648, 20065}, {5247, 17367}, {7750, 17245}, {7772, 16712}, {7795, 31090}, {7893, 17300}, {7945, 30761}, {16997, 26100}, {16998, 26978}, {17291, 24549}, {26244, 31276}, {27288, 31638}


X(33828) =  X(2)X(3)∩X(10)X(4482)

Barycentrics    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 - a*c^3 - b*c^3 : :

As a point on the Euler line, X(33828) has Shinagawa coefficients (S2+(E+F)$bc$-abc$a$,-S2).

X(33828) lies on these lines: {2, 3}, {10, 4482}, {56, 27299}, {86, 5277}, {100, 27097}, {101, 24170}, {169, 25918}, {214, 30128}, {274, 26244}, {333, 23447}, {344, 31448}, {673, 26959}, {978, 24586}, {1046, 24628}, {1193, 24602}, {1220, 27324}, {1376, 27248}, {1434, 17499}, {2238, 17206}, {2271, 30962}, {3216, 29473}, {3662, 20269}, {3721, 4561}, {3732, 7187}, {3736, 29459}, {3754, 30132}, {3953, 32029}, {4254, 26106}, {4384, 11512}, {4511, 26562}, {5088, 25994}, {5253, 26965}, {5276, 27162}, {5883, 30127}, {9342, 27026}, {16752, 26243}, {16822, 24174}, {17184, 25593}, {17257, 25583}, {17260, 25068}, {17738, 25079}, {20255, 21008}, {20880, 26279}, {24046, 30108}, {24918, 30761}, {25440, 30110}, {27523, 31859}, {30167, 32922}


X(33829) =  X(2)X(3)∩X(69)X(24364)

Barycentrics    a^4 - a^3*b - a^2*b^2 - a*b^3 - b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a^2*c^2 + a*b*c^2 + b^2*c^2 - a*c^3 - b*c^3 - c^4 : :

As a point on the Euler line, X(33829) has Shinagawa coefficients ((E+F)2+S2+2(E+F)$bc$-2abc$a$,-4S2).

X(33829) lies on these lines: {2, 3}, {69, 24364}, {3336, 30165}, {4429, 6645}, {17889, 27954}, {20077, 20158}, {25270, 33102}, {26079, 27162}


X(33830) =  X(1)X(24602)∩X(2)X(3)

Barycentrics    a^4 - a^3*b - a^2*b^2 - a*b^3 - a^3*c - b^3*c - a^2*c^2 - a*c^3 - b*c^3 : :

As a point on the Euler line, X(33830) has Shinagawa coefficients (2S2+2(E+F)$bc$-abc$a$,-2S2).

X(33830) lies on these lines: {1, 24602}, {2, 3}, {6, 27162}, {35, 30110}, {36, 30107}, {55, 27097}, {56, 26965}, {100, 27248}, {183, 26978}, {187, 25497}, {325, 26085}, {386, 29473}, {1001, 27169}, {1193, 24586}, {1975, 27040}, {2271, 30941}, {2975, 27299}, {3670, 30108}, {3673, 26279}, {3891, 30167}, {3933, 17007}, {4267, 27185}, {4413, 27026}, {4429, 27323}, {4660, 30062}, {4680, 30170}, {5013, 27109}, {5264, 30106}, {5275, 16705}, {5278, 24598}, {5687, 26759}, {5902, 30127}, {5903, 30132}, {7750, 26099}, {7754, 18600}, {7836, 16991}, {10448, 29968}, {11509, 28777}, {12514, 26689}, {16788, 24170}, {16822, 24443}, {17030, 24596}, {17034, 24614}, {17738, 25591}, {18755, 30945}, {26590, 28734}, {26770, 31859}, {27283, 27306}


X(33831) =  X(2)X(3)∩X(148)X(27040)

Barycentrics    a^4 - a^3*b - a^2*b^2 - a*b^3 - b^4 - a^3*c - b^3*c - a^2*c^2 + b^2*c^2 - a*c^3 - b*c^3 - c^4 : :

As a point on the Euler line, X(33831) has Shinagawa coefficients ((E+F)2+S2+2(E+F)$bc$-abc$a$,-4S2).

X(33831) lies on these lines: {2, 3}, {148, 27040}, {194, 26085}, {1975, 16991}, {2896, 26978}, {3053, 17003}, {3120, 27954}, {3585, 27324}, {4972, 6645}, {6292, 29479}, {6650, 17164}, {6653, 26759}, {7779, 18600}, {7785, 27162}, {7802, 25497}, {7898, 26099}, {16705, 26079}, {17007, 20081}, {17752, 32948}, {21287, 25470}, {24248, 25270}, {24366, 33295}


X(33832) =  X(2)X(3)∩X(86)X(7823)

Barycentrics    a^4 - a^3*b - a^2*b^2 - a*b^3 - b^4 - a^3*c - a^2*b*c - a*b^2*c - b^3*c - a^2*c^2 - a*b*c^2 + b^2*c^2 - a*c^3 - b*c^3 - c^4 : :

As a point on the Euler line, X(33832) has Shinagawa coefficients ((E+F)2+S2+2(E+F)$bc$,-4S2).

X(33832) lies on these lines: {2, 3}, {86, 7823}, {191, 30165}, {484, 30164}, {1213, 32819}, {1654, 20081}, {1655, 26085}, {1975, 31090}, {3944, 27954}, {4352, 7779}, {4660, 17752}, {5224, 17128}, {6645, 32773}, {7759, 16712}, {7864, 17277}, {7891, 30761}, {7928, 17234}, {7929, 17300}, {9598, 17280}, {17379, 20088}, {17738, 30177}, {25270, 33100}


X(33833) =  X(1)X(3836)∩X(2)X(3)

Barycentrics    a^3*b + a^2*b^2 + a*b^3 + b^4 + a^3*c - a^2*b*c - a*b^2*c + b^3*c + a^2*c^2 - a*b*c^2 + a*c^3 + b*c^3 + c^4 : :

As a point on the Euler line, X(33833) has Shinagawa coefficients ((E+F)2+(E+F)$bc$-abc$a$,-S2).

X(33833) lies on these lines: {1, 3836}, {2, 3}, {8, 30614}, {10, 982}, {11, 25492}, {36, 19846}, {72, 3662}, {75, 24204}, {88, 9780}, {141, 9534}, {274, 4283}, {277, 1257}, {312, 23537}, {341, 18739}, {386, 18134}, {387, 18141}, {496, 26093}, {614, 5015}, {936, 24781}, {975, 19786}, {976, 33123}, {978, 2887}, {986, 24169}, {1043, 17283}, {1104, 17356}, {1125, 32773}, {1193, 25957}, {1330, 4383}, {1468, 29850}, {1698, 4438}, {1714, 14829}, {1724, 17352}, {1770, 4676}, {2292, 33125}, {2886, 25914}, {3120, 25591}, {3210, 3695}, {3216, 4417}, {3338, 33121}, {3454, 5233}, {3616, 4972}, {3618, 4340}, {3702, 33131}, {3811, 33124}, {3826, 19853}, {3876, 17184}, {3915, 32948}, {3927, 26840}, {3944, 25079}, {3976, 29673}, {4011, 24851}, {4255, 25650}, {4292, 17353}, {4385, 23536}, {4420, 33122}, {4645, 16466}, {4648, 19766}, {4751, 19857}, {4968, 29679}, {5009, 17381}, {5044, 27184}, {5263, 19836}, {5293, 26128}, {5300, 7191}, {5484, 9708}, {5791, 24627}, {5815, 26047}, {6646, 15650}, {7283, 17279}, {7354, 25992}, {7741, 19847}, {9709, 26073}, {11680, 26094}, {12514, 33068}, {15048, 27523}, {16735, 24598}, {16752, 32782}, {16817, 17278}, {17232, 20018}, {17733, 33132}, {17757, 26029}, {18139, 19767}, {23542, 27383}, {24170, 33298}, {25760, 27627}, {25958, 27625}, {25960, 28257}, {26561, 27299}, {26582, 27248}, {27318, 31090}, {27680, 32784}, {31339, 32781}

X(33833) = complement of X(17697)


X(33834) =  X(2)X(3)∩X(76)X(31090)

Barycentrics    a^3*b + a*b^3 + b^4 + a^3*c + a^2*b*c + a*b^2*c + b^3*c + a*b*c^2 - b^2*c^2 + a*c^3 + b*c^3 + c^4 : :

As a point on the Euler line, X(33834) has Shinagawa coefficients ((E+F)2-S2+2(E+F)$bc$,-2S2).

X(33834) lies on these lines: {2, 3}, {76, 31090}, {86, 7785}, {1654, 17129}, {1698, 17738}, {3454, 17034}, {3662, 17048}, {3814, 27324}, {3846, 16827}, {4352, 7906}, {4680, 30138}, {4894, 30141}, {4972, 26752}, {5224, 31276}, {5692, 30165}, {5903, 30164}, {7764, 16712}, {7773, 15668}, {7797, 17277}, {7836, 30761}, {7851, 17259}, {7920, 17349}, {7921, 17379}, {7938, 17234}, {7939, 17300}, {7946, 17378}, {16991, 18135}, {16997, 26085}, {17033, 25760}, {17046, 17291}, {20486, 32773}, {24995, 31004}, {25639, 27274}, {30174, 31237}


X(33835) =  X(2)X(3)∩X(86)X(7797)

Barycentrics    a^3*b + a*b^3 - b^4 + a^3*c + a^2*b*c + a*b^2*c + b^3*c + a*b*c^2 + b^2*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33835) has Shinagawa coefficients ((E+F)2-S2-2(E+F)$bc$,-2S2).

X(33835) lies on these lines: {2, 3}, {86, 7797}, {626, 31090}, {894, 17046}, {1654, 7939}, {2896, 26244}, {5224, 7938}, {5902, 30150}, {7765, 16712}, {7773, 17259}, {7785, 17277}, {7832, 24275}, {7851, 15668}, {7920, 17379}, {7921, 17349}, {7946, 17346}, {16998, 26099}, {17129, 17300}, {17234, 31276}, {26807, 31058}, {30175, 30837}


X(33836) =  X(2)X(3)∩X(385)X(26099)

Barycentrics    a^3*b + a*b^3 - b^4 + a^3*c + b^3*c + b^2*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33836) has Shinagawa coefficients ((E+F)2-S2-2(E+F)$bc$+abc$a$,-2S2).

X(33836) lies on these lines: {2, 3}, {385, 26099}, {626, 16991}, {758, 30150}, {1089, 30169}, {3314, 27040}, {3754, 30156}, {6645, 28734}, {7777, 27109}, {7828, 17003}, {7864, 27162}, {7885, 26085}, {7906, 26770}, {7939, 17007}, {17046, 24514}, {30174, 30837}, {30175, 30816}


X(33837) =  X(2)X(3)∩X(5179)X(7187)

Barycentrics    a^3*b + a*b^3 - b^4 + a^3*c - a^2*b*c - a*b^2*c + b^3*c - a*b*c^2 + b^2*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33837) has Shinagawa coefficients ((E+F)2-S2-2(E+F)$bc$+2abc$a$,-2S2).

X(33837) lies on these lines: {2, 3}, {5179, 7187}, {5692, 30150}, {5903, 30156}, {7906, 27523}, {16997, 26099}, {18134, 30863}, {18140, 25683}, {20138, 25446}, {24045, 24190}, {26687, 30825}, {30174, 30816}


X(33838) =  X(2)X(3)∩X(9)X(4911)

Barycentrics    a^3*b - a^2*b^2 + a*b^3 - b^4 + a^3*c + a^2*b*c + a*b^2*c + b^3*c - a^2*c^2 + a*b*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33838) has Shinagawa coefficients ((E+F)2-(E+F)$bc$,-S2).

X(33838) lies on these lines: {2, 3}, {9, 4911}, {76, 17234}, {83, 17352}, {86, 7803}, {142, 3673}, {315, 17277}, {392, 27129}, {1565, 27340}, {1654, 7879}, {3096, 5224}, {3295, 20533}, {3501, 17062}, {3753, 26531}, {3877, 26548}, {3912, 4385}, {4352, 15048}, {4384, 5015}, {4429, 30107}, {4648, 5286}, {5045, 31038}, {5253, 28734}, {5254, 17245}, {5290, 17284}, {5815, 29611}, {7179, 25066}, {7247, 17742}, {7272, 17744}, {7705, 26676}, {7745, 17337}, {7754, 17300}, {7760, 17378}, {7762, 17349}, {7768, 17346}, {7784, 17259}, {7800, 26244}, {7822, 24275}, {7859, 17381}, {7938, 31090}, {13161, 29571}, {16549, 33298}, {16593, 25466}, {16818, 32773}, {17046, 17754}, {17307, 18747}, {18250, 29604}, {25244, 31071}, {25524, 30825}, {26561, 27248}, {26582, 27299}, {26964, 31031}, {27146, 31058}, {27304, 31419}

X(33838) = complement of X(17691)


X(33839) =  X(2)X(3)∩X(6)X(26099)

Barycentrics    a^3*b - a^2*b^2 + a*b^3 - b^4 + a^3*c + b^3*c - a^2*c^2 + a*c^3 + b*c^3 - c^4 : :

As a point on the Euler line, X(33839) has Shinagawa coefficients (2(E+F)2-2(E+F)$bc$+abc$a$,-2S2).

X(33839) lies on these lines: {2, 3}, {6, 26099}, {12, 16593}, {56, 28734}, {116, 16549}, {141, 27040}, {169, 27132}, {171, 29980}, {218, 21285}, {325, 27109}, {355, 26653}, {388, 28740}, {392, 26548}, {496, 26964}, {517, 26526}, {672, 17046}, {750, 30016}, {1228, 18137}, {1319, 28969}, {1334, 17062}, {2899, 29627}, {3476, 28967}, {3600, 28756}, {3619, 18747}, {3701, 3912}, {3732, 26793}, {3753, 26532}, {3820, 27025}, {3871, 20533}, {3877, 27129}, {3889, 31038}, {3933, 26770}, {3948, 18139}, {4766, 29960}, {4904, 20244}, {4972, 30107}, {5088, 27006}, {5179, 26563}, {5252, 28961}, {5253, 30857}, {5254, 26978}, {5290, 30813}, {5433, 28761}, {7179, 25082}, {7264, 21090}, {7784, 26085}, {7834, 25497}, {7879, 17007}, {7932, 17003}, {7938, 16991}, {15048, 18600}, {17181, 26690}, {17234, 18135}, {17245, 26100}, {17337, 26145}, {17353, 24995}, {17614, 26660}, {17619, 26676}, {17717, 29969}, {17757, 27096}, {18134, 28809}, {24390, 31031}, {24582, 25440}, {25237, 31071}, {26561, 27097}, {26590, 26965}, {30051, 33109}, {30086, 33104}


X(33840) =  X(2)X(3)∩X(8)X(26561)

Barycentrics    a^2*b^2 + b^4 - a^2*b*c - a*b^2*c + a^2*c^2 - a*b*c^2 + c^4 : :

As a point on the Euler line, X(33840) has Shinagawa coefficients (2(E+F)2-abc$a$,-2S2).

X(33840) lies on these lines: {2, 3}, {8, 26561}, {214, 30120}, {239, 5300}, {274, 3096}, {978, 4766}, {1180, 16735}, {1441, 31360}, {1655, 7864}, {1740, 29990}, {2275, 20541}, {2896, 16998}, {3616, 26590}, {3661, 4968}, {3662, 20880}, {3754, 30124}, {3836, 29966}, {3912, 23536}, {4045, 5283}, {4429, 26965}, {5080, 26687}, {5224, 26035}, {5254, 18135}, {5276, 7803}, {5277, 7834}, {5305, 17001}, {5883, 30119}, {7767, 17002}, {7790, 18140}, {7797, 16997}, {7923, 16999}, {7928, 17000}, {7938, 27318}, {9780, 26558}, {11680, 26959}, {11681, 27091}, {16502, 20553}, {16890, 27005}, {17030, 33108}, {17234, 26978}, {17277, 26085}, {17352, 26079}, {17754, 24995}, {20432, 33146}, {20913, 33172}, {23682, 25957}, {24222, 29697}, {25440, 30104}, {25760, 29991}, {25779, 25857}, {25961, 29968}, {30149, 33089}, {30173, 32862}

X(33840) = complement of X(16920)
X(33840) = anticomplement of X(17540)


X(33841) =  X(2)X(3)∩X(12)X(26582)

Barycentrics    -b^4 + a^2*b*c + a*b^2*c + a*b*c^2 + b^2*c^2 - c^4 : :

As a point on the Euler line, X(33841) has Shinagawa coefficients ((E+F)2-S2-abc$a$,-2S2).

X(33841) lies on these lines: {2, 3}, {12, 26582}, {75, 16886}, {115, 18140}, {141, 23897}, {274, 626}, {315, 16998}, {894, 24995}, {1089, 30173}, {1441, 9229}, {1655, 5254}, {1909, 20541}, {2886, 26561}, {3767, 16997}, {3822, 27020}, {3841, 16819}, {3871, 6653}, {3925, 26558}, {4766, 16827}, {4968, 30179}, {5275, 7851}, {5276, 7797}, {5277, 7828}, {5283, 7790}, {7784, 16992}, {7861, 16589}, {7885, 17000}, {7893, 17002}, {7912, 27318}, {7929, 16996}, {7951, 27091}, {10895, 26687}, {16889, 16890}, {17751, 31041}, {20132, 26131}, {21241, 30038}, {24160, 30113}, {25248, 27690}, {25466, 26590}, {25639, 26959}, {26035, 31090}

X(33841) = complement of X(17692)


X(33842) =  X(4)X(39)∩X(6)X(3531)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 6*b^2*c^2 - c^4) : :

X(33842) lies on these lines: {4, 39}, {6, 3531}, {24, 15513}, {25, 187}, {32, 1598}, {51, 3331}, {53, 115}, {112, 10985}, {216, 381}, {235, 27371}, {264, 9466}, {297, 7853}, {317, 7845}, {378, 8589}, {382, 22401}, {393, 5309}, {427, 7603}, {428, 14537}, {574, 1597}, {577, 18534}, {1194, 7408}, {1196, 6995}, {1506, 1595}, {1843, 2971}, {1906, 27376}, {1968, 10594}, {1990, 5355}, {2207, 5007}, {3088, 31455}, {3089, 7746}, {3269, 32062}, {3517, 5206}, {3543, 15355}, {3830, 14961}, {3839, 22240}, {4194, 16589}, {4232, 21843}, {5008, 10311}, {6623, 18424}, {6748, 7753}, {6756, 7747}, {7378, 31415}, {7749, 21841}, {7756, 13488}, {10110, 32445}, {10312, 26863}, {11403, 31652}, {12083, 22052}, {13596, 15602}

X(33842) = X(63)-isoconjugate of X(11169)
X(33842) = polar conjugate of isotomic conjugate of X(373)


X(33843) =  X(4)X(39)∩X(6)X(1597)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 - 6*b^2*c^2 - c^4) : :

X(33843) lies on these lines: {3, 10314}, {4, 39}, {5, 22401}, {6, 1597}, {25, 574}, {30, 216}, {32, 1593}, {33, 1015}, {34, 1500}, {51, 3269}, {53, 15048}, {112, 5008}, {115, 427}, {186, 8589}, {187, 378}, {217, 11381}, {235, 1506}, {264, 538}, {297, 4045}, {317, 7761}, {340, 7848}, {381, 14961}, {393, 7739}, {403, 7603}, {458, 3734}, {472, 6772}, {473, 6775}, {475, 16589}, {570, 18494}, {577, 9818}, {754, 27377}, {800, 3087}, {1180, 7409}, {1194, 7378}, {1344, 15166}, {1345, 15167}, {1504, 3093}, {1505, 3092}, {1569, 12131}, {1571, 7713}, {1573, 1861}, {1595, 5254}, {1596, 3815}, {1598, 5013}, {1625, 16194}, {1692, 19124}, {1885, 7747}, {1906, 9698}, {1907, 7765}, {1968, 5007}, {1971, 11430}, {2207, 7772}, {3088, 3767}, {3089, 31401}, {3146, 26216}, {3284, 31861}, {3289, 15030}, {3331, 32062}, {3515, 15515}, {3516, 5206}, {3517, 15815}, {3520, 15513}, {3541, 7746}, {3542, 31455}, {3543, 22240}, {3575, 7756}, {3839, 15355}, {4196, 21838}, {4200, 5283}, {5024, 18535}, {5041, 8743}, {5052, 12294}, {5058, 11473}, {5062, 11474}, {5064, 11648}, {5107, 8541}, {5355, 16318}, {6623, 31415}, {6749, 18907}, {7514, 22052}, {7527, 10313}, {7528, 15075}, {7745, 13488}, {7798, 9308}, {7804, 15014}, {8588, 11410}, {9651, 11392}, {9664, 11393}, {10312, 14865}, {10594, 31652}, {11109, 24275}, {11398, 31451}, {13474, 32445}, {13509, 15033}, {14901, 15472}, {28710, 32826}

X(33843) = polar conjugate of isotomic conjugate of X(5650)


X(33844) =  X(3)X(6)∩X(36)X(674)

Barycentrics    a^2*(a^4 + a^2*b^2 - 2*b^4 + a^2*b*c + a*b^2*c + a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - 2*c^4) : :

X(33844) lies on these lines: {3, 6}, {36, 674}, {46, 16496}, {100, 518}, {141, 11112}, {209, 7293}, {377, 3619}, {692, 3792}, {753, 813}, {902, 16796}, {1055, 1818}, {1428, 9047}, {2194, 6636}, {3220, 5526}, {3612, 16491}, {3620, 4190}, {3662, 5263}, {3763, 17528}, {3917, 5347}, {4299, 12587}, {5279, 5784}, {5820, 6955}, {5846, 10609}, {16376, 17139}, {28838, 32722}


X(33845) =  X(1)X(6)∩X(100)X(2726)

Barycentrics    a*(a^4*b - a^2*b^3 + a^4*c - 2*a^3*b*c + a^2*b^2*c + a^2*b*c^2 + 4*a*b^2*c^2 - 2*b^3*c^2 - a^2*c^3 - 2*b^2*c^3) : :

X(33845) lies on these lines: {1, 6}, {100, 2726}, {104, 898}, {344, 5657}, {667, 900}, {1145, 3932}, {1284, 3911}, {1402, 4011}, {2223, 4432}, {2932, 20872}, {3912, 15507}, {3967, 18613}, {4413, 30818}, {4557, 4702}, {5744, 30947}, {17613, 33811}, {23853, 30568}, {26093, 27334}, {28978, 31395}


X(33846) =  X(1)X(88)∩X(902)X(20470)

Barycentrics    a^2*(a^3*b - a^2*b^2 - 2*a*b^3 + a^3*c + 2*a^2*b*c - a*b^2*c - 2*b^3*c - a^2*c^2 - a*b*c^2 + 8*b^2*c^2 - 2*a*c^3 - 2*b*c^3) : :

X(33846) lies on these lines: {1, 88}, {902, 20470}, {4257, 19245}, {9350, 14829}, {19998, 32919}


X(33847) =  X(1)X(5132)∩X(100)X(16574)

Barycentrics    a*(3*a^5*b^2 + a^4*b^3 - 3*a^3*b^4 - a^2*b^5 + 6*a^5*b*c + 3*a^4*b^2*c - 4*a^3*b^3*c - 3*a^2*b^4*c - 2*a*b^5*c + 3*a^5*c^2 + 3*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^3*b*c^3 - 4*a^2*b^2*c^3 + 2*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) : :

X(33847) lies on these lines: {1, 5132}, {100, 16574}, {579, 3588}


X(33848) =  X(3)X(8)∩X(6)X(109)

Barycentrics    a^2*(a^6*b - a^5*b^2 - 2*a^4*b^3 + 2*a^3*b^4 + a^2*b^5 - a*b^6 + a^6*c - 2*a^5*b*c + 5*a^4*b^2*c - 5*a^2*b^4*c + 2*a*b^5*c - b^6*c - a^5*c^2 + 5*a^4*b*c^2 - 12*a^3*b^2*c^2 + 6*a^2*b^3*c^2 + 5*a*b^4*c^2 - 3*b^5*c^2 - 2*a^4*c^3 + 6*a^2*b^2*c^3 - 12*a*b^3*c^3 + 4*b^4*c^3 + 2*a^3*c^4 - 5*a^2*b*c^4 + 5*a*b^2*c^4 + 4*b^3*c^4 + a^2*c^5 + 2*a*b*c^5 - 3*b^2*c^5 - a*c^6 - b*c^6) : :

X(33848) lies on these lines: {3, 8}, {6, 109}, {1155, 22313}, {3911, 20470}, {16560, 23981}


X(33849) =  X(2)X(3)∩X(8)X(26264)

Barycentrics    a*(a^5 - a*b^4 + a^3*b*c - a^2*b^2*c - a*b^3*c + b^4*c - a^2*b*c^2 + 4*a*b^2*c^2 - b^3*c^2 - a*b*c^3 - b^2*c^3 - a*c^4 + b*c^4) : :

As a point on the Euler line, X(33849) has Shinagawa coefficients ((E-2F)S2-$bc$S2+$bcSBSC$, 2(E+F)S2).

X(33849) lies on these lines: {2, 3}, {8, 26264}, {11, 20989}, {19, 9817}, {36, 5121}, {43, 2187}, {51, 81}, {100, 2726}, {105, 2006}, {108, 1465}, {154, 4383}, {184, 32911}, {197, 497}, {499, 8185}, {612, 1697}, {614, 1420}, {651, 26884}, {3737, 5053}, {667, 10006}, {908, 27401}, {940, 17810}, {953, 9058}, {1155, 1633}, {1350, 25934}, {1473, 5435}, {1486, 5218}, {1503, 26005}, {1610, 1837}, {1788, 3556}, {1828, 4296}, {1936, 2183}, {2051, 17188}, {2328, 21363}, {2728, 8074}, {2734, 9107}, {3006, 26262}, {3035, 20872}, {3085, 11365}, {3086, 9798}, {3220, 3911}, {3271, 5061}, {3452, 5285}, {3920, 9957}, {4266, 5276}, {5126, 7292}, {5432, 20988}, {5739, 14826}, {5744, 24320}, {6223, 26927}, {7080, 12410}, {7081, 23528}, {7085, 18228}, {7191, 24928}, {7288, 22654}, {7677, 20999}, {8192, 14986}, {9364, 9365}, {10046, 10321}, {11502, 15494}, {14997, 26864}, {17074, 26892}, {17987, 23978}, {20368, 25938}


X(33850) =  X(25)X(15300)∩X(574)X(21448)

Barycentrics    a^2*(a^8 - 10*a^6*b^2 + 10*a^2*b^6 - b^8 - 10*a^6*c^2 + 120*a^4*b^2*c^2 - 138*a^2*b^4*c^2 - 4*b^6*c^2 - 138*a^2*b^2*c^4 + 138*b^4*c^4 + 10*a^2*c^6 - 4*b^2*c^6 - c^8) : :

X(33850) lies on the cubic K1117 and these lines: {25, 15300}, {574, 21448}, {1350, 9027}


X(33851) =  X(3)X(2854)∩X(6)X(15035)

Barycentrics    a^2*(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 - 6*a^6*b^2*c^2 + 13*a^4*b^4*c^2 - 8*a^2*b^6*c^2 + 2*b^8*c^2 - 6*a^6*c^4 + 13*a^4*b^2*c^4 - 8*a^2*b^4*c^4 + b^6*c^4 + 4*a^4*c^6 - 8*a^2*b^2*c^6 + b^4*c^6 + 4*a^2*c^8 + 2*b^2*c^8 - 3*c^10) : :

X(33851) lies on these lines: {3, 2854}, {6, 15035}, {20, 14982}, {22, 110}, {67, 10519}, {69, 32233}, {74, 2930}, {113, 29181}, {141, 17702}, {159, 11820}, {182, 12893}, {265, 6698}, {376, 5648}, {511, 1511}, {524, 32110}, {542, 8703}, {895, 5085}, {1351, 15040}, {1352, 12121}, {1503, 5181}, {1539, 29317}, {2420, 28343}, {2780, 11616}, {2836, 11709}, {3098, 5663}, {3523, 25320}, {3631, 32275}, {3763, 14644}, {3917, 32235}, {5480, 5972}, {5622, 15036}, {5642, 15448}, {6699, 21167}, {7464, 12367}, {8705, 10564}, {9970, 32609}, {9976, 17508}, {10113, 24206}, {10272, 32271}, {10516, 10733}, {10752, 15034}, {11430, 12039}, {11454, 15069}, {11477, 15020}, {12099, 22112}, {14643, 31670}, {14805, 32154}, {15041, 32254}, {15055, 16010}, {20304, 32273}, {20772, 32237}


X(33852) =  X(2)X(51)∩X(21)X(5482)

Barycentrics    a*(a^3*b^2 - a*b^4 - a^3*b*c + a^2*b^2*c + a*b^3*c - b^4*c + a^3*c^2 + a^2*b*c^2 - 3*a*b^2*c^2 + b^3*c^2 + a*b*c^3 + b^2*c^3 - a*c^4 - b*c^4) : :

X(33852) lies on these lines: {2, 51}, {21, 5482}, {404, 18465}, {517, 4881}, {940, 5096}, {1216, 6952}, {1370, 18141}, {1401, 33153}, {1764, 4210}, {1993, 16434}, {1995, 25934}, {3784, 31053}, {3937, 17484}, {4188, 10441}, {5012, 19649}, {5303, 22299}, {5447, 6853}, {5562, 6972}, {5752, 17566}, {5889, 6891}, {5905, 26910}, {6833, 11444}, {6847, 15056}, {6862, 7999}, {6888, 11793}, {6890, 12111}, {6926, 10574}, {6949, 10625}, {6958, 11412}, {6960, 15644}, {6967, 15043}, {7191, 20359}, {9013, 17297}, {17531, 18180}, {26892, 27131}

X(33852) = anticomplement of isotomic conjugate of polar conjugate of X(33853)


X(33853) =  X(4)X(39)∩X(32)X(4186)

Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^3*b^2 - a*b^4 + 2*a^3*b*c - 2*a^2*b^2*c - 2*a*b^3*c + 2*b^4*c + a^3*c^2 - 2*a^2*b*c^2 + 6*a*b^2*c^2 - 2*b^3*c^2 - 2*a*b*c^3 - 2*b^2*c^3 - a*c^4 + 2*b*c^4) : :

X(33853) lies on these lines: {4, 39}, {32, 4186}, {216, 6929}, {1015, 1877}, {1506, 1883}, {2207, 17516}, {11105, 16589}

X(33853) = polar conjugate of isotomic conjugate of complement of X(33852)


X(33854) =  X(2)X(6)∩X(9)X(38)

Barycentrics    a*(a^3 + a*b^2 - a*b*c - b^2*c + a*c^2 - b*c^2) : :

X(33854) lies on these lines: {1, 1390}, {2, 6}, {8, 16502}, {9, 38}, {10, 5299}, {11, 17737}, {21, 39}, {25, 5120}, {31, 17754}, {32, 404}, {37, 3108}, {41, 978}, {42, 16503}, {43, 2280}, {44, 3290}, {55, 17756}, {76, 17541}, {78, 16780}, {83, 274}, {88, 2243}, {100, 1575}, {105, 238}, {145, 16781}, {149, 21956}, {171, 21764}, {172, 5253}, {187, 13587}, {194, 16916}, {198, 27639}, {213, 16823}, {218, 3487}, {239, 3263}, {244, 3509}, {251, 1333}, {294, 3008}, {315, 33840}, {386, 16783}, {405, 9605}, {427, 1172}, {474, 30435}, {475, 8743}, {519, 16784}, {551, 16785}, {572, 4220}, {573, 19649}, {574, 17549}, {579, 4224}, {583, 1778}, {594, 33090}, {595, 16549}, {612, 1449}, {644, 3230}, {651, 1447}, {5053, 16612}, {894, 26234}, {899, 3684}, {910, 16610}, {976, 16787}, {982, 5282}, {995, 16788}, {1015, 5291}, {1030, 15246}, {1100, 3920}, {1107, 5260}, {1125, 5280}, {1180, 5069}, {1201, 2329}, {1279, 3693}, {1332, 26247}, {1384, 16371}, {1462, 9436}, {1475, 5247}, {1506, 7504}, {1580, 2112}, {1616, 4513}, {1621, 2276}, {1627, 2220}, {1655, 7839}, {1722, 2082}, {1724, 4223}, {1739, 5011}, {1743, 5272}, {1759, 24046}, {1783, 1870}, {1975, 16920}, {2023, 5985}, {2207, 4200}, {2241, 3871}, {2271, 19314}, {2275, 2975}, {2278, 7465}, {2298, 4071}, {2300, 3757}, {2321, 16488}, {2323, 3011}, {2345, 24552}, {2475, 7745}, {2476, 2548}, {2478, 5286}, {2549, 11114}, {3053, 4188}, {3061, 3924}, {3216, 4251}, {3305, 16517}, {3315, 3726}, {3496, 24443}, {3501, 3915}, {3598, 6180}, {3681, 16973}, {3747, 24578}, {3759, 30758}, {3767, 4193}, {3877, 9620}, {3897, 9619}, {3933, 17540}, {3997, 5315}, {4187, 5305}, {4189, 5013}, {4239, 5035}, {4254, 7484}, {4277, 15302}, {4360, 31087}, {4361, 31130}, {4366, 17759}, {4386, 5332}, {4393, 16524}, {4396, 20530}, {4435, 31131}, {5007, 5277}, {5021, 19310}, {5024, 16370}, {5041, 16589}, {5046, 5254}, {5047, 5283}, {5124, 6636}, {5154, 13881}, {5250, 9593}, {5259, 25092}, {5266, 25068}, {5268, 16667}, {5279, 20227}, {5297, 16666}, {5475, 17577}, {5540, 16546}, {5706, 7407}, {5802, 26052}, {5838, 30706}, {5839, 10327}, {6175, 7753}, {6872, 7738}, {6910, 31400}, {6933, 31404}, {7031, 25440}, {7081, 20228}, {7483, 31406}, {7737, 17579}, {7754, 18135}, {7760, 18140}, {7762, 17670}, {7783, 17692}, {7785, 33841}, {7787, 16915}, {7797, 17669}, {7803, 17550}, {7823, 33823}, {7864, 33824}, {7920, 33046}, {8844, 25834}, {9310, 21214}, {9456, 26278}, {9575, 19860}, {9599, 11680}, {11112, 18907}, {11113, 15048}, {11353, 28809}, {11688, 30646}, {13740, 26035}, {13741, 27040}, {14537, 15679}, {15484, 17532}, {15655, 19705}, {15815, 17548}, {15905, 25947}, {16060, 27162}, {16318, 26020}, {16417, 21309}, {16523, 29570}, {16685, 31111}, {16777, 17024}, {16830, 20963}, {16857, 22246}, {16884, 29815}, {16968, 26690}, {17127, 26241}, {17275, 29679}, {17303, 20483}, {17314, 19993}, {17348, 30748}, {17350, 26274}, {17362, 33091}, {17490, 21775}, {17565, 20088}, {17681, 26978}, {17735, 20331}, {20553, 26582}, {20769, 28254}, {21101, 32923}, {21511, 24598}, {21840, 29821}, {25849, 25857}, {26085, 33833}, {26099, 33838}, {27109, 33821}


X(33855) =  MIDPOINT OF X(3) AND X(1138)

Barycentrics    8*S^4-3*(9*R^2*(17*R^2+2*SA-8*SW)-4*SA^2+8*SW^2)*S^2+3*(27*(5*R^2-2*SW)*R^2+4*SW^2)*SB*SC : :
X(33855) = 2*X(1511)+X(11749)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29279.

X(33855) lies on these lines: {3, 1138}, {30, 110}, {1511, 11749}, {5663, 18285}, {14677, 32417}, {16168, 31378}

X(33855) = midpoint of X(3) and X(1138)


X(33856) =  MIDPOINT OF X(3) AND X(3065)

Barycentrics    a*(2*a^9-3*(b+c)*a^8-2*(3*b^2-5*b*c+3*c^2)*a^7+2*(b+c)*(5*b^2-6*b*c+5*c^2)*a^6+6*(b^4+c^4-3*(b^2-b*c+c^2)*b*c)*a^5-(b+c)*(12*b^4+12*c^4-(24*b^2-29*b*c+24*c^2)*b*c)*a^4-2*(b^6+c^6-(3*b^2-b*c+3*c^2)*(b^2-b*c+c^2)*b*c)*a^3+3*(b^2-c^2)*(b-c)*(2*b^4+3*b^2*c^2+2*c^4)*a^2+2*(b^2-c^2)^2*(b-c)^2*b*c*a-(b^2-c^2)^4*(b+c)) : :
Trilinears    (10*sin(A/2)-8*sin(3*A/2)+3*sin(5*A/2))*cos((B-C)/2)+2*(cos(A)-1)*cos(B-C)+2*sin(A)*cos(A/2)*cos(3*(B-C)/2)+cos(3*A) +6*cos(A)-5*cos(2*A) -7/2 : :
X(33856) = 3*X(21)-X(6265), 3*X(191)+X(6264), X(12119)-3*X(28460), X(12247)+3*X(15677)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29279.

X(33856) lies on these lines: {3, 3065}, {5, 26202}, {21, 104}, {80, 3579}, {191, 6264}, {214, 12104}, {517, 1749}, {952, 3647}, {1768, 7489}, {2800, 31649}, {2829, 22798}, {5441, 19914}, {5531, 32613}, {5533, 16142}, {5690, 22937}, {6713, 10021}, {6852, 16128}, {7508, 10176}, {7701, 32612}, {8068, 18977}, {10058, 16141}, {10074, 16140}, {10738, 16113}, {11684, 12737}, {12119, 28460}, {12247, 15677}, {12515, 21669}, {12611, 16617}

X(33856) = midpoint of X(i) and X(j) for these {i,j}: {3, 3065}, {104, 3652}, {5441, 19914}, {10738, 16113}, {11684, 12737}, {12515, 21669}
X(33856) = reflection of X(i) in X(j) for these (i,j): (214, 12104), (12611, 16617)


X(33857) =  X(1)X(30)∩X(21)X(60)

Barycentrics    a*(-a+b+c)*(a^5-(b+c)*a^4-(2*b^2+3*b*c+2*c^2)*a^3+2*(b+c)*(b^2-3*b*c+c^2)*a^2+(b^2-c^2)^2*a-(b^3+c^3)*(b-c)^2) : :
Barycentrics    (24 a R^2-12 b R^2+4 b SB+c SB+b SC+4 c SC-4 a SW+3 b SW)S^2 + 4 R S^3+3 b SB SC^2-3 c SB SC^2-3 b SB SC SW : :
X(33857) = 2*X[3647]-3*X[16370], 4*X[6701]-3*X[17532], X[6938]+X[16116], X[16140]-4*X[24929]

See Antreas Hatzipolakis, Ercole Suppa and César Lozada, Hyacinthos 29287 and Hyacinthos 29288.

X(33857) lies on these lines: {1, 30}, {11, 26725}, {21, 60}, {35, 16139}, {55, 758}, {56, 10122}, {65, 3651}, {78, 18253}, {104, 33667}, {191, 3601}, {200, 21677}, {354, 18444}, {390, 17482}, {442, 1837}, {950, 11263}, {958, 31938}, {997, 15670}, {1479, 33592}, {1697, 16126}, {1749, 7508}, {2475, 3486}, {2771, 10058}, {3057, 3957}, {3065, 5424}, {3255, 6596}, {3576, 5427}, {3584, 12738}, {3612, 5428}, {3647, 16370}, {3652, 5693}, {3671, 10123}, {3746, 14988}, {3962, 4640}, {4305, 18977}, {4313, 14450}, {4666, 11281}, {5426, 13384}, {5698, 15677}, {5919, 10698}, {6701, 17532}, {6841, 11375}, {6938, 16116}, {7680, 17718}, {10572, 14526}, {10738, 33593}, {10950, 31419}, {11604, 12743}, {12635, 20835}, {12688, 21669}, {12740, 14100}, {15726, 16133}, {17606, 31254}, {17728, 18443}

X(33857) = midpoint of X(i) and X(j) for these {i,j}: {5441, 16152}, {6938, 16116}
X(33857) = reflection of X(i) in X(j) for these (i,j): (1836, 3649), (3652, 6914), (11684, 4640), (17637, 10391)
X(33857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 16132, 3649), (21, 17637, 16141), (2646, 17637, 21)


X(33858) =  X(1)X(30)∩X(3)X(758)

Barycentrics    a*(a^6-(b+c)*(2*a^2-4*b^2+5*b*c-4*c^2)*a^3-(b^2-b*c+c^2)*a^4-(b^4-4*b^2*c^2+c^4)*a^2-(b^2-c^2)*(b-c)*((2*b^2-b*c+2*c^2)*a-b^3-c^3)) : :
Barycentrics    (20 a R^2-20 b R^2+4 b SB-c SB-b SC+4 c SC-4 a SW+5 b SW)S^2 + 4 R S SB SC+5 b SB SC^2-5 c SB SC^2-5 b SB SC SW : :
X(33858) = 2*X[5]-3*X[26725], X[40]+X[16126], X[191]-3*X[3576], X[355]-2*X[442], X[944]+X[2475], X[1482]+X[16117], 5*X[3616]-2*X[22798], 2*X[3647]-X[13465], 3*X[3653]-2*X[15670], 3*X[5426]-X[7701], X[5690]-2*X[11277], 3*X[5731]+X[14450], 2*X[5901]-X[16160], X[6264]+X[13146], 4*X[6701]-X[18525], 2*X[8261]-3*X[10202], 4*X[9956]-5*X[31254], 2*X[12104]-X[19919], X[15680]+X[16116], 2*X[21677]-3*X[26446], 2*X[26202]-3*X[28461]

See Antreas Hatzipolakis, Ercole Suppa and César Lozada, Hyacinthos 29287 and Hyacinthos 29288.

X(33858) lies on these lines: {1, 30}, {3, 758}, {4, 33592}, {5, 26725}, {10, 12738}, {21, 104}, {35, 11571}, {40, 16126}, {100, 13145}, {140, 6326}, {191, 3576}, {355, 442}, {381, 30143}, {515, 11263}, {517, 3651}, {548, 5538}, {944, 2475}, {952, 5499}, {956, 31938}, {960, 13151}, {991, 29097}, {997, 18253}, {999, 10122}, {1006, 5694}, {1319, 17637}, {1482, 16117}, {1483, 11014}, {2646, 13369}, {3579, 4018}, {3616, 22798}, {3647, 13465}, {3653, 15670}, {3654, 3811}, {3754, 18524}, {3916, 4511}, {3957, 11278}, {4653, 5492}, {5426, 7701}, {5690, 11277}, {5731, 14450}, {5787, 5886}, {5882, 12737}, {5885, 6905}, {5901, 16160}, {6001, 24299}, {6175, 28204}, {6264, 13146}, {6598, 6907}, {6675, 8583}, {6701, 18525}, {6853, 9803}, {6912, 31828}, {6914, 15071}, {6924, 15016}, {6940, 22935}, {7489, 31803}, {7986, 19765}, {8261, 10202}, {9856, 15178}, {9943, 33596}, {9956, 31254}, {10052, 16142}, {10074, 33667}, {10246, 12114}, {10572, 13273}, {10902, 14988}, {11012, 24475}, {12104, 19919}, {12608, 33594}, {12709, 24929}, {12740, 30538}, {15680, 16116}, {15911, 28186}, {16113, 30264}, {16120, 30283}, {16133, 30284}, {16141, 21842}, {16146, 18448}, {16147, 18456}, {16151, 18454}, {21677, 26446}, {24680, 33557}, {26202, 28461}, {26285, 31660}, {27086, 32612}, {28174, 31651}

X(33858) = midpoint of X(i) and X(j) for these {i,j}: {1, 16132}, {40, 16126}, {944, 2475}, {1482, 16117}, {6264, 13146}, {15680, 16116}, {16159, 18481}
X(33858) = reflection of X(i) in X(j) for these (i,j): (4, 33592), (21, 1385), (79, 33668), (191, 5428), (355, 442), (3652, 21), (5690, 11277), (6841, 11281), (7701, 31649), (11684, 22937), (13465, 3647), (16138, 13743), (16139, 3), (16159, 3649), (16160, 5901), (19919, 12104), (22937, 13624)
X(33858) = X(6288)-of-2nd circumperp triangle
X(33858) = X(10610)-of-hexyl triangle
X(33858) = X(16132)-of-anti-Aquila triangle
X(33858) = X(16139)-of-ABC-X3 reflections triangle
X(33858) = X(22804)-of-excentral triangle
X(33858) = X(33592)-of-anti-Euler triangle
X(33858) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1385, 21740, 6265), (1385, 26201, 104), (3649, 7354, 79)


X(33859) =  X(1)X(22461)∩X(7)X(10266)

Barycentrics    a (a+b-c) (a-b+c) (a^3-a^2 b-a b^2+b^3-a^2 c-a b c+3 b^2 c-a c^2+3 b c^2+c^3) (a^3 b-a^2 b^2-a b^3+b^4+a^3 c+6 a^2 b c+2 a b^2 c-a^2 c^2+2 a b c^2-2 b^2 c^2-a c^3+c^4) : :
X(33859) = 3*X[354]-2*X[18244]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29291.

X(33859) lies on these lines: {1,22461}, {7,10266}, {30,13375}, {65,17643}, {145,12849}, {224,12524}, {354,18244}, {518,12682}, {3174,12660}, {3467,22936}, {3649,12267}, {5586,12409}, {7701,12957}, {10044,13128}, {10052,13129}, {10427,12639}, {10940,13130}, {10941,13131}, {11570,12433}, {13089,14882}, {15481,18259}

X(33859) = reflection of X(10266) in X(12917)


X(33860) =  X(30)X(13100)∩X(2077)X(3651)

Barycentrics    a (a^9-2 a^8 b-2 a^7 b^2+6 a^6 b^3-6 a^4 b^5+2 a^3 b^6+2 a^2 b^7-a b^8-2 a^8 c+6 a^7 b c+2 a^6 b^2 c-11 a^5 b^3 c-a^4 b^4 c+4 a^3 b^5 c+4 a^2 b^6 c+a b^7 c-3 b^8 c-2 a^7 c^2+2 a^6 b c^2+19 a^5 b^2 c^2-3 a^4 b^3 c^2-12 a^3 b^4 c^2-2 a^2 b^5 c^2-5 a b^6 c^2+3 b^7 c^2+6 a^6 c^3-11 a^5 b c^3-3 a^4 b^2 c^3+4 a^3 b^3 c^3-4 a^2 b^4 c^3-a b^5 c^3+9 b^6 c^3-a^4 b c^4-12 a^3 b^2 c^4-4 a^2 b^3 c^4+12 a b^4 c^4-9 b^5 c^4-6 a^4 c^5+4 a^3 b c^5-2 a^2 b^2 c^5-a b^3 c^5-9 b^4 c^5+2 a^3 c^6+4 a^2 b c^6-5 a b^2 c^6+9 b^3 c^6+2 a^2 c^7+a b c^7+3 b^2 c^7-a c^8-3 b c^8) : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29291.

X(33860) lies on these lines: {30,13100}, {2077,3651}, {5441,10106}, {6920,7701}, {9856,15178}, {12255,13743}, {12556,17768}, {16116,22782}


X(33861) =  X(6)X(373)∩X(23)X(33582)

Barycentrics   a^2*(a^8 - 10*a^6*b^2 + 10*a^2*b^6 - b^8 - 10*a^6*c^2 + 72*a^4*b^2*c^2 - 18*a^2*b^4*c^2 + 20*b^6*c^2 - 18*a^2*b^2*c^4 - 102*b^4*c^4 + 10*a^2*c^6 + 20*b^2*c^6 - c^8) : :

X(33861) lies on the cubic K1117 and these lines: {6, 373}, {23, 33582}


X(33862) =  MIDPOINT OF X(3) AND X(35)

Barycentrics    a^2*(2*a^5-2*(b+c)*a^4-2*(2*b^2-b*c+2*c^2)*a^3+(b+c)*(4*b^2-3*b*c+4*c^2)*a^2+2*(b^4+c^4-(b^2-b*c+c^2)*b*c)*a+(b^2-c^2)*(b-c)*(-2*b^2-b*c-2*c^2)) : :
X(33862) = 7*X(3523)+X(20066), 3*X(4995)+X(30264), 3*X(5054)-X(31159), X(5086)-3*X(26446), X(11491)+3*X(17549)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29299.

X(33862) lies on these lines: {1, 3}, {5, 20104}, {10, 7508}, {20, 10599}, {21, 9956}, {24, 1900}, {30, 31659}, {140, 25639}, {182, 9047}, {355, 4189}, {411, 28146}, {549, 3829}, {944, 17548}, {952, 5267}, {960, 22935}, {993, 32141}, {1012, 33697}, {2771, 33597}, {2779, 12041}, {3523, 20066}, {3530, 6713}, {3647, 31835}, {3828, 28463}, {4302, 6863}, {4330, 10738}, {4640, 5694}, {4995, 30264}, {5054, 31159}, {5086, 6875}, {5218, 10526}, {5248, 6924}, {5258, 12331}, {5303, 32900}, {5428, 6684}, {5432, 7491}, {5777, 22936}, {5886, 6942}, {6796, 6914}, {6842, 15338}, {6862, 18407}, {6892, 18517}, {6905, 9955}, {6906, 28160}, {6950, 18481}, {6954, 10525}, {11231, 25440}, {11491, 17549}, {11499, 16370}, {17100, 33598}, {19535, 22758}, {19925, 31649}, {22937, 31837}, {31660, 33595}

X(33862) = midpoint of X(i) and X(j) for these {i,j}: {3, 35}, {6842, 15338}, {11012, 11849}
X(33862) = reflection of X(i) in X(j) for these (i,j): (11011, 15178), (25639, 140), (33281, 1385)
X(33862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 26285, 3579), (1155, 24299, 5885), (3746, 22765, 33179)


X(33863) =  X(3)X(6)∩X(36)X(213)

Barycentrics    a^2*(a^2 + a*b - b^2 + a*c + b*c - c^2) : :

X(33863) lies on these lines: {1, 17735}, {2, 1931}, {3, 6}, {21, 24512}, {31, 2275}, {35, 20963}, {36, 213}, {46, 3959}, {55, 20985}, {56, 292}, {57, 16968}, {86, 33047}, {99, 17034}, {100, 3780}, {141, 16061}, {160, 33722}, {171, 1107}, {172, 672}, {230, 21554}, {238, 16604}, {325, 21993}, {395, 21898}, {396, 21869}, {404, 2238}, {590, 21992}, {593, 8041}, {595, 1015}, {597, 21937}, {615, 21909}, {902, 17474}, {940, 16367}, {975, 31442}, {980, 21981}, {982, 16974}, {988, 16972}, {992, 1778}, {993, 17750}, {999, 14974}, {1014, 28350}, {1078, 17499}, {1412, 2056}, {1468, 2276}, {1473, 21771}, {1475, 1914}, {1500, 24047}, {1575, 5247}, {1724, 19329}, {2200, 7113}, {2242, 3730}, {2251, 17745}, {2295, 2975}, {2350, 16064}, {2549, 5292}, {2911, 22127}, {3052, 16781}, {3061, 4650}, {3125, 3336}, {3216, 9509}, {3218, 3721}, {3230, 5563}, {3249, 4057}, {3290, 32636}, {3361, 16970}, {3497, 16560}, {3589, 16060}, {3618, 22267}, {3734, 29455}, {3746, 16971}, {3815, 6998}, {3954, 6763}, {4210, 21753}, {4383, 11329}, {4386, 21384}, {4426, 17754}, {4641, 20769}, {4646, 31443}, {4675, 25500}, {4973, 16600}, {5230, 9597}, {5254, 6996}, {5255, 17448}, {5264, 16975}, {5275, 19314}, {5277, 16552}, {5291, 16549}, {5306, 13635}, {5337, 18206}, {5347, 16876}, {5711, 31449}, {7745, 13727}, {7783, 33296}, {8301, 16476}, {8584, 22355}, {9300, 13634}, {9346, 31451}, {9359, 18754}, {9598, 11269}, {11110, 17398}, {13567, 21940}, {14389, 22377}, {14829, 21024}, {15668, 33036}, {16349, 19701}, {16502, 21793}, {16886, 33119}, {16917, 17277}, {16948, 33854}, {17245, 17687}, {17259, 33035}, {17300, 17695}, {17349, 33062}, {17352, 33825}, {17379, 33063}, {17696, 30962}, {17796, 22126}, {19308, 32911}, {21764, 23649}, {21903, 23303}, {21932, 23302}, {21991, 32786}, {23572, 23867}, {24273, 29562}, {24549, 24691}, {27644, 27656}, {30116, 31456}, {30945, 33819}

X(33863) = Brocard-circle-inverse of X(18755)
X(33863) = isogonal conjugate of the isotomic conjugate of X(17300)
X(33863) = isogonal conjugate of the polar conjugate of X(4212)
X(33863) = X(2350)-Ceva conjugate of X(6)
X(33863) = crosspoint of X(4212) and X(17300)
X(33863) = crosssum of X(115) and X(4151)
X(33863) = crossdifference of every pair of points on line {523, 3716}
X(33863) = barycentric product X(i)*X(j) for these {i,j}: {1, 32913}, {3, 4212}, {6, 17300}, {58, 29653}
X(33863) = barycentric quotient X(i)/X(j) for these {i,j}: {4212, 264}, {17300, 76}, {29653, 313}, {32913, 75}
X(33863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 18755}, {3, 5021, 6}, {6, 5023, 4258}, {6, 5124, 5110}, {6, 15815, 4255}, {32, 4253, 6}, {36, 213, 21008}, {39, 58, 6}, {56, 2176, 9259}, {57, 16968, 20271}, {58, 5030, 39}, {573, 5042, 6}, {579, 5019, 6}, {583, 1333, 6}, {999, 14974, 16969}, {2245, 5035, 6}, {2278, 5165, 6}, {4252, 5022, 6}, {4253, 4257, 32}, {4261, 5115, 6}, {4274, 5053, 6}, {4275, 5069, 6}, {16061, 17206, 141}


X(33864) =  ISOTOMIC CONJUGATE OF X(1311)

Barycentrics    a^2*b^2 - b^4 - a*b^2*c + b^3*c + a^2*c^2 - a*b*c^2 + b*c^3 - c^4 : :

X(33864) lies on these lines: {2, 7}, {5, 20880}, {8, 17181}, {42, 24241}, {75, 11680}, {77, 21286}, {78, 21285}, {85, 11681}, {99, 7424}, {100, 4872}, {150, 4511}, {320, 6163}, {325, 523}, {326, 21270}, {348, 3436}, {350, 30993}, {377, 25583}, {404, 4911}, {405, 25581}, {515, 17136}, {529, 7181}, {664, 5176}, {675, 6099}, {857, 25083}, {910, 24582}, {946, 20244}, {958, 27187}, {1018, 5074}, {1111, 3814}, {1193, 24211}, {1210, 20247}, {1229, 21239}, {1329, 3665}, {1565, 17757}, {2887, 30801}, {2975, 17095}, {3061, 26526}, {3212, 25005}, {3673, 4193}, {3674, 24982}, {3684, 24712}, {3701, 3933}, {3705, 31130}, {3825, 7264}, {3869, 33298}, {4056, 25440}, {4384, 5826}, {4438, 30746}, {4920, 24443}, {5080, 5088}, {5121, 24191}, {5253, 7247}, {5300, 7776}, {5552, 17170}, {5804, 7407}, {6691, 7198}, {6735, 21272}, {6872, 25592}, {7146, 26575}, {7176, 20060}, {7223, 11236}, {7289, 27507}, {8728, 25585}, {9310, 26660}, {13161, 18600}, {13407, 17169}, {14011, 16749}, {16603, 26581}, {17001, 17364}, {17046, 33299}, {17062, 26548}, {17081, 20076}, {17198, 30941}, {17211, 24170}, {17451, 26532}, {17671, 25082}, {17672, 25068}, {17742, 28734}, {18589, 27514}, {20248, 20262}, {20930, 30758}, {20940, 20947}, {24172, 28096}, {24471, 24986}, {25066, 33839}, {25681, 30617}, {25760, 30800}, {28391, 30075}, {30767, 33115}

X(33864) = isotomic conjugate of X(1311)
X(33864) = X(i)-isoconjugate of X(j) for these (i,j): {31, 1311}, {650, 32689}
X(33864) = crossdifference of every pair of points on line {32, 663}
X(33864) = barycentric product X(i)*X(j) for these {i,j}: {76, 8679}, {3267, 7463}
X(33864) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1311}, {109, 32689}, {7463, 112}, {8679, 6}
X(33864) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 26229}, {2, 144, 26258}, {2, 329, 26265}, {2, 5905, 26267}, {2, 6646, 26279}, {2, 31071, 142}, {2, 31080, 9}, {2, 31086, 3452}, {2, 31117, 4357}, {2, 31121, 226}, {7, 30740, 2}, {9, 30742, 2}, {57, 30757, 2}, {63, 30782, 2}, {325, 3263, 3006}, {894, 30798, 2}, {908, 9436, 20347}, {1329, 3665, 26563}, {1565, 17757, 30806}


X(33865) =  X(1)X(7)∩X(2)X(1759)

Barycentrics    a^4 + a^3*b - a*b^3 - b^4 + a^3*c + a^2*b*c + a*b^2*c + b^3*c + a*b*c^2 - a*c^3 + b*c^3 - c^4 : :

X(33865) lies on these lines:s {1, 7}, {2, 1759}, {36, 17084}, {46, 7179}, {57, 17181}, {65, 150}, {79, 1111}, {85, 16091}, {171, 4920}, {320, 17762}, {329, 17308}, {517, 7247}, {664, 18990}, {942, 4872}, {1330, 20911}, {1434, 1565}, {1447, 12047}, {1478, 3212}, {1654, 17746}, {1836, 3673}, {1930, 4645}, {2893, 14054}, {3661, 5905}, {3665, 11246}, {3933, 32939}, {3970, 20533}, {4056, 5902}, {5211, 24166}, {5224, 15650}, {5244, 6996}, {5903, 7272}, {6147, 14828}, {6542, 17483}, {7198, 24203}, {9776, 29603}, {10030, 17866}, {10436, 19865}, {14450, 20347}, {16887, 26840}, {17141, 20553}, {17169, 17190}, {17175, 17202}, {17484, 29591}, {17761, 26839}, {20292, 20880}, {24172, 33106}, {26801, 26811}, {29608, 31018}

X(33865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 4295, 17753}, {65, 4911, 150}, {481, 482, 5018}, {1565, 24470, 1434}, {3674, 4292, 5088}


X(33866) =  X(1)X(7)∩X(65)X(4056)

Barycentrics    a^4 + a^3*b - a*b^3 - b^4 + a^3*c + a*b^2*c + b^3*c + a*b*c^2 - a*c^3 + b*c^3 - c^4 : :

X(33866) lies on these lines: {1, 7}, {65, 4056}, {79, 85}, {319, 5904}, {484, 7179}, {517, 7272}, {1111, 1836}, {1447, 18393}, {1565, 11246}, {3212, 3585}, {3336, 17181}, {3661, 17484}, {4084, 21285}, {4799, 24254}, {4872, 5902}, {4911, 5903}, {4920, 5264}, {5561, 7261}, {5697, 7247}, {5905, 17294}, {6205, 24318}, {7198, 22791}, {7223, 18541}, {7264, 12699}, {7278, 10404}, {7280, 17084}, {11813, 26229}, {16566, 17368}, {17308, 31018}, {17361, 17762}, {17389, 17483}

X(33866) = crosssum of X(3730) and X(4262)
X(33866) = {X(7),X(5195)}-harmonic conjugate of X(1)


X(33867) =  X(1)X(7)∩X(2)X(3496)

Barycentrics    a^4 + a^3*b - a*b^3 - b^4 + a^3*c - a^2*b*c + a*b^2*c + b^3*c + a*b*c^2 - a*c^3 + b*c^3 - c^4 : :

X(33867) lies on these lines: {1, 7}, {2, 3496}, {3, 17084}, {4, 3212}, {8, 315}, {40, 7179}, {46, 17181}, {65, 4872}, {69, 17762}, {76, 30660}, {85, 1836}, {149, 20247}, {150, 4056}, {304, 4645}, {329, 3661}, {348, 3474}, {517, 4911}, {664, 7354}, {946, 1447}, {1155, 17095}, {1334, 26790}, {1434, 11246}, {1902, 7282}, {2112, 4209}, {2795, 14450}, {2898, 14256}, {3057, 7247}, {3649, 14828}, {3673, 12699}, {4388, 20911}, {4920, 5255}, {5057, 26563}, {5697, 7272}, {5905, 6542}, {6999, 7146}, {7291, 23620}, {7384, 16609}, {7747, 24281}, {9312, 9579}, {9776, 17397}, {11415, 30946}, {17308, 18228}, {17483, 29588}, {17777, 18066}, {18600, 33102}, {20060, 21272}, {20295, 21132}, {20535, 24247}, {22791, 24203}, {24280, 32830}, {26062, 30740}, {29591, 31018}

X(33867) = anticomplement of X(3496)
X(33867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {315, 24282, 8}, {4056, 5903, 150}, {4295, 17170, 7}
X(33867) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3497, 8}, {7224, 69}, {18836, 315}
X(33867) = barycentric product X(7)*X(27547)
X(33867) = barycentric quotient X(27547)/X(8)


X(33868) =  X(1)X(7)∩X(36)X(4920)

Barycentrics    a^4 - a^2*b^2 - a*b^3 - b^4 + a^2*b*c + b^3*c - a^2*c^2 - a*c^3 + b*c^3 - c^4 : :

X(3368) lies on these lines: {1, 7}, {36, 4920}, {982, 4056}, {986, 7272}, {2896, 4440}, {3336, 24211}, {3337, 24241}, {3583, 24172}, {3670, 4911}, {3782, 5337}, {3953, 4872}, {3954, 17276}, {4424, 7247}, {5046, 21208}, {7264, 24851}


X(33869) =  X(1)X(7)∩X(3)X(4920)

Barycentrics    a^4 - a^2*b^2 - a*b^3 - b^4 + b^3*c - a^2*c^2 - a*c^3 + b*c^3 - c^4 : :

X(33869) lies on these lines: {1, 7}, {3, 4920}, {46, 24211}, {57, 24241}, {69, 726}, {75, 4660}, {712, 7761}, {982, 4872}, {986, 4911}, {1122, 17635}, {1423, 1766}, {1447, 3944}, {1463, 12721}, {1479, 24172}, {2796, 17274}, {3551, 7261}, {3576, 15903}, {3661, 3729}, {3662, 17738}, {3670, 4056}, {3673, 24851}, {3785, 8669}, {3821, 10436}, {3875, 17766}, {3905, 7750}, {3923, 4357}, {3926, 8720}, {4136, 7784}, {4424, 7272}, {4788, 6542}, {7179, 17596}, {7791, 17760}, {7854, 22036}, {9436, 24283}, {10008, 28526}, {10030, 17861}, {12610, 30097}, {14828, 33103}, {17132, 17294}, {17257, 17308}, {17304, 17397}, {20347, 33098}, {21629, 24213}, {29588, 32093}, {30946, 33099}, {31130, 32948}

X(33869) = {X(7),X(24248)}-harmonic conjugate of X(3663)


X(33870) =  X(1)X(7)∩X(35)X(4920)

Barycentrics    a^4 - a^2*b^2 - a*b^3 - b^4 - a^2*b*c + b^3*c - a^2*c^2 - a*c^3 + b*c^3 - c^4 : :

X(33870) lies on these lines: {1, 7}, {35, 4920}, {484, 24211}, {986, 4056}, {1111, 24851}, {3336, 24241}, {3670, 4872}, {4424, 4911}, {4857, 24172}, {7264, 33095}, {17192, 17738}, {17211, 25645}


X(33871) =  X(3)X(6)∩X(112)X(5702)

Barycentrics    a^4*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 10*b^2*c^2 + c^4) : :

X(33871) lies on these lines: {3, 6}, {112, 5702}, {157, 22829}, {160, 33578}, {184, 9407}, {1990, 15048}, {3163, 7739}, {4232, 10311}, {5309, 16310}, {7113, 14827}, {7736, 10314}, {9813, 22143}, {10313, 14930}, {11672, 32740}, {14836, 19220}, {19137, 20794}

X(33871) = isogonal conjugate of the polar conjugate of X(1597)
X(33871) = barycentric product X(i)*X(j) for these {i,j}: {3, 1597}, {32, 32836}
X(33871) = barycentric quotient X(i)/X(j) for these {i,j}: {1597, 264}, {32836, 1502}
X(33871) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 39, 5158}, {6, 571, 13342}, {6, 5063, 32}, {6, 5065, 577}, {32, 5063, 577}, {32, 5065, 5063}, {32, 13342, 13338}, {371, 372, 16836}, {571, 13338, 32}, {15905, 26899, 577}


X(33872) =  X(3)X(6)∩X(231)X(7735)

Barycentrics    a^4*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 8*b^2*c^2 + c^4) : :

X(33872) lies on these lines: {3, 6}, {231, 7735}, {1968, 6749}, {1990, 10301}, {3018, 5304}, {4558, 5032}, {5306, 16310}, {9407, 19136}

X(33872) = barycentric product X(54)*X(14845)
X(33872) = barycentric quotient X(14845)/X(311)
X(33872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32, 5063}, {6, 566, 7772}, {6, 1609, 5421}, {6, 2965, 5065}, {6, 8573, 570}, {6, 11063, 13337}, {6, 13338, 32}, {6, 13345, 571}, {32, 5063, 571}, {32, 13338, 13345}, {1609, 5421, 14806}, {5063, 13345, 32}, {11063, 13337, 574}


X(33873) =  X(2)X(51)∩X(183)X(13240)

Barycentrics    a^2*(a^4*b^4 - a^2*b^6 + a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 + b^4*c^4 - a^2*c^6 - 2*b^2*c^6) : :
X(33873) = X[316] + 2 X[14962],X[9879] - 3 X[14041]

X(33873) lies on these lines: {2, 51}, {183, 13240}, {211, 7899}, {237, 15107}, {251, 1691}, {316, 512}, {385, 6784}, {694, 20977}, {805, 8842}, {1370, 32529}, {1613, 15514}, {2076, 7485}, {2080, 14096}, {2387, 7809}, {2456, 5012}, {2987, 14510}, {3051, 5111}, {3231, 8586}, {3266, 25332}, {3580, 18322}, {4173, 7941}, {5103, 5133}, {5106, 13192}, {5107, 9463}, {5207, 11442}, {6310, 32993}, {6324, 6787}, {7832, 27375}, {7840, 13207}, {7901, 27374}, {9140, 13170}, {9879, 14041}, {10717, 12149}, {13137, 20021}, {14135, 19691}, {14712, 32442}, {22735, 32515}, {32006, 32547}

X(33873) = midpoint of X(7840) and X(13207)
X(33873) = reflection of X(i) in X(j) for these {i,j}: {385, 6784}, {6787, 31173}, {11673, 2}, {14712, 32442} on K794
X(33873) = orthoptic-circle-of-Steiner-inellipe-inverse of X(15819)
X(33873) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(6194)
X(33873) = circumcircle-of-inner-Napoleon-triangle-inverse of X(22715)
X(33873) = circumcircle-of-outer-Napoleon-triangle-inverse of X(22714)
X(33873) = psi-transform of X(7697)
X(33873) = crossdifference of every pair of points on line {3051, 3288}
X(33873) = X(22735)-of-1st-anti-Brocard-triangle
X(33873) = centroid of (degenerate) reflection triangle of 1st anti-Brocard triangle


X(33874) =  X(4)X(39)∩X(32)X(11325)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^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(33874) lies on these lines: {4, 39}, {32, 11325}, {419, 3229}, {512, 1692}, {538, 17984}, {3117, 6620}, {5140, 17980}, {5149, 15014}, {5167, 9419}

X(33874) = barycentric product X(25)*X(32515)
X(33874) = barycentric quotient X(32515)/X(305)


X(33875) =  X(3)X(6)∩X(183)X(30749)

Barycentrics    a^4*(a^2*b^2 + a^2*c^2 - 2*b^2*c^2) : :

X(33875) lies on these lines: {3, 6}, {183, 30749}, {237, 1084}, {308, 17128}, {385, 3266}, {524, 8623}, {669, 688}, {1576, 14602}, {1634, 3229}, {3228, 13586}, {3231, 6786}, {3291, 9149}, {3329, 26257}, {4558, 19599}, {7766, 31088}, {8265, 20775}, {9468, 17938}, {17129, 33769}

X(33875) = isogonal conjugate of the isotomic conjugate of X(3231)
X(33875) = X(32717)-Ceva conjugate of X(9426)
X(33875) = X(1645)-cross conjugate of X(887)
X(33875) = X(i)-isoconjugate of X(j) for these (i,j): {75, 3228}, {561, 729}, {661, 886}, {1577, 9150}, {20948, 32717}
X(33875) = cevapoint of X(887) and X(1645)
X(33875) = crosspoint of X(4590) and X(32717)
X(33875) = crosssum of X(i) and X(j) for these (i,j): {76, 30736}, {3124, 9148}
X(33875) = trilinear pole of line {887, 14406}
X(33875) = crossdifference of every pair of points on line {76, 523}
X(33875) = barycentric product X(i)*X(j) for these {i,j}: {6, 3231}, {31, 2234}, {32, 538}, {99, 887}, {110, 888}, {187, 14609}, {512, 5118}, {669, 23342}, {1501, 30736}, {1576, 9148}, {1645, 4590}, {1976, 6786}, {2205, 30938}, {4577, 14406}
X(33875) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 3228}, {110, 886}, {538, 1502}, {887, 523}, {888, 850}, {1501, 729}, {1576, 9150}, {1645, 115}, {2234, 561}, {3231, 76}, {5118, 670}, {14406, 826}, {14567, 14608}, {14574, 32717}, {14609, 18023}, {23342, 4609}


X(33876) =  X(3)X(8925)∩X(6)X(6784)

Barycentrics    a^2*(4*a^8*b^4 - 5*a^6*b^6 + 2*a^4*b^8 - a^2*b^10 + 7*a^8*b^2*c^2 - 4*a^6*b^4*c^2 - 5*a^4*b^6*c^2 + 4*a^2*b^8*c^2 - 2*b^10*c^2 + 4*a^8*c^4 - 4*a^6*b^2*c^4 - 3*a^4*b^4*c^4 + 3*a^2*b^6*c^4 + 3*b^8*c^4 - 5*a^6*c^6 - 5*a^4*b^2*c^6 + 3*a^2*b^4*c^6 - 2*b^6*c^6 + 2*a^4*c^8 + 4*a^2*b^2*c^8 + 3*b^4*c^8 - a^2*c^10 - 2*b^2*c^10) : :

X(33876) lies on the Thomson-Gibert-Moses hyperbola, the cubic K1119, and on these lines: {3, 8925}, {6, 6784}, {237, 5104}, {263, 694}, {804, 5652}, {1976, 5038}, {5106, 11173}, {5653, 11186}, {5939, 8842}, {6030, 9157}

X(33876) = isogonal conjugate of isotomic conjugate of X(9772)
X(33876) = Thomson-isogonal conjugate of X(11676)
X(33876) = barycentric product X(6)*X(9772)
X(33876) = barycentric quotient X(9772)/X(76)


X(33877) =  X(3)X(8925)∩X(99)X(1350)

Barycentrics    a^2*(a^12*b^4 - 6*a^8*b^8 + 8*a^6*b^10 - 3*a^4*b^12 + a^12*b^2*c^2 + 9*a^10*b^4*c^2 - 14*a^8*b^6*c^2 + 6*a^6*b^8*c^2 + 5*a^4*b^10*c^2 - 7*a^2*b^12*c^2 + a^12*c^4 + 9*a^10*b^2*c^4 - 5*a^8*b^4*c^4 - 2*a^6*b^6*c^4 + a^4*b^8*c^4 + a^2*b^10*c^4 - 5*b^12*c^4 - 14*a^8*b^2*c^6 - 2*a^6*b^4*c^6 - 6*a^4*b^6*c^6 + 6*a^2*b^8*c^6 + 4*b^10*c^6 - 6*a^8*c^8 + 6*a^6*b^2*c^8 + a^4*b^4*c^8 + 6*a^2*b^6*c^8 + 2*b^8*c^8 + 8*a^6*c^10 + 5*a^4*b^2*c^10 + a^2*b^4*c^10 + 4*b^6*c^10 - 3*a^4*c^12 - 7*a^2*b^2*c^12 - 5*b^4*c^12) : :

X(33877) lies on the cubic K1119 and these lines: {3, 8925}, {99, 1350}, {7770, 33537}

X(33877) = reflection of X(8925) in X(3)


X(33878) =  X(3)X(6)∩X(30)X(69)

Barycentrics    a^2*(a^4 + 4*a^2*b^2 - 5*b^4 + 4*a^2*c^2 - 2*b^2*c^2 - 5*c^4) : :
Trilinears    a - 3 R cot ω cos A : :
Trilinears    cos(A - ω) + 5 cos(A + ω) : :
X(33878) = 3 X[3] - 2 X[6],5 X[3] - 4 X[182],11 X[3] - 8 X[575],7 X[3] - 4 X[576],3 X[3] - 4 X[3098],4 X[3] - 3 X[5050],7 X[3] - 6 X[5085],9 X[3] - 8 X[5092],5 X[3] - 3 X[5093],13 X[3] - 8 X[5097],11 X[3] - 6 X[5102],3 X[4] - 5 X[3620],3 X[4] - 4 X[18358],6 X[5] - 7 X[3619],2 X[5] - 3 X[10519],5 X[6] - 6 X[182],11 X[6] - 12 X[575],7 X[6] - 6 X[576],X[6] - 3 X[1350],4 X[6] - 3 X[1351],8 X[6] - 9 X[5050],7 X[6] - 9 X[5085],3 X[6] - 4 X[5092],10 X[6] - 9 X[5093],13 X[6] - 12 X[5097],11 X[6] - 9 X[5102],3 X[20] + X[20080],5 X[69] - 3 X[11180],4 X[140] - 3 X[14853],4 X[141] - 3 X[381],4 X[159] - 3 X[32063],11 X[182] - 10 X[575],7 X[182] - 5 X[576],2 X[182] - 5 X[1350],8 X[182] - 5 X[1351],3 X[182] - 5 X[3098],16 X[182] - 15 X[5050],14 X[182] - 15 X[5085],9 X[182] - 10 X[5092],4 X[182] - 3 X[5093],13 X[182] - 10 X[5097],22 X[182] - 15 X[5102],X[193] - 3 X[376],3 X[381] - 2 X[31670],3 X[382] - 8 X[3631]

The bicentric pairs PU(1), PU(188) and PU(189) lie on an ellipse centered at X(3), with the Brocard axis as its major axis. The tangents to the ellipse at PU(189) intersect at X(33878). (Randy Hutson, August 19, 2019)

X(33878) lies on the cubic K1120 and on these lines: {2, 21850}, {3, 6}, {4, 3620}, {5, 3619}, {20, 3564}, {22, 323}, {23, 6090}, {25, 2979}, {30, 69}, {51, 16419}, {67, 12902}, {74, 3565}, {106, 28528}, {140, 14853}, {141, 381}, {159, 399}, {183, 33706}, {186, 19118}, {193, 376}, {206, 22115}, {378, 12167}, {382, 1352}, {394, 1495}, {517, 1721}, {518, 12702}, {524, 3534}, {541, 32114}, {542, 15681}, {548, 1353}, {549, 3618}, {550, 6776}, {597, 15693}, {599, 3818}, {631, 18583}, {842, 10425}, {895, 12041}, {956, 25304}, {999, 3056}, {1092, 16195}, {1154, 19459}, {1205, 15085}, {1216, 1598}, {1385, 16491}, {1460, 7186}, {1469, 3295}, {1503, 1657}, {1511, 10752}, {1593, 6403}, {1597, 1843}, {1656, 5480}, {1992, 8703}, {1993, 15080}, {2782, 14532}, {2854, 10620}, {2930, 12308}, {2937, 15577}, {3060, 7484}, {3066, 5650}, {3242, 8148}, {3416, 18525}, {3516, 7691}, {3522, 14912}, {3526, 14561}, {3527, 7393}, {3529, 5921}, {3531, 9822}, {3579, 3751}, {3580, 31152}, {3589, 5054}, {3629, 11179}, {3763, 5055}, {3792, 7083}, {3819, 17810}, {3843, 10516}, {3845, 21356}, {3851, 24206}, {3917, 5020}, {4220, 14996}, {5032, 19708}, {5073, 29317}, {5181, 7728}, {5198, 11444}, {5473, 25235}, {5474, 25236}, {5476, 15694}, {5544, 5640}, {5621, 9976}, {5663, 11820}, {5695, 29301}, {5846, 18526}, {5847, 18481}, {5891, 7716}, {5899, 20987}, {5969, 12188}, {6000, 9924}, {6101, 7387}, {6144, 15689}, {6194, 13860}, {6210, 16484}, {6329, 15700}, {6393, 7776}, {6467, 10605}, {6515, 7667}, {6593, 15040}, {6636, 11004}, {6642, 10627}, {6676, 33522}, {6697, 23049}, {6767, 10387}, {6800, 23061}, {7400, 31802}, {7467, 9463}, {7470, 7754}, {7485, 9777}, {7496, 16981}, {7502, 19125}, {7574, 18382}, {7722, 32240}, {7734, 18928}, {7868, 9993}, {7998, 10545}, {8548, 14914}, {8617, 13192}, {8718, 11412}, {9024, 12773}, {9037, 12329}, {9047, 22769}, {9306, 20850}, {9655, 12588}, {9668, 12589}, {9708, 17792}, {9715, 11464}, {9798, 31737}, {9818, 13391}, {9911, 31738}, {9925, 12174}, {9970, 32609}, {10008, 32006}, {10168, 15707}, {10201, 28408}, {10323, 12160}, {10601, 21852}, {10691, 11433}, {10753, 33813}, {10754, 12042}, {10759, 33814}, {10839, 33435}, {10840, 33434}, {11001, 11160}, {11178, 14269}, {11202, 19132}, {11204, 17813}, {11579, 15041}, {11645, 15533}, {12082, 12112}, {12295, 32257}, {12310, 15106}, {12315, 18436}, {12355, 19905}, {12602, 23249}, {13321, 31521}, {13624, 16475}, {13634, 17379}, {13635, 17349}, {13754, 19588}, {14093, 32455}, {14530, 19149}, {14927, 15704}, {14997, 19649}, {15069, 17800}, {15081, 31180}, {15360, 32216}, {15534, 15695}, {15606, 17814}, {15720, 21167}, {15750, 19128}, {15812, 18536}, {15934, 24471}, {15988, 16370}, {16063, 26869}, {16072, 26156}, {17528, 26543}, {17702, 32306}, {17710, 32608}, {17811, 31860}, {17825, 21849}, {18324, 22151}, {18325, 32113}, {18534, 23039}, {18906, 32521}, {19276, 25898}, {19709, 21358}, {21487, 32911}, {21733, 22260}, {21734, 33748}, {21737, 23267}, {22677, 22728}, {32247, 32423}

X(33878) = reflection of X(11477) in X(182)
X(33878) = anticomplement of X(21850)
X(33878) = midpoint of X(i) and X(j) for these {i,j}: {1657, 11898}, {3529, 5921}, {11001, 11160}
X(33878) = reflection of X(i) in X(j) for these {i,j}: {3, 1350}, {6, 3098}, {382, 1352}, {895, 12041}, {1351, 3}, {1353, 548}, {1992, 8703}, {3751, 3579}, {3830, 599}, {6776, 550}, {7728, 5181}, {8148, 3242}, {9301, 5104}, {9970, 33851}, {10752, 1511}, {10753, 33813}, {10754, 12042}, {10759, 33814}, {12294, 1216}, {12295, 32257}, {12308, 2930}, {12355, 19905}, {12902, 67}, {14927, 15704}, {17813, 11204}, {18325, 32113}, {18440, 69}, {18525, 3416}, {18906, 32521}, {22728, 22677}, {31670, 141}
X(33878) = Brocard-circle-inverse of X(12017)
X(33878) = Schoutte-circle-inverse of X(3053)
X(33878) = orthocentroidal-to-ABC similarity image of X(18440)
X(33878) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 12017}, {3, 1160, 12314}, {3, 1161, 12313}, {3, 1351, 5050}, {3, 5093, 182}, {3, 6243, 11432}, {3, 9301, 1384}, {3, 21309, 26316}, {4, 3620, 18358}, {6, 1350, 3098}, {6, 3098, 3}, {6, 5210, 5033}, {6, 12017, 5050}, {15, 16, 3053}, {22, 323, 26864}, {141, 31670, 381}, {182, 11477, 5093}, {182, 31884, 3}, {323, 26864, 3167}, {394, 9909, 8780}, {548, 1353, 25406}, {576, 14810, 5085}, {1350, 11477, 31884}, {1351, 5050, 11482}, {1351, 12017, 6}, {2979, 15107, 15066}, {3581, 18438, 6}, {3763, 19130, 5055}, {3917, 33586, 5020}, {5033, 5107, 6}, {5085, 14810, 3}, {5093, 11477, 1351}, {5864, 14541, 3}, {5865, 14540, 3}, {6200, 6396, 5210}, {6221, 6398, 1384}, {6409, 7690, 3}, {6410, 7692, 3}, {7393, 10263, 3527}, {9732, 9733, 5171}, {9732, 11825, 3}, {9733, 11824, 3}, {9738, 12305, 3}, {9739, 12306, 3}, {9786, 13348, 3}, {9970, 33851, 32609}, {11412, 11414, 12164}, {11477, 31884, 182}, {11485, 11486, 30435}, {12055, 13330, 6}, {13340, 18438, 3313}, {15066, 15107, 25}, {15644, 17834, 3}


X(33879) =  X(2)X(51)∩X(3)X(5888)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 - 9*b^2*c^2 - c^4) : :
X(33879) = 11 X[2] - 2 X[51],5 X[2] - 2 X[373],8 X[2] + X[2979],10 X[2] - X[3060],5 X[2] + 4 X[3819],7 X[2] + 2 X[3917],4 X[2] - X[5640],X[2] + 2 X[5650],13 X[2] - 4 X[5943],17 X[2] - 8 X[6688],2 X[2] + X[7998],25 X[2] - 16 X[10219],7 X[2] - X[11002],14 X[2] - 5 X[11451],11 X[2] - 8 X[12045],X[2] - 4 X[15082],13 X[2] - X[16981],31 X[2] - 4 X[21849],29 X[2] - 2 X[21969],2 X[3] + X[16261],5 X[51] - 11 X[373],16 X[51] + 11 X[2979],20 X[51] - 11 X[3060],5 X[51] + 22 X[3819],7 X[51] + 11 X[3917],8 X[51] - 11 X[5640],X[51] + 11 X[5650],13 X[51] - 22 X[5943],17 X[51] - 44 X[6688],4 X[51] + 11 X[7998],25 X[51] - 88 X[10219],14 X[51] - 11 X[11002],28 X[51] - 55 X[11451],X[51] - 4 X[12045],X[51] - 22 X[15082],26 X[51] - 11 X[16981],31 X[51] - 22 X[21849],29 X[51] - 11 X[21969],32 X[140] - 5 X[10574],8 X[140] + X[11459],8 X[141] + X[15531],16 X[373] + 5 X[2979],4 X[373] - X[3060],X[373] + 2 X[3819],7 X[373] + 5 X[3917],8 X[373] - 5 X[5640],X[373] + 5 X[5650],13 X[373] - 10 X[5943],17 X[373] - 20 X[6688],4 X[373] + 5 X[7998],5 X[373] - 8 X[10219],14 X[373] - 5 X[11002],28 X[373] - 25 X[11451],11 X[373] - 20 X[12045],X[373] - 10 X[15082],26 X[373] - 5 X[16981],31 X[373] - 10 X[21849],29 X[373] - 5 X[21969],8 X[549] + X[15305],X[568] - 10 X[632],2 X[568] + 7 X[7999],4 X[568] - 13 X[15028],10 X[620] - X[27779],5 X[631] + 4 X[10170],25 X[631] + 2 X[12162],20 X[631] + 7 X[15056],10 X[631] - X[15072],20 X[632] + 7 X[7999],40 X[632] - 13 X[15028],5 X[2979] + 4 X[3060],5 X[2979] - 32 X[3819],7 X[2979] - 16 X[3917],X[2979] + 2 X[5640],X[2979] - 16 X[5650],13 X[2979] + 32 X[5943],17 X[2979] + 64 X[6688],X[2979] - 4 X[7998]

X(33879) lies on these lines: {2, 51}, {3, 5888}, {23, 16187}, {39, 8617}, {110, 5085}, {140, 10574}, {141, 15531}, {323, 22112}, {352, 5034}, {549, 15305}, {568, 632}, {620, 27779}, {631, 10170}, {1350, 10545}, {1351, 5643}, {1570, 7708}, {1995, 31884}, {2854, 21358}, {3098, 16042}, {3231, 13331}, {3523, 12279}, {3524, 14915}, {3525, 9730}, {3526, 5889}, {3533, 15043}, {3567, 16239}, {3619, 12272}, {3628, 13340}, {3763, 11188}, {5012, 6090}, {5050, 11422}, {5054, 5663}, {5072, 11592}, {5093, 23061}, {5102, 15019}, {5651, 7496}, {5890, 15694}, {5891, 15702}, {5946, 15723}, {6000, 15708}, {6241, 14869}, {6786, 16986}, {6800, 7484}, {7426, 21167}, {7485, 26881}, {7514, 15035}, {7703, 24206}, {7868, 12093}, {9027, 21356}, {10124, 23039}, {10303, 12111}, {11284, 15107}, {11412, 13363}, {11439, 15717}, {11455, 12100}, {11539, 15045}, {11812, 18435}, {13348, 15022}, {13754, 15709}, {14002, 14810}, {14855, 15719}, {15018, 15520}, {15024, 32142}, {15055, 32620}, {15058, 15720}, {15060, 15701}, {15106, 19123}, {15698, 16194}, {26910, 27065}, {26911, 27003}, {30439, 33417}, {30440, 33416}

X(33879) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3819, 3060}, {2, 3917, 11451}, {2, 5650, 7998}, {2, 7998, 5640}, {373, 3060, 5640}, {373, 5650, 3819}, {631, 10170, 15072}, {632, 7999, 15028}, {5640, 7998, 2979}, {5650, 15082, 2}, {5651, 7496, 15080}, {10170, 15072, 15056}, {11002, 11451, 5640}, {11284, 21766, 15107}


X(33880) =  X(4)X(39)∩X(25)X(8588)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 18*b^2*c^2 - c^4) : :

X(33880) lies on these lines: {4, 39}, {25, 8588}, {216, 3845}, {1384, 18535}, {1598, 5023}, {3853, 22401}, {6781, 10301}, {8589, 13596}

X(33880) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 33842, 33843}, {33842, 33843, 3199}


X(33881) =  X(3)X(6)∩X(5702)X(10311)

Barycentrics    a^4*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 26*b^2*c^2 + c^4) : :

X(33881) lies on these lines: {3, 6}, {5702, 10311}

X(33881) = barycentric product X(32)*X(32874)
X(33881) = barycentric quotient X(32874)/X(1502)
X(33881) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 13342, 5065}, {577, 13338, 32}


X(33882) =  X(3)X(6)∩X(44)X(765)

Barycentrics    a^3*(a^2 + a*b + a*c - 3*b*c) : :

X(33882) lies on these lines: {3, 6}, {44, 765}, {45, 2241}, {172, 16666}, {597, 5337}, {692, 2210}, {1015, 19297}, {1404, 1415}, {1743, 5301}, {2174, 20228}, {2251, 7113}, {3204, 21769}, {3248, 18266}, {3770, 17128}, {4969, 5291}, {7031, 16670}, {8610, 16784}, {11349, 16726}

X(33882) = X(9268)-Ceva conjugate of X(692)
X(33882) =crosspoint of X(i) and X(j) for these (i,j): {1252, 32665}, {9456, 28615}
X(33882) =crosssum of X(i) and X(j) for these (i,j): {1086, 3762}, {4358, 4359}
X(33882) =crossdifference of every pair of points on line {523, 764}
X(33882) =barycentric product X(i)*X(j) for these {i,j}: {31, 17160}, {32, 18145}, {58, 31855}, {100, 4491}, {101, 21385}, {110, 4145}, {692, 21297}, {1783, 23141}, {21606, 32739}
X(33882) =barycentric quotient X(i)/X(j) for these {i,j}: {4145, 850}, {4491, 693}, {17160, 561}, {18145, 1502}, {21385, 3261}, {23141, 15413}, {31855, 313}
X(33882) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32, 5035}, {6, 2220, 1333}, {6, 3285, 5053}, {6, 4251, 4273}, {6, 4254, 4261}, {6, 4289, 5114}, {6, 16946, 2220}, {6, 18755, 5109}, {32, 5035, 1333}, {2220, 5035, 32}


X(33883) =  X(1)X(33848)∩X(3)X(25934)

Barycentrics    a*(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 + a^5*b^2*c + a^4*b^3*c - 4*a^3*b^4*c - 2*a^2*b^5*c + 3*a*b^6*c - b^7*c + a^6*c^2 + a^5*b*c^2 - 10*a^4*b^2*c^2 + 6*a^3*b^3*c^2 + 7*a^2*b^4*c^2 - 7*a*b^5*c^2 + 2*b^6*c^2 - a^5*c^3 + a^4*b*c^3 + 6*a^3*b^2*c^3 - 12*a^2*b^3*c^3 + 5*a*b^4*c^3 + b^5*c^3 - 2*a^4*c^4 - 4*a^3*b*c^4 + 7*a^2*b^2*c^4 + 5*a*b^3*c^4 - 4*b^4*c^4 + 2*a^3*c^5 - 2*a^2*b*c^5 - 7*a*b^2*c^5 + b^3*c^5 + a^2*c^6 + 3*a*b*c^6 + 2*b^2*c^6 - a*c^7 - b*c^7) : :

X(33883) lies on the Thomson-Gibert-Moses hyprbola, the cubic K1122, and on these lines: {1, 33848}, {3, 25934}, {6, 18191}, {37, 7004}, {65, 244}, {110, 33852}, {392, 2800}, {1155, 20470}, {1635, 14414}, {1638, 8677}, {5784, 30818}, {5888, 7465}, {6890, 32605}, {10609, 22306}, {33844, 33849}

X(33883) = Thomson-isogonal conjugate of X(6905)
X(33882) = crosssum of X(1) and X(33848)


X(33884) =  X(2)X(51)∩X(3)X(323)

Barycentrics    a^2*(2*a^2*b^2 - 2*b^4 + 2*a^2*c^2 - 3*b^2*c^2 - 2*c^4) : :
X(33884) = 7 X[2] - 4 X[51],5 X[2] - 4 X[373],X[2] + 2 X[2979],5 X[2] - 2 X[3060],5 X[2] - 8 X[3819],X[2] - 4 X[3917],3 X[2] - 4 X[5650],11 X[2] - 8 X[5943],19 X[2] - 16 X[6688],35 X[2] - 32 X[10219],13 X[2] - 10 X[11451],17 X[2] - 16 X[12045],7 X[2] - 8 X[15082],17 X[2] - 8 X[21849],13 X[2] - 4 X[21969],X[4] + 8 X[10627],X[4] + 2 X[13340],7 X[4] - 16 X[14128],X[4] - 4 X[15067],X[20] + 8 X[1216],X[20] + 2 X[11459],5 X[20] + 4 X[12162],7 X[20] + 2 X[12290],5 X[51] - 7 X[373],2 X[51] + 7 X[2979],10 X[51] - 7 X[3060],5 X[51] - 14 X[3819],X[51] - 7 X[3917],6 X[51] - 7 X[5640],3 X[51] - 7 X[5650],11 X[51] - 14 X[5943],19 X[51] - 28 X[6688],2 X[51] - 7 X[7998],5 X[51] - 8 X[10219],8 X[51] - 7 X[11002],26 X[51] - 35 X[11451],17 X[51] - 28 X[12045],12 X[51] - 7 X[16981],17 X[51] - 14 X[21849],13 X[51] - 7 X[21969],4 X[52] - 13 X[10303],5 X[69] + 4 X[17710],5 X[99] - 2 X[27779],8 X[143] - 17 X[3533],4 X[185] - 13 X[21734],7 X[193] - 16 X[22829],2 X[373] + 5 X[2979],X[373] - 5 X[3917],6 X[373] - 5 X[5640],3 X[373] - 5 X[5650],11 X[373] - 10 X[5943],19 X[373] - 20 X[6688],2 X[373] - 5 X[7998],7 X[373] - 8 X[10219],8 X[373] - 5 X[11002],26 X[373] - 25 X[11451],17 X[373] - 20 X[12045],7 X[373] - 10 X[15082],12 X[373] - 5 X[16981],17 X[373] - 10 X[21849],13 X[373] - 5 X[21969],X[376] + 2 X[23039],2 X[568] - 5 X[631],X[568] + 2 X[6101],5 X[568] - 8 X[12006],5 X[631] + 4 X[6101],25 X[631] - 16 X[12006],4 X[1216] - X[11459],10 X[1216] - X[12162],28 X[1216] - X[12290],5 X[2979] + X[3060],5 X[2979] + 4 X[3819],X[2979] + 2 X[3917],3 X[2979] + X[5640],3 X[2979] + 2 X[5650],11 X[2979] + 4 X[5943],19 X[2979] + 8 X[6688],35 X[2979] + 16 X[10219],4 X[2979] + X[11002],13 X[2979] + 5 X[11451],17 X[2979] + 8 X[12045],7 X[2979] + 4 X[15082],6 X[2979] + X[16981],17 X[2979] + 4 X[21849],13 X[2979] + 2 X[21969],X[3060] - 4 X[3819],X[3060] - 10 X[3917],3 X[3060] - 5 X[5640],3 X[3060] - 10 X[5650],11 X[3060] - 20 X[5943],19 X[3060] - 40 X[6688],X[3060] - 5 X[7998],7 X[3060] - 16 X[10219],4 X[3060] - 5 X[11002],13 X[3060] - 25 X[11451],17 X[3060] - 40 X[12045],7 X[3060] - 20 X[15082],6 X[3060] - 5 X[16981],17 X[3060] - 20 X[21849],13 X[3060] - 10 X[21969]

X(33884) lies on these lines: {2, 51}, {3, 323}, {4, 10627}, {6, 7496}, {20, 1216}, {22, 6090}, {23, 1350}, {52, 10303}, {67, 69}, {99, 11593}, {110, 3098}, {141, 5169}, {143, 3533}, {182, 11004}, {183, 13207}, {185, 21734}, {193, 22829}, {343, 31101}, {376, 5663}, {394, 6636}, {568, 631}, {599, 8705}, {1154, 3524}, {1180, 3787}, {1351, 15018}, {1352, 5189}, {1370, 3410}, {1383, 5104}, {1993, 5085}, {1994, 5050}, {2396, 14907}, {3090, 32142}, {3091, 7999}, {3094, 9463}, {3124, 8617}, {3146, 11444}, {3164, 11794}, {3292, 14810}, {3313, 3620}, {3522, 5562}, {3523, 5447}, {3525, 6243}, {3528, 18436}, {3529, 11591}, {3543, 5891}, {3545, 13391}, {3616, 31737}, {3619, 16776}, {3763, 7570}, {3792, 17126}, {3832, 11793}, {3854, 13598}, {4259, 14996}, {4430, 9049}, {4563, 26233}, {4661, 9026}, {5012, 17508}, {5052, 15302}, {5059, 5907}, {5067, 10263}, {5077, 9879}, {5092, 11422}, {5093, 7484}, {5102, 5422}, {5446, 7486}, {5468, 6031}, {5645, 5888}, {5651, 14002}, {5752, 17572}, {5876, 17538}, {5889, 15606}, {5890, 15692}, {5892, 15721}, {5946, 15702}, {6102, 10299}, {6786, 7897}, {6787, 7898}, {7186, 17127}, {7502, 32609}, {7527, 32620}, {7533, 31670}, {7708, 8586}, {8041, 13331}, {8352, 20326}, {8717, 14094}, {9019, 21356}, {9027, 11160}, {10298, 15035}, {10304, 13754}, {10545, 16187}, {11001, 18435}, {11130, 14538}, {11131, 14539}, {11161, 12149}, {11441, 16661}, {11442, 15108}, {11488, 11624}, {11489, 11626}, {11539, 13321}, {11574, 15531}, {12082, 15052}, {12087, 17814}, {12111, 13348}, {12112, 33532}, {12525, 14041}, {13416, 16051}, {13451, 15703}, {13595, 17811}, {14096, 32447}, {14826, 20062}, {15045, 15708}, {15056, 17578}, {15060, 15682}, {15305, 15683}, {15544, 21843}, {15640, 16194}, {15696, 31834}, {15705, 20791}, {17548, 22076}, {23958, 26893}

X(33884) = midpoint of X(2979) and X(7998)
X(33884) = reflection of X(i) in X(j) for these {i,j}: {2, 7998}, {51, 15082}, {373, 3819}, {3060, 373}, {3543, 16261}, {5640, 5650}, {7998, 3917}, {11002, 2}, {13321, 11539}, {16261, 5891}, {16981, 5640}, {21849, 12045}
X(33884) = complement of X(16981)
X(33884) = anticomplement of X(5640)
X(33884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14853, 7605}, {2, 16981, 5640}, {3, 323, 11003}, {6, 21766, 7496}, {69, 4576, 9464}, {69, 16063, 3448}, {110, 3098, 7492}, {110, 7492, 7712}, {182, 23061, 11004}, {323, 11003, 9716}, {394, 6636, 9544}, {394, 31884, 6800}, {1350, 15066, 23}, {2979, 3917, 2}, {3060, 3819, 2}, {3292, 14810, 15080}, {5447, 11412, 3523}, {5640, 5650, 2}, {5640, 7998, 5650}, {5640, 16981, 11002}, {5651, 15107, 14002}, {5888, 15019, 22112}, {6800, 31884, 6636}, {7999, 10625, 3091}, {10627, 15067, 13340}, {11444, 15644, 3146}, {13340, 15067, 4}, {13416, 18438, 16051}


X(33885) =  X(4)X(39)∩X(25)X(111)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 3*b^2*c^2 - c^4) : :

X(33885) lies on these lines: {4, 39}, {6, 14157}, {24, 5023}, {25, 111}, {30, 15355}, {33, 9331}, {34, 9336}, {53, 403}, {186, 8588}, {216, 3545}, {217, 9781}, {381, 22240}, {546, 26216}, {574, 13596}, {1180, 15484}, {1196, 1285}, {1596, 5523}, {1598, 8743}, {1625, 3060}, {1629, 6529}, {1968, 3518}, {1970, 26882}, {2207, 10312}, {3269, 11455}, {3331, 5890}, {3543, 14961}, {3567, 32445}, {7530, 10313}, {8744, 10311}, {9465, 10301}, {10985, 14581}, {15340, 18390}, {16868, 27371}, {18535, 22246}, {22401, 33703}

X(33885) = polar conjugate of the isotomic of X(5640)
X(33885) = barycentric product X(4)*X(5640)
X(33885) = barycentric quotient X(5640)/X(69)
X(33885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 112, 10986}, {232, 33842, 4}, {2207, 10594, 10312}, {3199, 33842, 232}


X(33886) =  X(3)X(6)∩X(5304)X(20063)

Barycentrics    a^4*(2*a^4 - 4*a^2*b^2 + 2*b^4 - 4*a^2*c^2 - 7*b^2*c^2 + 2*c^4) : :

X(33886) lies on these lines: {3, 6}, {5304, 20063}, {7533, 7735}, {7755, 9220}

X(33886) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 5063, 2965}, {32, 13338, 6}, {32, 13345, 13338}, {566, 5007, 6}


X(33887) =  X(3)X(7712)∩X(64)X(3843)

Barycentrics    a^2*(4*a^8 - 24*a^4*b^4 + 32*a^2*b^6 - 12*b^8 + 51*a^4*b^2*c^2 - 31*a^2*b^4*c^2 - 20*b^6*c^2 - 24*a^4*c^4 - 31*a^2*b^2*c^4 + 64*b^4*c^4 + 32*a^2*c^6 - 20*b^2*c^6 - 12*c^8) : :
X(33887) = 5 X[3] - 4 X[7712],X[3] + 4 X[11738],15 X[3843] - 16 X[15432],5 X[3843] - 4 X[18550],7 X[3851] - 8 X[7703],X[7712] + 5 X[11738],4 X[15432] - 3 X[18550]

X(33887) lies on these lines: {3, 7712}, {64, 3843}, {1350, 11645}, {1351, 9976}, {3167, 12302}, {3830, 9140}, {3851, 7703}, {5055, 11472}, {5070, 33539}, {5073, 12163}, {5646, 15701}, {9914, 13621}, {10117, 16219}, {12307, 17800}, {13093, 32345}, {14926, 15694}, {15689, 33544}


X(33888) =  X(1)X(6651)∩X(2)X(38)

Barycentrics    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 + b^2*c^2 - a*c^3 + b*c^3 : :
X(33888) = 3 X[2] - 4 X[17755],4 X[37] - 5 X[4473],X[335] - 3 X[31349],2 X[673] - 3 X[27484],4 X[1086] - 5 X[4699],8 X[4422] - 7 X[27268],4 X[6651] - 3 X[31308],2 X[6651] - 3 X[31310],2 X[17755] - 3 X[31349]

X(33888) lies on the cubic K323 and these lines: {1, 6651}, {2, 38}, {6, 190}, {8, 6653}, {37, 4473}, {63, 2319}, {75, 1654}, {144, 1278}, {145, 25270}, {239, 726}, {518, 2113}, {536, 17487}, {545, 4740}, {673, 5220}, {740, 20016}, {742, 20072}, {899, 31348}, {903, 17251}, {1086, 4699}, {1655, 17141}, {2108, 27920}, {2786, 21832}, {2796, 29617}, {3121, 28606}, {3151, 20243}, {3212, 21219}, {3617, 31329}, {3634, 31335}, {3666, 21893}, {3807, 20331}, {3993, 29584}, {4422, 17381}, {4437, 17230}, {6763, 30167}, {8301, 27926}, {9451, 27945}, {9780, 31347}, {14621, 32935}, {14839, 20670}, {16593, 29572}, {16614, 27676}, {16815, 27478}, {17027, 32925}, {17034, 24068}, {17147, 21224}, {17327, 27191}, {17379, 24358}, {17449, 30967}, {18061, 27348}, {18787, 25800}, {19308, 24826}, {20142, 32922}, {21226, 25332}, {21272, 31298}, {24080, 29455}, {24817, 29010}, {24841, 27949}, {26582, 29593}, {27480, 32108}, {27495, 29591}, {28582, 29590}

X(33888) = reflection of X(i) in X(j) for these {i,j}: {2, 31349}, {192, 190}, {335, 17755}, {4440, 75}, {6542, 3797}, {31308, 31310}
X(33888) = isogonal conjugate of X(2109)
X(33888) = anticomplement of X(335)
X(33888) = polar conjugate of the isogonal of X(20797)
X(33888) = anticomplementary-isogonal conjugate of X(20553)
X(33888) = X(i)-Ceva conjugate of X(j) for these (i,j): {239, 2}, {726, 192}, {1757, 1654}, {17738, 20533}, {24821, 17487}
X(33888) = X(1)-isoconjugate of X(2109)
X(33888) = crosspoint of X(239) and X(27920)
X(33888) = crossdifference of every pair of points on line {6373, 8632}
X(33888) = barycentric product X(i)*X(j) for these {i,j}: {75, 2108}, {190, 25381}, {264, 20797}, {335, 27920}, {1575, 33679}
X(33888) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 2109}, {2108, 1}, {20797, 3}, {25381, 514}, {27920, 239}, {33679, 32020}
X(33888) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 20553}, {6, 4645}, {31, 6542}, {32, 17759}, {58, 30941}, {100, 21303}, {238, 69}, {239, 6327}, {242, 21270}, {256, 5207}, {350, 315}, {560, 19565}, {659, 150}, {692, 812}, {740, 21287}, {812, 21293}, {825, 30665}, {874, 21304}, {904, 7779}, {1252, 23354}, {1284, 2893}, {1333, 740}, {1415, 2254}, {1428, 7}, {1429, 3434}, {1438, 13576}, {1447, 21285}, {1580, 30660}, {1911, 6653}, {1914, 8}, {1921, 21275}, {1922, 30669}, {2194, 1959}, {2201, 4}, {2210, 2}, {2238, 1330}, {3253, 20561}, {3570, 21301}, {3573, 20295}, {3684, 3436}, {3685, 21286}, {3747, 2895}, {4010, 21294}, {4366, 20554}, {4435, 33650}, {4455, 21221}, {4556, 4155}, {4570, 874}, {5009, 75}, {6654, 20556}, {7104, 17493}, {7122, 30662}, {7193, 4329}, {8299, 20552}, {8300, 20345}, {8632, 149}, {8852, 7261}, {9456, 24715}, {9472, 20353}, {10030, 21280}, {14599, 192}, {14602, 30661}, {18891, 33796}, {18892, 194}, {18894, 17486}, {20663, 20355}, {20769, 1370}, {21832, 3448}, {28615, 32846}, {30940, 17138}, {31905, 20242}, {33295, 17137}
X(33888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 32029, 4366}, {335, 17755, 2}, {335, 31349, 17755}, {984, 31317, 2}, {4366, 32029, 4393}, {24325, 31323, 2}, {24841, 27949, 29570}, {27481, 31314, 31308}


X(33889) =  X(1)X(17741)∩X(2)X(37)

Barycentrics    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 - b^2*c^2 + a*c^3 - b*c^3 : :

X(33889) lies on the cubic K985 and these lines: {1, 17741}, {2, 37}, {31, 983}, {100, 8844}, {183, 17262}, {190, 385}, {256, 756}, {257, 4095}, {325, 3943}, {594, 31090}, {726, 2108}, {740, 4518}, {846, 3971}, {894, 21101}, {1228, 27057}, {1959, 3930}, {2238, 3807}, {2309, 3920}, {2321, 30179}, {3056, 3681}, {3177, 21219}, {3314, 17233}, {3329, 4360}, {3508, 8782}, {3905, 17743}, {3969, 31089}, {4389, 16986}, {4419, 16990}, {4579, 18262}, {4583, 19565}, {4645, 5992}, {4782, 4926}, {5988, 6541}, {6392, 32034}, {7179, 17242}, {7774, 17314}, {7788, 17309}, {7792, 17340}, {7837, 17377}, {7868, 17269}, {7875, 17354}, {10327, 21299}, {11174, 17318}, {15589, 20073}, {16988, 17305}, {17475, 33854}, {17489, 26752}, {17497, 30730}, {17499, 21067}, {17744, 30167}, {17752, 17760}, {20081, 25242}, {20924, 27295}, {21278, 33091}, {26801, 28598}, {28597, 33090}, {29838, 32771}, {29840, 32915}

X(33889) = crosspoint of X(4562) and X(5383)
X(33889) = crosssum of X(6377) and X(8632)
X(33889) = anticomplement of X(33891)
X(33889) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {983, 20345}, {8684, 20295}, {17743, 20554}
X(33889) = X(6)-isoconjugate of X(7166)
X(33889) = barycentric product X(75)*X(3507)
X(33889) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7166}, {3507, 1}


X(33890) =  X(1)X(1281)∩X(2)X(17760)

Barycentrics    (a*b + a*c - b*c)*(b^2 - b*c + c^2) : :
X(33890) = X[76] - 2 X[22036],5 X[3616] - 3 X[7985]

X(33890) lies on the cubic K1032 and these lines: {1, 1281}, {2, 17760}, {8, 726}, {39, 4850}, {43, 3502}, {63, 194}, {75, 257}, {76, 321}, {85, 335}, {190, 17743}, {192, 1423}, {304, 31028}, {385, 3905}, {511, 3868}, {538, 3578}, {696, 4443}, {732, 17363}, {894, 18906}, {982, 7187}, {1655, 27481}, {1916, 7179}, {2292, 17247}, {3061, 10335}, {3094, 3662}, {3123, 21337}, {3124, 27706}, {3314, 4136}, {3616, 7985}, {3705, 3865}, {3729, 17741}, {3759, 32449}, {3934, 29613}, {3981, 23502}, {4357, 30177}, {4568, 27091}, {4642, 4712}, {4920, 5025}, {5145, 5262}, {6376, 21138}, {8620, 28397}, {9055, 24524}, {14839, 14923}, {17027, 20247}, {17033, 17489}, {17244, 21808}, {17248, 27697}, {17292, 31276}, {17368, 24256}, {20338, 21941}, {20590, 29641}, {20880, 26538}, {20893, 24190}, {21129, 30519}, {21140, 25746}, {21404, 25021}, {21432, 26562}, {23764, 28565}, {25237, 25248}

X(33890) = anticomplement of X(17760)
X(33890) = {X(192),X(3212)}-harmonic conjugate of X(17752)
X(33890) = isotomic conjugate of isogonal conjugate of X(20284)
X(33890) = X(18299)-anticomplementary conjugate of X(315)
X(33890) = X(i)-Ceva conjugate of X(j) for these (i,j): {75, 3705}, {190, 3835}, {982, 3662}
X(33890) = X(i)-isoconjugate of X(j) for these (i,j): {983, 2162}, {2053, 7132}, {6378, 7305}, {7121, 17743}
X(33890) = crosspoint of X(75) and X(30545)
X(33890) = crossdifference of every pair of points on line {1980, 23472}
X(33890) = barycentric product X(i)*X(j) for these {i,j}: {76, 20284}, {192, 3662}, {982, 6376}, {1969, 20783}, {2275, 6382}, {2887, 33296}, {3061, 30545}, {3212, 3705}, {3721, 31008}, {3776, 4595}, {3888, 20906}, {7185, 27538}, {7304, 16886}, {20234, 27644}
X(33890) = barycentric quotient X(i)/X(j) for these {i,j}: {43, 983}, {192, 17743}, {982, 87}, {1423, 7132}, {2275, 2162}, {3056, 2053}, {3061, 2319}, {3662, 330}, {3705, 7155}, {3721, 16606}, {3778, 23493}, {3784, 23086}, {3888, 932}, {4595, 4621}, {6376, 7033}, {7032, 7121}, {7237, 7148}, {16584, 21759}, {17217, 7255}, {20284, 6}, {20783, 48}


X(33891) =  X(2)X(37)∩X(7)X(7774)

Barycentrics    (a^2 - b*c)*(b^2 - b*c + c^2) : :

X(33891) lies on the cubic K1035 and these lines: {2, 37}, {7, 7774}, {8, 16990}, {38, 31004}, {57, 19591}, {85, 330}, {141, 30179}, {183, 4361}, {193, 3598}, {194, 3673}, {230, 4395}, {238, 1281}, {239, 385}, {244, 2227}, {257, 30038}, {320, 7779}, {325, 1086}, {335, 20335}, {354, 17300}, {614, 1740}, {712, 18061}, {726, 4518}, {730, 19950}, {894, 3329}, {982, 2887}, {1015, 20924}, {1581, 18208}, {1755, 3218}, {1921, 1926}, {1930, 26959}, {1964, 7191}, {2140, 24166}, {2228, 3006}, {2234, 7292}, {2235, 33854}, {2275, 7187}, {2348, 17349}, {2896, 5015}, {3061, 10335}, {3661, 4119}, {3726, 3862}, {3759, 7766}, {3815, 7263}, {3920, 17445}, {4010, 4926}, {4070, 7875}, {4357, 31090}, {4363, 11174}, {4385, 31276}, {4402, 17008}, {4405, 15598}, {4541, 29617}, {4911, 7785}, {5222, 16989}, {5272, 16571}, {5275, 26240}, {7081, 17117}, {7179, 7777}, {7232, 7788}, {7249, 27447}, {7264, 25264}, {7792, 17366}, {7837, 17364}, {7868, 17290}, {9263, 30806}, {9865, 18904}, {10027, 21232}, {10030, 17493}, {15271, 17119}, {16584, 20234}, {16708, 16710}, {16738, 16739}, {16817, 19312}, {16823, 16994}, {16987, 29630}, {16988, 17292}, {16997, 26229}, {17184, 31089}, {17244, 19584}, {17304, 17591}, {17396, 17592}, {17448, 20955}, {18277, 18891}, {19565, 20435}, {20911, 26801}, {21208, 30109}, {21226, 26563}, {24046, 24190}, {24172, 29960}, {24185, 24189}, {24199, 24239}, {24786, 27020}, {25532, 30113}, {27912, 27942}, {31019, 31120}

X(33891) = complement of X(33889)
X(33891) = X(7166)-complementary conjugate of X(141)
X(33891) = X(2481)-Ceva conjugate of X(3056)
X(33891) = X(i)-isoconjugate of X(j) for these (i,j): {292, 983}, {649, 8684}, {875, 4621}, {1911, 17743}, {1922, 7033}, {3864, 18898}, {7034, 18897}, {7077, 7132}
X(33891) = crossdifference of every pair of points on line {667, 18758}
X(33891) = barycentric product X(i)*X(j) for these {i,j}: {239, 3662}, {274, 18904}, {350, 982}, {668, 3808}, {874, 3777}, {1447, 3705}, {1921, 2275}, {1966, 3865}, {2887, 33295}, {3056, 18033}, {3061, 10030}, {3570, 3776}, {3685, 7185}, {3721, 30940}, {3766, 3888}, {3863, 3978}, {4087, 7248}, {7032, 18891}, {7187, 17493}, {7188, 30643}
X(33891) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 8684}, {238, 983}, {239, 17743}, {350, 7033}, {982, 291}, {1429, 7132}, {2275, 292}, {3056, 7077}, {3061, 4876}, {3094, 3862}, {3570, 4621}, {3662, 335}, {3705, 4518}, {3776, 4444}, {3777, 876}, {3784, 295}, {3808, 513}, {3863, 694}, {3865, 1581}, {3888, 660}, {7032, 1911}, {7184, 18787}, {7185, 7233}, {7187, 30669}, {18891, 7034}, {18904, 37}, {19563, 4039}
X(33891) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 1447, 385}, {3662, 3705, 3314}, {21264, 28358, 19786}


X(33892) =  X(122)X(154)∩X(5878)X(10745)

Barycentrics    SA*(S^2-2*SB*SC)*((8*R^2-SA-3*SW)*S^4+(1536*R^6-16*(11*SA+53*SW)*R^4+8*(9*SA+19*SW)*SW*R^2-(2*SA^2+5*SA*SW+9*SW^2)*SW)*S^2-4*(4*R^2-SW)*(20*R^2-3*SW)*SB*SC*SW) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33892) lies on these lines: {122, 154}, {5878, 10745}


X(33893) =  X(2)X(31361)∩X(3)X(16251)

Barycentrics    SC*SB*(S^2-4*SA*SB)*(S^2-4*SA*SC)*(S^2-2*SB*SC) : :
X(33893) = 3*X(2)-4*X(33531)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33893) lies on these lines: {2, 31361}, {3, 16251}, {4, 1192}, {30, 3346}, {253, 3146}, {1249, 5895}, {1294, 3529}, {1503, 22049}, {2777, 3183}, {3668, 9579}, {6616, 10152}, {14249, 15005}, {15319, 15682}

X(33893) = anticomplement of the anticomplement of X(33531)
X(33893) = polar conjugate of X(14572)
X(33893) = Kirikami-Euler image of X(20)
X(33893) = antigonal conjugate of X(33897)


X(33894) =  X(597)X(11165)∩X(1351)X(8724)

Barycentrics    27*S^4-3*(9*SB*SC+8*SW^2)*S^2-4*(3*SA+SW)*(3*SA-2*SW)*SW^2 : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33894) lies on these lines: {597, 11165}, {1351, 8724}, {5304, 9741}, {8359, 32872}, {11148, 27088}, {15271, 32457}, {18841, 33237}


X(33895) =  X(1)X(474)∩X(5)X(519)

Barycentrics    a*(2*a^2-(b+c)*a-3*b^2+8*b*c-3*c^2)*(-a+b+c) : :
X(33895) = 5*X(1)-X(2136), 7*X(1)-3*X(3158), 3*X(1)-X(3913), 3*X(551)-X(12640), 7*X(2136)-15*X(3158), 3*X(2136)-5*X(3913), X(2136)+5*X(10912), 9*X(3158)-7*X(3913), 3*X(3158)+7*X(10912), X(3189)-5*X(3623), 9*X(3241)-X(12536), X(3625)-3*X(24386), X(3633)+3*X(24392), 3*X(3753)+X(17648), X(3811)-3*X(10247), X(3913)+3*X(10912), 3*X(5603)-X(32049), X(5881)-3*X(11235), 2*X(8666)-3*X(11260), X(8666)-3*X(22837)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33895) lies on these lines: {1, 474}, {5, 519}, {8, 1392}, {10, 1387}, {21, 643}, {35, 12653}, {145, 3485}, {210, 5330}, {355, 22835}, {377, 3241}, {392, 5506}, {515, 13463}, {517, 5450}, {518, 1351}, {528, 5882}, {529, 4301}, {551, 12640}, {758, 11278}, {952, 12608}, {956, 30323}, {958, 7962}, {960, 2098}, {999, 8668}, {1012, 7982}, {1054, 15854}, {1071, 6264}, {1212, 4919}, {1319, 4188}, {1385, 2802}, {1386, 15955}, {2099, 11520}, {2170, 30618}, {2551, 4345}, {2646, 3885}, {3169, 3723}, {3189, 3623}, {3244, 11263}, {3555, 11009}, {3625, 24386}, {3632, 23708}, {3633, 10827}, {3635, 4743}, {3698, 17535}, {3746, 19525}, {3811, 10247}, {3877, 5302}, {3884, 15254}, {3890, 16859}, {3893, 4511}, {3916, 16558}, {4018, 11280}, {4051, 6603}, {4640, 5697}, {4662, 4853}, {4857, 13272}, {4866, 15829}, {5119, 19535}, {5603, 32049}, {5694, 23960}, {5734, 6957}, {5844, 10916}, {5881, 11235}, {5901, 10915}, {6762, 11224}, {7991, 11194}, {8715, 15178}, {9802, 11015}, {10165, 32157}, {10179, 19860}, {10698, 11256}, {11236, 11522}, {11375, 12648}, {11523, 16189}, {12541, 20057}, {12625, 17532}, {12629, 12635}, {12650, 15726}, {15347, 16863}, {16173, 17619}, {22836, 33179}, {24160, 24864}, {24390, 25416}, {25405, 25440}, {30147, 31792}

X(33895) = midpoint of X(i) and X(j) for these {i,j}: {1, 10912}, {3244, 21627}, {3680, 3913}, {7982, 12513}, {10698, 11256}, {12629, 12635}, {12653, 22560}
X(33895) = reflection of X(i) in X(j) for these (i,j): (8715, 15178), (10915, 5901), (11260, 22837), (12607, 13464), (22836, 33179), (32537, 5)
X(33895) = X(5878)-of-K798i triangle
X(33895) = X(10912)-of-anti-Aquila triangle
X(33895) = X(32537)-of-Johnson triangle
X(33895) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8, 11376, 5123), (1320, 4861, 3057)


X(33896) =  X(5)X(7615)∩X(3589)X(12040)

Barycentrics    18*S^4-9*(3*SA+4*SW)*(SA-SW)*S^2+4*(3*SA+SW)*(3*SA-2*SW)*SW^2 : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33896) lies on these lines: {5, 7615}, {3589, 12040}, {6722, 16509}, {11165, 14535}, {18841, 33237}, {20112, 32538}

X(33896) = reflection of X(32538) in X(20112)


X(33897) =  X(4)X(3184)∩X(2777)X(3346)

Barycentrics    (S^2-2*SB*SC)*(S^2+(4*R^2-SW)*(48*R^2+SB-8*SW))*(S^2+(4*R^2-SW)*(48*R^2-SA-SB-7*SW)) : :

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33897) lies on these lines: {4, 3184}, {2777, 3346}, {10152, 27089}, {15318, 23241}

X(33897) = antigonal conjugate of X(33893)
X(33897) = Kirikami concurrent circles image of X(20)


X(33898) =  X(3)X(119)∩X(4)X(1387)

Barycentrics    a^10-2*(b+c)*a^9-(b^2-13*b*c+c^2)*a^8+(b-4*c)*(4*b-c)*(b+c)*a^7-2*(b^4+c^4+3*(2*b^2-7*b*c+2*c^2)*b*c)*a^6+2*(b+c)*(11*b^2-23*b*c+11*c^2)*b*c*a^5+(2*b^4+2*c^4-9*(b^2+4*b*c+c^2)*b*c)*(b-c)^2*a^4-(b^2-c^2)*(b-c)*(4*b^4+4*c^4+(b^2-28*b*c+c^2)*b*c)*a^3+(b^2-c^2)^2*(b^4+c^4+2*(5*b^2-13*b*c+5*c^2)*b*c)*a^2+2*(b^2-c^2)^3*(b-c)*(b^2-4*b*c+c^2)*a-(b^2-c^2)^4*(b-c)^2 : :
X(33898) = 3*X(5658)-X(6224)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33898) lies on these lines: {3, 119}, {4, 1387}, {80, 971}, {84, 12619}, {104, 1532}, {144, 153}, {495, 10728}, {515, 10738}, {517, 12641}, {952, 12667}, {1319, 1538}, {1537, 12115}, {2771, 18239}, {2800, 6259}, {3057, 12763}, {5281, 6938}, {5658, 6224}, {5691, 13273}, {5787, 6246}, {6001, 19914}, {6223, 12247}, {6260, 6265}, {6713, 18516}, {6834, 12248}, {6929, 22799}, {10057, 12688}, {10073, 12680}, {10085, 20118}, {11570, 12678}, {12679, 12758}, {12762, 16139}

X(33898) = reflection of X(i) in X(j) for these (i,j): (84, 12619), (6265, 6260), (10738, 12761), (10742, 6256)
X(33898) = {X(153), X(6925)}-harmonic conjugate of X(1145)


X(33899) =  X(3)X(1610)∩X(4)X(653)

Barycentrics    2*(b+c)*a^6-3*(b^2+c^2)*a^5-(b+c)*(3*b^2-8*b*c+3*c^2)*a^4+2*(3*b^2+5*b*c+3*c^2)*(b-c)^2*a^3-6*(b^2-c^2)*(b-c)*b*c*a^2-(b^2-c^2)^2*(3*b^2-2*b*c+3*c^2)*a+(b^2-c^2)^3*(b-c) : :
X(33899) = X(3)-3*X(14647), 3*X(5)-2*X(12608), X(1490)-3*X(26446), X(3146)+3*X(14646), 3*X(3679)+X(10864), 3*X(5587)-X(6259), 3*X(5587)+X(7992), 3*X(5657)+X(9799), 3*X(5658)-7*X(9780), 3*X(5770)-X(22770), 3*X(5790)-X(12667), 3*X(5790)+X(12684), 5*X(5818)-X(6223), 3*X(5886)-X(7971), X(8158)-3*X(24477), X(12608)-3*X(12616)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29306.

X(33899) lies on these lines: {3, 1610}, {4, 653}, {5, 3812}, {8, 6244}, {10, 971}, {12, 15071}, {30, 1158}, {40, 3358}, {46, 20420}, {56, 13226}, {63, 31799}, {65, 8727}, {84, 355}, {140, 6261}, {165, 21677}, {484, 6253}, {495, 1071}, {496, 12672}, {515, 550}, {517, 6245}, {758, 5763}, {942, 20330}, {946, 31794}, {952, 3913}, {1210, 7956}, {1329, 31803}, {1385, 6705}, {1387, 10785}, {1484, 2800}, {1490, 26446}, {1519, 10593}, {1709, 1837}, {1737, 12688}, {1768, 7354}, {1788, 19541}, {1854, 15252}, {2096, 9655}, {2551, 5779}, {2801, 12607}, {3146, 14646}, {3256, 10950}, {3295, 5768}, {3339, 5805}, {3419, 31777}, {3427, 5770}, {3452, 31821}, {3560, 12330}, {3679, 10864}, {3820, 5777}, {4847, 31798}, {5128, 5691}, {5252, 10085}, {5450, 32613}, {5499, 18242}, {5587, 6259}, {5657, 9799}, {5658, 9780}, {5722, 12705}, {5730, 6890}, {5731, 19535}, {5789, 19843}, {5790, 12667}, {5791, 30503}, {5806, 21628}, {5818, 6223}, {5884, 6147}, {5886, 7971}, {5887, 6922}, {5927, 24982}, {6256, 18357}, {6260, 9956}, {6907, 12664}, {6911, 18237}, {7681, 10265}, {7995, 9581}, {8158, 24477}, {8582, 10157}, {9578, 30304}, {9711, 15064}, {9952, 10573}, {10039, 12680}, {10167, 24987}, {10826, 12679}, {10827, 12678}, {10896, 12832}, {11496, 12433}, {11681, 13257}, {12520, 26066}, {12528, 17757}, {12619, 31828}, {13243, 20060}, {15251, 17054}, {18249, 31658}, {19925, 22792}, {24470, 26332}, {25466, 31657}, {31419, 31788}, {31870, 33335}

X(33899) = midpoint of X(i) and X(j) for these {i,j}: {10, 9948}, {40, 5787}, {84, 355}, {6259, 7992}, {12667, 12684}
X(33899) = reflection of X(i) in X(j) for these (i,j): (5, 12616), (1385, 6705), (6256, 18357), (6260, 9956), (6261, 140), (22792, 19925)
X(33899) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1210, 9856, 7956), (3812, 12617, 5)


X(33900) =  X(3)X(543)∩X(6)X(110)

Barycentrics    a^2*(a^8 - 4*a^6*b^2 + 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 + 8*b^6*c^2 - 3*a^2*b^2*c^4 - 18*b^4*c^4 + 4*a^2*c^6 + 8*b^2*c^6 - c^8) : :

X(33900) lies on the cubic K1116 and these lines: {3, 543}, {6, 110}, {23, 7669}, {25, 6094}, {126, 5522}, {1634, 9172}, {2080, 11258}, {2805, 13205}, {2847, 14673}, {7418, 16010}, {7464, 14654}, {7492, 14652}, {7496, 14360}, {7575, 14657}, {7615, 10204}, {13558, 33801}, {31861, 32424}

X(33900) = circumcircle-inverse of X(6055)
X(33900) = anti-Artzt-to-4th-anti-Brocard similarity image of X(3)
X(33900) = {X(1995),X(9149)}-harmonic conjugate of X(2930)


X(33901) =  X(1)X(1389)∩X(5844)X(11696)

Barycentrics    a (a^2-b^2+3 b c-c^2) (2 a^7-7 a^6 b+2 a^5 b^2+13 a^4 b^3-10 a^3 b^4-5 a^2 b^5+6 a b^6-b^7-7 a^6 c+26 a^5 b c-22 a^4 b^2 c-13 a^3 b^3 c+28 a^2 b^4 c-13 a b^5 c+b^6 c+2 a^5 c^2-22 a^4 b c^2+46 a^3 b^2 c^2-23 a^2 b^3 c^2-6 a b^4 c^2+3 b^5 c^2+13 a^4 c^3-13 a^3 b c^3-23 a^2 b^2 c^3+26 a b^3 c^3-3 b^4 c^3-10 a^3 c^4+28 a^2 b c^4-6 a b^2 c^4-3 b^3 c^4-5 a^2 c^5-13 a b c^5+3 b^2 c^5+6 a c^6+b c^6-c^7) : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29309.

X(33901) lies on these lines: {1,1389}, {5844,11696}


X(33902) =  X(1)X(227)∩X(1319)X(5577)

Barycentrics    a (a^2-b^2+4 b c-c^2) (2 a^7-9 a^6 b+4 a^5 b^2+17 a^4 b^3-14 a^3 b^4-7 a^2 b^5+8 a b^6-b^7-9 a^6 c+40 a^5 b c-33 a^4 b^2 c-20 a^3 b^3 c+41 a^2 b^4 c-20 a b^5 c+b^6 c+4 a^5 c^2-33 a^4 b c^2+68 a^3 b^2 c^2-34 a^2 b^3 c^2-8 a b^4 c^2+3 b^5 c^2+17 a^4 c^3-20 a^3 b c^3-34 a^2 b^2 c^3+40 a b^3 c^3-3 b^4 c^3-14 a^3 c^4+41 a^2 b c^4-8 a b^2 c^4-3 b^3 c^4-7 a^2 c^5-20 a b c^5+3 b^2 c^5+8 a c^6+b c^6-c^7) : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29309.

X(33902) lies on these lines: {1,227}, {1319,5577}


X(33903) =  X(1)X(10308)∩X(484)X(5951)

Barycentrics    a (a^2-b^2-b c-c^2) (2 a^7+a^6 b-6 a^5 b^2-3 a^4 b^3+6 a^3 b^4+3 a^2 b^5-2 a b^6-b^7+a^6 c+10 a^5 b c+2 a^4 b^2 c-5 a^3 b^3 c-4 a^2 b^4 c-5 a b^5 c+b^6 c-6 a^5 c^2+2 a^4 b c^2-2 a^3 b^2 c^2+a^2 b^3 c^2+2 a b^4 c^2+3 b^5 c^2-3 a^4 c^3-5 a^3 b c^3+a^2 b^2 c^3+10 a b^3 c^3-3 b^4 c^3+6 a^3 c^4-4 a^2 b c^4+2 a b^2 c^4-3 b^3 c^4+3 a^2 c^5-5 a b c^5+3 b^2 c^5-2 a c^6+b c^6-c^7) : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29309.

X(33903) lies on these lines: {1,10308}, {484,5951}, {1319,3024}, {2605,14838}

leftri

Points on the line at infinity: X(33904)-X(33922)

rightri

Centers X(33904)-X(33922) were contributed by Clark Kimberling, August 13, 2019.

Suppose that U = u : v : w = u(a,b,c) : v(a,b,c) : w(a,b,c) is a point on the line L at infinity, which consists of all points X = x : y : z : = x(a,b,c) : y(a,b,c): z(a,b,c) that satisfy x+y+z = 0. Suppose also that D = d : e : f is a point, and define

g(D) = u(d,e,f) : v(d,e,f) : w(d,e,f).

Clearly, g(D) lies on L. For example, if D = U = b-c : c-a : a-b, then

g(D) = c-a - (a-b) : a-b - (b-c) : b-c - (c-a) = 2a-b-c : 2b-c-a : 2c-a-b, and g(g(D)) = D; also,

if D = 2a-b-c : 2b-c-a : 2c-a-b, then g(D) = D.

In those examples, a,b,c can be replaced by am, bm,cm for any nonzero real number, so that that following family of triangle centers, all on L, can be regarded as a basis for generating, by composition, many more centers on L:

bm - cm : cm - am : am - bm and b-m - c-m : c-m - a-m : a-m - b-m = am(bm - cm) : bm(cm - am) : cm(am - bm),

where m ranges through the positive integers. Writing these as (m) and (-m), respectively, and concatenating (e.g., (2)(-1) means (2) is performed first, and then (-1)), we have, for example,

(2) = b^2-c^2 : :
(3) = b^3-c^3 : :
(2)(3) = (c^2-a^2)^3 - (a^2-b^2)^3 : : = 2a^2-b^2-c^2 : : (after cancellations)
(3)(2) = (c^3-a^3)^2 - (a^3-b^3)^2 : : = (b^3-c^3)(2a^3-b^3-c^3) : :

The appearance of (i,k) in the following list means that a^i : b^i : c^i = X(k). The appearance of (i,j,k) means that (i)(j) = X(k); and the appearance of (h,i,j,k) means that (h)(i)(j) = X(k):

(1,514), (2,523), (3,824), (4,826), (-1,513), (-2,512), (-3,788, (-4,688),

(1,1,519), (1,2,900), (2,1,524), (2,2,690),

(1,3,519), (3,1,752), (2,3,524), (3,2,33904), (3,3,752),

(1,4,33905), (4,1,754), (2,4,33906), (4,2,33907), (3,4,754), (-1,2,1,33908), (4,4,33909),

((1,5,33910),(5,1,33911), (2,5,33912), (5,2,33913), (3,5,33914), (5,3,33911), (2,1,-2,33915), (5,4,33916),

(1,-1,900), (-1,1,536), (-1,-1,6550), (-2,1,536), (-1,-2,33917), (-2,-1,888), (-2,-2,33918), (2,-1,690), (-1,2,891), (2,-2,33919), (-2,2,888),

(1,1,1,514), (1,1,2,900), (1,2,1,545), (2,1,1,523), (1,2,2,33920), (2,1,2,690), (2,2,1,543), (2,2,2,33921),

(1,1,-1,900), (1,1,-2,33922), (1,2,-1,33919), (2,1,-1,690)


X(33904) =  (name pending)

Barycentrics    (b^3-c^3)(2a^3-b^3-c^3) : :

X(33904) lies on these lines: {30, 511}, {4809, 14402}

X(33904) = crossdifference of every pair of points on line X(6)X(753)


X(33905) =  (name pending)

Barycentrics    (b - c)(2a - b - c)(2a^2 + b^2 + c^2 - 2a b - 2a c) : :

X(33905) lies on these lines: {30, 511}, {1960, 5440}, {3573, 6632}, {3625, 24093}, {3633, 24097}, {3635, 24099}, {4543, 30583}, {6161, 6546}, {20053, 24128}


X(33906) =  (name pending)

Barycentrics    (b^2 - c^2) (2 a^2 - b^2 - c^2) (2 a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4) : :

X(33906) lies on these lines: {30, 511}, {3630, 13232}, {5468, 31614}, {8859, 9191}, {11123, 21135}


X(33907) =  (name pending)

Barycentrics    (b^4 - c^4) (2 a^4 - b^4 - c^4) : :

X(33907) lies on these lines: {30, 511}, {3569, 23642}, {4577, 4630}, {11205, 14398}, {14403, 14420}, {14416, 14424}

X(33907) = crossdifference of every pair of points on line X(6)X(755)


X(33908) =  (name pending)

Barycentrics    a^2 b^2 + a^2 c^2 + 2 a b^2 c + 2 a b c^2 - 4 a^2 b c - 2 b^2 c^2 : :

X(33908) lies on these lines: {1, 4465}, {2, 668}, {6, 4482}, {30, 511}, {39, 24524}, {75, 4403}, {291, 3679}, {330, 1574}, {551, 17793}, {1500, 21226}, {1909, 16829}, {3241, 17794}, {3570, 8649}, {3913, 7781}, {3934, 17448}, {4400, 5288}, {4421, 8671}, {4479, 14711}, {4510, 17119}, {4738, 7208}, {4986, 7200}, {6683, 25102}, {7751, 12513}, {7757, 20671}, {7764, 12607}, {7775, 11236}, {7780, 8666}, {9318, 9457}, {11235, 18546}, {16100, 31154}, {16589, 25303}, {17946, 31143}, {18146, 32020}, {20331, 23891}, {20691, 32450}, {24281, 32029}, {31491, 33033}

X(33908) = crossdifference of every pair of points on line X(6)X(890)


X(33909) =  (name pending)

Barycentrics    (b^4 - c^4)(2 a^4 - b^4 - c^4) (2 a^8 - 2 a^4 b^4 + b^8 - 2 a^4 c^4 + c^8) : :

X(33909) lies on these lines: {30, 511}


X(33910) =  (name pending)

Barycentrics    (2 a - b - c) (a^4 - 2 a^3 b + 4 a^2 b^2 - 3 a b^3 + b^4 - 2 a^3 c - 2 a^2 b c + a b^2 c - b^3 c + 4 a^2 c^2 + a b c^2 + b^2 c^2 - 3 a c^3 - b c^3 + c^4) : :

X(33910) lies on these lines: {30, 511}, {145, 24416}, {20042, 24188}}


X(33911) =  (name pending)

Barycentrics    2 a^5 - b^5 - c^5 : :

X(33911) lies on these lines: {1, 4837}, {2, 560}, {10, 4836}, {30, 511}, {4381, 4769}


X(33912) =  (name pending)

Barycentrics    (2 a^2 - b^2 - c^2) (a^8 - 2 a^6 b^2 + 4 a^4 b^4 - 3 a^2 b^6 + b^8 - 2 a^6 c^2 - 2 a^4 b^2 c^2 + a^2 b^4 c^2 - b^6 c^2 + 4 a^4 c^4 + a^2 b^2 c^4 + b^4 c^4 - 3 a^2 c^6 - b^2 c^6 + c^8) : :

X(33912) lies on these lines: {30, 511}


X(33913) =  (name pending)

Barycentrics    (b - c) (b^4 + b^3 c + b^2 c^2 + b c^3 + c^4) (2 a^5 - b^5 - c^5) : :

X(33913) lies on these lines: {30, 511}


X(33914) =  (name pending)

Barycentrics    (2 a^3 - b^3 - c^3) (a^12 - 2 a^9 b^3 + 4 a^6 b^6 - 3 a^3 b^9 + b^12 - 2 a^9 c^3 - 2 a^6 b^3 c^3 + a^3 b^6 c^3 - b^9 c^3 + 4 a^6 c^6 + a^3 b^3 c^6 + b^6 c^6 - 3 a^3 c^9 - b^3 c^9 + c^12) : :

X(33914) lies on these lines: {30, 511}


X(33915) =  (name pending)

Barycentrics    (b^2 - c^2) (2 a^2 - b^2 - c^2)^3 : :

X(33915) lies on these lines: {30, 511}, {298, 9194}, {299, 9195}, {325, 9189}, {385, 9191}, {1648, 23991}, {1649, 8030}, {3292, 9125}, {4590, 5468}, {7840, 9185}, {14444, 23992}

X(33915) = isogonal conjugate of Ψ(X(351), X(111))
X(33915) = infinite point of trilinear polars of X(1649) and X(2482)
X(33915) = crossdifference of every pair of points on line X(6)X(10630)


X(33916) =  (name pending)

Barycentrics    (2 a^5 - b^5 - c^5) (a^20 - 2 a^15 b^5 + 4 a^10 b^10 - 3 a^5 b^15 + b^20 - 2 a^15 c^5 - 2 a^10 b^5 c^5 + a^5 b^10 c^5 - b^15 c^5 + 4 a^10 c^10 + a^5 b^5 c^10 + b^10 c^10 - 3 a^5 c^15 - b^5 c^15 + c^20) : :

X(33916) lies on these lines: {30, 511}


X(33917) =  (name pending)

Barycentrics    a^3 (b - c)^3 (a b + a c - 2 b c) : :

X(33917) lies on these lines: {30, 511}, {875, 23345}, {1646, 8027}

X(33917) = crossdifference of every pair of points on line X(6)X(1016)


X(33918) =  (name pending)

Barycentrics    a^6 (b^2 - c^2)^3 (a^2 b^2 + a^2 c^2 - 2 b^2 c^2) : :

X(33918) lies on these lines: {30, 511}, {1645, 23099}

X(33918) = crossdifference of every pair of points on the line through X(6) and the polar conjugate of X(2971)


X(33919) =  (name pending)

Barycentrics    (b^2 - c^2)^3 (2a^2 - b^2 - c^2) : :

X(33919) lies on these lines: {30, 511}, {141, 13232}, {325, 13186}, {1640, 9171}, {1641, 11123}, {1648, 8029}, {2682, 14443}, {5027, 18374}, {5468, 31632}, {7750, 13237}, {8859, 9185}, {10190, 11053}, {11183, 18311}, {13196, 13197}

X(33919) = isogonal conjugate of Ψ(X(351), X(110))
X(33919) = infinite point of trilinear polars of X(115) and X(1648)
X(33919) = crossdifference of every pair of points on line X(6)X(249)


X(33920) =  (name pending)

Barycentrics    (2 a - b - c) (b - c) (2 a^2 - 2 a b - b^2 - 2 a c + 4 b c - c^2) : :

X(33920) lies on these lines: {30, 511}, {1644, 14410}, {1647, 2087}, {3244, 24093}, {3251, 21129}, {3626, 24099}, {3632, 24097}, {3912, 28603}, {4555, 4618}, {4867, 21343}, {6545, 8028}, {6547, 24188}, {9269, 21198}, {20050, 24128}, {20924, 21433}, {30580, 31992}

X(33920) = crossdifference of every pair of points on line X(6)X(901)


X(33921) =  (name pending)

Barycentrics    (b^2 - c^2)(2 a^2 - b^2 - c^2) (2 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 4 b^2 c^2 - c^4) : :

X(33921) lies on these lines: {30, 511}, {385, 9185}, {892, 5466}, {1641, 8371}, {1648, 1649}, {3629, 13232}, {7840, 9191}, {8029, 8030}, {9123, 15360}, {9124, 15475}, {9125, 32225}, {9168, 18823}, {9181, 9182}, {9189, 22329}, {10510, 14277}, {17948, 18007}

X(33921) = isogonal conjugate of Ψ(X(351), X(6))
X(33921) = infinite point of trilinear polar of X(8371)
X(33921) = crossdifference of every pair of points on line X(6)X(691)


X(33922) =  (name pending)

Barycentrics    (b - c)(2a - b - c)^3 : :

X(33922) lies on these lines: {30, 511}, {1016, 17780}, {1647, 6547}, {1960, 3689}, {3251, 4543}, {4730, 8661}, {4895, 21805}

X(33922) = infinite point of trilinear polars of X(4370) and X(6544)
X(33922) = crossdifference of every pair of points on line X(6)X(2226)


X(33923) =  37TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    10 a^4-9 a^2 b^2-b^4-9 a^2 c^2+2 b^2 c^2-c^4 : :
X(33923) = 3 X[2] - 11 X[3],27 X[2] - 11 X[4],15 X[2] - 11 X[5],21 X[2] + 11 X[20],9 X[2] - 11 X[140],5 X[2] + 11 X[376],19 X[2] - 11 X[381],51 X[2] - 11 X[382],21 X[2] - 11 X[546],13 X[2] - 11 X[547],3 X[2] + 11 X[548],7 X[2] - 11 X[549],9 X[2] + 11 X[550],39 X[2] - 55 X[631],51 X[2] - 55 X[632],63 X[2] - 55 X[1656],45 X[2] + 11 X[1657],93 X[2] - 77 X[3090],87 X[2] - 55 X[3091],75 X[2] - 11 X[3146],9 X[2] + 55 X[3522],45 X[2] - 77 X[3523],17 X[2] - 33 X[3524],105 X[2] - 121 X[3525],69 X[2] - 77 X[3526],3 X[2] + 77 X[3528],69 X[2] + 11 X[3529],6 X[2] - 11 X[3530],171 X[2] - 187 X[3533],13 X[2] + 11 X[3534],43 X[2] - 11 X[3543],49 X[2] - 33 X[3545],39 X[2] - 11 X[3627],12 X[2] - 11 X[3628],35 X[2] - 11 X[3830],141 X[2] - 77 X[3832],65 X[2] - 33 X[3839],111 X[2] - 55 X[3843],23 X[2] - 11 X[3845],18 X[2] - 11 X[3850],117 X[2] - 77 X[3851],315 X[2] - 187 X[3854],201 X[2] - 121 X[3855],39 X[2] - 22 X[3856],129 X[2] - 77 X[3857],9 X[2] - 5 X[3858],93 X[2] - 55 X[3859],20 X[2] - 11 X[3860],24 X[2] - 11 X[3861],25 X[2] - 33 X[5054],41 X[2] - 33 X[5055],153 X[2] - 121 X[5056],117 X[2] + 11 X[5059],17 X[2] - 11 X[5066],159 X[2] - 143 X[5067],207 X[2] - 143 X[5068],129 X[2] - 121 X[5070],71 X[2] - 55 X[5071],177 X[2] - 121 X[5072],9 X[2] - X[5073],159 X[2] - 55 X[5076],183 X[2] - 143 X[5079],9 X[3] - X[4],5 X[3] - X[5],7 X[3] + X[20],3 X[3] - X[140],5 X[3] + 3 X[376],19 X[3] - 3 X[381],17 X[3] - X[382],7 X[3] - X[546],13 X[3] - 3 X[547],7 X[3] - 3 X[549],3 X[3] + X[550],13 X[3] - 5 X[631],17 X[3] - 5 X[632],21 X[3] - 5 X[1656],15 X[3] + X[1657],31 X[3] - 7 X[3090],29 X[3] - 5 X[3091],25 X[3] - X[3146],3 X[3] + 5 X[3522],15 X[3] - 7 X[3523],17 X[3] - 9 X[3524],35 X[3] - 11 X[3525],23 X[3] - 7 X[3526],X[3] + 7 X[3528],23 X[3] + X[3529],57 X[3] - 17 X[3533],13 X[3] + 3 X[3534],43 X[3] - 3 X[3543],49 X[3] - 9 X[3545]

As a point on the Euler line, X(33923) has Shinagawa coefficients (9,-11).

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29312.

X(33923) lies on these lines: {2,3}, {36,15172}, {74,26861}, {143,16836}, {146,22251}, {187,5368}, {389,13421}, {397,10645}, {398,10646}, {952,4701}, {1125,28178}, {1154,13348}, {1351,33750}, {1385,5493}, {1503,33751}, {1511,10990}, {1587,6451}, {1588,6452}, {1990,22052}, {3068,6496}, {3069,6497}, {3098,8550}, {3336,15174}, {3357,33533}, {3564,14810}, {3579,5844}, {3590,23269}, {3591,23275}, {3634,28168}, {3653,9589}, {3793,7783}, {3819,14641}, {3916,9945}, {3917,13491}, {4297,28224}, {4301,31666}, {4325,4995}, {4330,5298}, {4857,15325}, {5010,18990}, {5122,12433}, {5131,10543}, {5188,32516}, {5206,5305}, {5254,8588}, {5270,15326}, {5286,15655}, {5447,5663}, {5876,14855}, {5893,10182}, {5894,11202}, {5901,17502}, {6000,32142}, {6147,30282}, {6243,20791}, {6337,14929}, {6361,10283}, {6390,7768}, {6411,8981}, {6412,13966}, {6426,9681}, {6445,7581}, {6446,7582}, {6449,19117}, {6450,9541}, {6455,6460}, {6456,6459}, {6519,19054}, {6522,19053}, {6560,13925}, {6561,13993}, {6684,28186}, {6696,14864}, {6749,10979}, {6759,15105}, {7280,15171}, {7745,8589}, {7750,7871}, {7755,15513}, {7767,7782}, {7830,32459}, {7987,22791}, {7998,18439}, {9729,13391}, {9730,14449}, {9786,33543}, {9955,28182}, {9956,28190}, {10095,12002}, {10164,18357}, {10170,32137}, {10187,19107}, {10188,19106}, {10194,23261}, {10195,23251}, {10272,16111}, {10564,10610}, {10574,13340}, {10575,15067}, {10619,18914}, {10706,15023}, {10991,33813}, {10992,12042}, {11574,15471}, {11592,11793}, {11694,15063}, {12006,17704}, {12041,30714}, {12242,13568}, {12363,13148}, {12512,13464}, {13142,32110}, {13363,13598}, {13392,16534}, {13393,15605}, {13630,15644}, {14128,14915}, {14677,15035}, {14841,20421}, {14862,15311}, {14907,32821}, {15036,20127}, {15815,18907}, {16192,18481}, {17508,18583}, {18358,21167}, {25555,29181}, {25563,32903}, {32824,32890}, {32825,32891}

X(33923) = midpoint of X(i) and X(j) for these {i,j}: {3, 548}, {20, 546}, {140, 550}, {547, 3534}, {5188, 32516}, {5901, 31730}, {10272, 16111}, {12512, 13624}, {13491, 31834}, {13630, 15644}, {25563, 32903}
X(33923) = reflection of X(i) in X(j) for these {i,j}: {3530, 3}, {3627, 3856}, {3628, 3530}, {3850, 140}, {3861, 3628}, {11793, 11592}, {12006, 17704}, {13393, 20417}, {16881, 9729}
X(33923) = complement of X(3853)
X(33923) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {2, 3853, 12811}, {2, 5073, 3858}, {2, 15696, 15704}, {2, 15704, 3853}, {3, 4, 15712}, {3, 5, 12100}, {3, 20, 549}, {3, 376, 5}, {3, 381, 15717}, {3, 382, 3524}, {3, 550, 140}, {3, 631, 17504}, {3, 1656, 10299}, {3, 1657, 3523}, {3, 3522, 550}, {3, 3526, 15692}, {3, 3528, 8703}, {3, 3530, 14891}, {3, 3534, 631}, {3, 3843, 15700}, {3, 5070, 15706}, {3, 6909, 5428}, {3, 7512, 15646}, {3, 7525, 15331}, {3, 8703, 548}, {3, 12103, 12108}, {3, 12605, 16976}, {3, 14093, 3528}, {3, 14130, 15246}, {3, 15688, 20}, {3, 15689, 3526}, {3, 15690, 16239}, {3, 15695, 382}, {3, 15696, 2}, {3, 15717, 15711}, {3, 16117, 6940}, {3, 17538, 14869}, {3, 17800, 15693}, {3, 21312, 7516}, {3, 33703, 19711}, {4, 15712, 140}, {5, 376, 12103}, {5, 549, 3525}, {5, 550, 1657}, {5, 632, 15703}, {5, 3146, 14893}, {5, 3523, 140}, {5, 3627, 3839}, {5, 3830, 546}, {5, 10124, 3628}, {5, 12100, 12108}, {5, 12102, 3860}, {5, 12108, 10124}, {5, 19710, 3146}, {20, 549, 546}, {20, 3523, 3854}, {20, 3525, 3830}, {20, 10299, 1656}, {20, 15705, 3525}, {20, 19708, 3}, {140, 546, 1656}, {140, 548, 550}, {140, 1656, 16239}, {140, 3523, 12108}, {140, 3533, 11540}, {140, 3850, 3628}, {140, 5059, 3856}, {140, 5073, 12811}, {140, 12100, 3523}, {140, 15691, 5073}, {140, 16618, 18282}, {376, 1657, 550}, {376, 3523, 1657}, {376, 3525, 20}, {376, 3839, 3534}, {376, 5054, 19710}, {376, 15703, 15686}, {376, 15705, 3830}, {376, 19708, 15705}, {376, 21734, 3}, {381, 15710, 15711}, {381, 15717, 14869}, {382, 632, 5066}, {382, 3524, 632}, {546, 548, 15690}, {546, 549, 16239}, {546, 15690, 20}, {546, 16239, 10109}, {547, 3627, 3856}, {548, 3853, 15696}, {548, 12100, 12103}, {548, 12103, 376}, {548, 12812, 15689}, {548, 15714, 12811}, {548, 15759, 3628}, {548, 16197, 15332}, {549, 1656, 140}, {549, 8703, 15688}, {549, 15688, 15690}, {549, 15705, 12100}, {550, 1657, 12103}, {550, 3522, 548}, {550, 3858, 15704}, {550, 8703, 3522}, {550, 10299, 546}, {550, 15712, 4}, {550, 17504, 3851}, {631, 3534, 3627}, {631, 3627, 547}, {631, 5059, 3851}, {632, 15686, 382}, {1656, 1657, 3830}, {1656, 3830, 3854}, {1656, 3851, 15022}, {1656, 3854, 5}, {1656, 10299, 549}, {1657, 3523, 5}, {1657, 12108, 3850}, {1657, 15722, 5068}, {2043, 2044, 15685}, {2045, 2046, 15694}, {3090, 15687, 3859}, {3090, 17800, 15687}, {3146, 5054, 5}, {3522, 3523, 376}, {3522, 10304, 21735}, {3522, 19708, 1656}, {3522, 21734, 3523}, {3522, 21735, 3}, {3523, 3854, 3525}, {3523, 15705, 10299}, {3524, 15686, 5066}, {3524, 15695, 15686}, {3525, 3830, 5}, {3525, 3854, 1656}, {3525, 10299, 3523}, {3525, 16239, 10124}, {3526, 3529, 3845}, {3526, 3845, 12812}, {3526, 15689, 3529}, {3528, 10304, 3}, {3528, 21735, 3522}, {3529, 15692, 3526}, {3529, 15722, 5}, {3530, 3628, 11812}, {3530, 3850, 140}, {3530, 10124, 12108}, {3530, 12102, 10124}, {3530, 12103, 3860}, {3530, 15759, 3}, {3533, 14869, 140}, {3534, 3851, 5059}, {3534, 15718, 3839}, {3534, 17504, 547}, {3543, 5070, 3857}, {3543, 15706, 15713}, {3545, 15716, 549}, {3552, 8359, 19697}, {3627, 15022, 546}, {3627, 17504, 631}, {3628, 3860, 5}, {3628, 3861, 11737}, {3628, 14891, 3530}, {3830, 10109, 3860}, {3830, 15688, 376}, {3830, 15705, 549}, {3843, 10303, 15699}, {3843, 15700, 10303}, {3851, 3856, 3850}, {3851, 5059, 3627}, {3853, 15691, 15704}, {3854, 15705, 3523}, {3856, 14890, 3628}, {3857, 15713, 5070}, {3858, 5073, 3853}, {3858, 12811, 3850}, {3858, 15704, 5073}, {3860, 12100, 11812}, {3860, 12102, 3861}, {3861, 11812, 3628}, {3917, 13491, 31834}, {5054, 19710, 14893}, {5055, 15715, 19711}, {5056, 15695, 550}, {5059, 17504, 140}, {5067, 15683, 5076}, {5076, 15701, 5067}, {5079, 15685, 17578}, {5079, 17578, 23046}, {6450, 9541, 19116}, {6656, 33276, 27088}, {7486, 11541, 14269}, {7807, 33275, 8354}, {8703, 19708, 15690}, {8703, 21734, 12103}, {8703, 21735, 140}, {10109, 16239, 3628}, {10124, 12102, 5}, {10299, 15688, 550}, {10299, 21735, 19708}, {10303, 11001, 3843}, {10304, 14093, 8703}, {11001, 15700, 15699}, {11539, 15681, 12101}, {11541, 15719, 7486}, {12100, 12103, 5}, {12100, 12108, 3530}, {12100, 14893, 5054}, {12100, 15690, 3830}, {12102, 12108, 3628}, {12103, 12108, 12102}, {12103, 15705, 16239}, {12103, 15718, 3856}, {12108, 21734, 15759}, {14813, 14814, 3627}, {14869, 15711, 15717}, {15681, 15698, 11539}, {15685, 15702, 23046}, {15688, 19708, 549}, {15689, 15692, 3845}, {15693, 17800, 3090}, {15694, 33699, 14892}, {15696, 15704, 15691}, {15697, 15715, 5055}, {15702, 17578, 5079}, {15710, 15717, 3}, {15710, 17538, 15717}, {15717, 17538, 381}, {15718, 17504, 12100}, {16196, 25337, 10125}, {17502, 31730, 5901}, {17529, 17574, 15673}, {33008, 33235, 8362}, {33022, 33268, 8370}


X(33924) =  X(2)X(15274)∩X(3)X(64)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^8 - 2*a^6*b^2 + 8*a^4*b^4 - 14*a^2*b^6 + 7*b^8 - 2*a^6*c^2 - 16*a^4*b^2*c^2 + 14*a^2*b^4*c^2 + 4*b^6*c^2 + 8*a^4*c^4 + 14*a^2*b^2*c^4 - 22*b^4*c^4 - 14*a^2*c^6 + 4*b^2*c^6 + 7*c^8) : :

X(33924) lies on the cubic K1118 and these lines: {2, 15274}, {3, 64}, {6, 2972}, {122, 20208}, {216, 5646}, {1297, 1995}, {3090, 6523}, {7778, 16051}

X(33924) = crossdifference of every pair of points on line {2848, 6587}


X(33925) =  X(1)X(3)∩X(23)X(16272)

Barycentrics    a^2*(a^4 - 2*a^3*b + 2*a*b^3 - b^4 - 2*a^3*c + 4*a^2*b*c - 4*a*b^2*c + 2*b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4) : :

X(33925) lies on the cubic K1118 and these lines: {1, 3}, {23, 16272}, {25, 18613}, {105, 1995}, {225, 5198}, {388, 6912}, {404, 11240}, {405, 15888}, {528, 1004}, {908, 1001}, {1002, 2990}, {1012, 5434}, {1037, 14935}, {1066, 1497}, {1068, 10594}, {1210, 11501}, {1376, 4863}, {1486, 20999}, {1621, 3475}, {1797, 3423}, {1830, 7071}, {1998, 3689}, {2183, 2280}, {2348, 8557}, {2551, 5047}, {3011, 11284}, {3012, 23854}, {3058, 7580}, {3086, 6946}, {3090, 26481}, {3321, 14878}, {3722, 21346}, {3757, 20928}, {4413, 5231}, {4423, 30827}, {4428, 20835}, {5218, 7677}, {5230, 28250}, {5292, 16297}, {5324, 7419}, {5338, 26377}, {5733, 7416}, {6883, 10056}, {6911, 10072}, {6913, 11237}, {6915, 26475}, {6978, 10321}, {7083, 23404}, {7411, 10385}, {7484, 15621}, {7965, 26332}, {8192, 23383}, {10106, 12617}, {10198, 16842}, {10404, 11496}, {10527, 17531}, {10529, 17572}, {10532, 21669}, {10587, 16865}, {11019, 11502}, {11238, 19541}, {11269, 23858}, {12607, 25875}, {13615, 28609}, {15297, 17615}, {16283, 23653}, {16421, 33140}, {16862, 26363}, {17469, 20277}, {23845, 26866}, {23855, 24405}, {31721, 32624}

X(33925) = midpoint of X(5597) and X(5598)
X(33925) = crosspoint of X(59) and X(14074)
X(33925) = crosssum of X(11) and X(14077)
X(33925) = crossdifference of every pair of points on line {650, 2826}
X(33925) = harmonic center of incircle and OI-inverter
X(33925) = barycentric product X(1)*X(8257)
X(33925) = barycentric quotient X(8257)/X(75)
X(33925) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 57, 18839}, {1, 2078, 55}, {55, 56, 1155}, {999, 3295, 1159}, {999, 8069, 1470}, {999, 10679, 5902}, {1155, 3748, 3057}, {1155, 20323, 354}, {1159, 7742, 1470}, {2078, 10389, 10267}, {3513, 3514, 1470}, {5537, 5563, 57}, {6244, 10680, 5536}, {10389, 15931, 55}, {11492, 11493, 36}


X(33926) =  X(3)X(66)∩X(107)X(264)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^10 - a^8*b^2 - a^2*b^8 + b^10 - a^8*c^2 + 4*a^6*b^2*c^2 + 4*a^2*b^6*c^2 - 7*b^8*c^2 - 6*a^2*b^4*c^4 + 6*b^6*c^4 + 4*a^2*b^2*c^6 + 6*b^4*c^6 - a^2*c^8 - 7*b^2*c^8 + c^10) : :

X(33926) lies on the cubic K1118 and these lines: {3, 66}, {107, 264}, {216, 5651}, {1033, 11284}, {3148, 15526}


X(33927) =  X(2)X(523)∩X(3)X(74)

Barycentrics    a^2*(a^8*b^2 - 5*a^6*b^4 + 9*a^4*b^6 - 7*a^2*b^8 + 2*b^10 + a^8*c^2 + 4*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + b^8*c^2 - 5*a^6*c^4 - 6*a^4*b^2*c^4 + 12*a^2*b^4*c^4 - 3*b^6*c^4 + 9*a^4*c^6 - 3*b^4*c^6 - 7*a^2*c^8 + b^2*c^8 + 2*c^10) : :
X(33927) = 2 X[3] + X[14264],X[3] + 2 X[14670],5 X[1656] - 2 X[14254],X[14264] - 4 X[14670],X[15329] + 2 X[16186]

X(33927) lies on the cubic K1118 and these lines: {2, 523}, {3, 74}, {323, 5467}, {373, 18114}, {381, 15111}, {511, 15329}, {842, 1995}, {1656, 14254}, {14389, 15000}

X(33927) = crossdifference of every pair of points on line {187, 1637}
X(33927) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9717, 110}, {3, 14670, 14264}, {14685, 14687, 1995}


X(33928) =  X(3)X(512)∩X(6)X(110)

Barycentrics    a^2*(2*a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - 2*b^8 - 5*a^6*c^2 + 6*a^4*b^2*c^2 - 6*a^2*b^4*c^2 + 7*b^6*c^2 + 6*a^4*c^4 - 6*a^2*b^2*c^4 - 6*b^4*c^4 - a^2*c^6 + 7*b^2*c^6 - 2*c^8) : :

X(33928) lies on the cubic K1118 and these lines: {3, 512}, {6, 110}, {23, 2421}, {249, 14246}, {524, 7417}, {599, 9832}, {842, 1350}, {1495, 5467}, {5108, 9168}, {5642, 14995}, {5651, 9717}, {6054, 9830}, {9135, 15566}

X(33928) = crossdifference of every pair of points on line {230, 690}
X(33928) = {X(110),X(5968)}-harmonic conjugate of X(6)


X(33929) =  X(3)X(524)∩X(99)X(1995)

Barycentrics    a^2*(a^8 - 4*a^6*b^2 + 4*a^2*b^6 - b^8 - 4*a^6*c^2 + 36*a^4*b^2*c^2 - 48*a^2*b^4*c^2 + 8*b^6*c^2 - 48*a^2*b^2*c^4 + 18*b^4*c^4 + 4*a^2*c^6 + 8*b^2*c^6 - c^8) : :

X(33929) lies on the cubic K1118 and these lines: {3, 524}, {99, 1995}, {574, 5650}, {10204, 12040}, {11284, 33850}


X(33930) =  X(1)X(20924)∩X(2)X(16720)

Barycentrics    b*c*(b^2 - b*c + c^2) : :

X(33930) lies on these lines: {1, 20924}, {2, 16720}, {7, 8}, {10, 20893}, {58, 274}, {76, 334}, {81, 19805}, {86, 977}, {304, 350}, {310, 30984}, {312, 26132}, {316, 4056}, {321, 17230}, {325, 3665}, {327, 349}, {330, 7200}, {384, 4376}, {385, 4372}, {561, 21140}, {742, 17033}, {1086, 26561}, {2064, 25527}, {2227, 7242}, {2275, 7187}, {2292, 4389}, {3094, 3662}, {3096, 17192}, {3123, 23478}, {3125, 24190}, {3261, 21132}, {3263, 6376}, {3314, 16886}, {3661, 20432}, {3701, 20943}, {3702, 4479}, {3705, 7185}, {3758, 30892}, {4000, 17788}, {4359, 16816}, {4385, 20925}, {4412, 18209}, {4441, 17762}, {4647, 20894}, {4680, 7768}, {4754, 31317}, {4812, 17300}, {6063, 7018}, {6382, 21416}, {7264, 14210}, {7751, 30167}, {7764, 30152}, {7786, 24786}, {7794, 30149}, {7796, 30171}, {7828, 20267}, {8299, 32117}, {9351, 16820}, {16706, 20444}, {16822, 24333}, {16906, 25345}, {16916, 24358}, {17205, 24166}, {17234, 21808}, {17489, 26978}, {17753, 24282}, {17760, 18055}, {18066, 25959}, {18135, 20947}, {18156, 21605}, {18159, 31130}, {18208, 30953}, {19785, 20929}, {20247, 30941}, {20255, 21138}, {20440, 20899}, {20590, 25957}, {20892, 27424}, {20896, 33146}, {23989, 30632}, {24281, 30136}, {25263, 26100}, {25524, 26240}, {25994, 30748}, {26106, 28090}, {26234, 31997}, {27487, 29966}

X(33930) = isotomic conjugate of X(983)
X(33930) = {X(76),X(1930)}-harmonic conjugate of X(33931)
X(33930) = {X(33943),X(33944)}-harmonic conjugate of X(2)


X(33931) =  X(2)X(37)∩X(7)X(7211)

Barycentrics    b*c*(b^2 + b*c + c^2) : :

X(33931) lies on these lines: {1, 33939}, {2, 37}, {7, 7211}, {8, 7261}, {32, 30167}, {69, 3974}, {76, 334}, {86, 5311}, {100, 9075}, {190, 5282}, {194, 16720}, {201, 33298}, {304, 1909}, {313, 561}, {314, 983}, {316, 4680}, {319, 3681}, {325, 3703}, {335, 30945}, {341, 25280}, {384, 4372}, {385, 4376}, {594, 26590}, {626, 30149}, {693, 29204}, {742, 24514}, {756, 5224}, {984, 4476}, {985, 3923}, {1269, 21415}, {1441, 30545}, {1506, 30152}, {1961, 10436}, {1978, 4485}, {2227, 4493}, {3509, 3729}, {3596, 6382}, {3663, 4135}, {3701, 6376}, {3702, 17144}, {3726, 31028}, {3761, 20924}, {3790, 7179}, {3802, 16825}, {3807, 27474}, {3837, 21439}, {3875, 29821}, {3912, 21101}, {3930, 17233}, {3971, 4357}, {3994, 4389}, {4056, 7768}, {4066, 20888}, {4125, 6381}, {4360, 17017}, {4514, 5564}, {4692, 14210}, {4696, 24524}, {4967, 24210}, {4968, 31997}, {5025, 16886}, {5695, 8301}, {5904, 33297}, {7148, 23478}, {7283, 13723}, {7752, 30171}, {7832, 20267}, {16690, 32914}, {16887, 24068}, {16974, 33816}, {16991, 25345}, {16998, 24358}, {17152, 25253}, {17165, 30941}, {17378, 31161}, {17489, 27040}, {17731, 32912}, {18055, 29960}, {18059, 20932}, {18156, 25303}, {20334, 20434}, {20553, 33091}, {20943, 26563}, {21020, 23928}, {21240, 22036}, {21260, 21440}, {21301, 21613}, {24254, 30114}, {24349, 30962}, {24512, 31317}, {25263, 26035}, {25497, 30168}, {27487, 30949}, {30154, 31488}, {30596, 30636}

X(33931) = isotomic conjugate of X(985)
X(33931) = {X(76),X(1930)}-harmonic conjugate of X(33930)
X(33931) = {X(33939),X(33941)}-harmonic conjugate of X(1)
X(33931) = complement of polar conjugate of isogonal conjugate of X(23194)
X(33931) = anticomplement of polar conjugate of isogonal conjugate of X(23231)


X(33932) =  X(1)X(20947)∩X(27)X(19799)

Barycentrics    b*c*(-a*b + b^2 - a*c + b*c + c^2) : :

X(33932) lies on these lines: {1, 20947}, {27, 19799}, {75, 1089}, {76, 3263}, {115, 27570}, {190, 1759}, {264, 1969}, {274, 4385}, {304, 341}, {312, 728}, {314, 7162}, {315, 10327}, {316, 5300}, {321, 21816}, {762, 3661}, {1111, 20943}, {1928, 6386}, {1930, 3992}, {3006, 7752}, {3673, 18145}, {3679, 17762}, {3681, 33297}, {3952, 17137}, {4006, 17233}, {4125, 20888}, {4358, 17367}, {4360, 13741}, {4426, 30167}, {4692, 31997}, {4737, 18156}, {4986, 17144}, {7796, 33864}, {14210, 24524}, {17158, 20942}, {18055, 30109}, {18061, 30036}, {18135, 31130}, {18137, 29433}, {18743, 29598}, {20432, 31060}, {20541, 30153}, {21021, 27255}, {21101, 29968}, {24068, 24170}, {24080, 24190}, {26100, 31077}, {27040, 31087}, {27808, 28659}, {29387, 29511}


X(33933) =  X(1)X(75)∩X(2)X(20432)

Barycentrics    b*c*(-a*b + b^2 - a*c - b*c + c^2) : :

X(33933) lies on these lines: {1, 75}, {2, 20432}, {8, 20924}, {10, 20893}, {76, 3263}, {85, 668}, {99, 11101}, {115, 27706}, {190, 17682}, {277, 344}, {312, 32015}, {320, 5904}, {321, 17244}, {341, 20925}, {443, 1265}, {764, 20906}, {1016, 28961}, {1086, 17670}, {1089, 20894}, {1111, 6376}, {1266, 24178}, {1441, 7185}, {2087, 20899}, {2140, 4568}, {3006, 7796}, {3125, 33890}, {3644, 4099}, {3662, 3954}, {3673, 18140}, {3675, 6382}, {3679, 20955}, {3721, 24190}, {3760, 20947}, {3970, 17234}, {3992, 20943}, {4066, 20888}, {4359, 17367}, {4363, 11321}, {4384, 17789}, {4389, 33833}, {4699, 20234}, {4772, 21442}, {4986, 24524}, {5300, 7768}, {7187, 16975}, {7264, 30963}, {7752, 33864}, {8728, 30893}, {10009, 20435}, {16054, 32939}, {16408, 26240}, {16720, 17030}, {16752, 17147}, {17050, 17760}, {17247, 21816}, {17320, 27785}, {17347, 17746}, {18895, 22116}, {20236, 30090}, {20703, 25961}, {20911, 21432}, {24326, 27255}, {24357, 31996}, {24781, 33116}, {25244, 27109}, {26035, 31077}, {26978, 31087}, {28605, 29569}, {31129, 33841}


X(33934) =  X(1)X(20955)∩X(2)X(20924)

Barycentrics    b*c*(a*b + b^2 + a*c - b*c + c^2) : :

X(33934) lies on these lines: {1, 20955}, {2, 20924}, {10, 20893}, {57, 85}, {75, 537}, {76, 321}, {141, 21138}, {304, 17284}, {312, 18145}, {320, 5902}, {742, 30114}, {999, 26240}, {1089, 20943}, {1930, 3992}, {3125, 3662}, {3570, 30108}, {3673, 17143}, {3732, 16551}, {3735, 31004}, {3760, 17762}, {3783, 24293}, {4125, 6381}, {4358, 18146}, {4389, 4424}, {4461, 32869}, {4475, 25760}, {4812, 17287}, {4828, 23598}, {4850, 16712}, {5016, 7768}, {6537, 27706}, {7264, 17144}, {7769, 27187}, {8682, 17027}, {14210, 30963}, {16720, 27091}, {16975, 33891}, {17236, 21442}, {17238, 20234}, {17306, 17788}, {17307, 20444}, {17308, 17789}, {17346, 30892}, {17740, 32833}, {18054, 31017}, {18135, 29587}, {20432, 29593}, {20569, 24589}, {20906, 30583}, {21951, 24190}, {24254, 24514}, {24282, 30946}, {26234, 30806}, {33775, 33780}

X(33934) = {X(76),X(20911)}-harmonic conjugate of X(33935)


X(33935) =  X(1)X(75)∩X(8)X(315)

Barycentrics    b*c*(a*b + b^2 + a*c + b*c + c^2) : :

X(33935) lies on these lines: {1, 75}, {8, 315}, {69, 33865}, {76, 321}, {85, 4102}, {305, 19835}, {312, 17308}, {316, 5016}, {319, 5904}, {668, 4385}, {746, 5291}, {891, 21439}, {1089, 6376}, {1231, 6063}, {1278, 4352}, {1698, 20947}, {3674, 4431}, {3702, 26234}, {3761, 20955}, {3797, 5283}, {3868, 33297}, {3970, 17233}, {4063, 21613}, {4066, 6381}, {4083, 21440}, {4099, 4664}, {4358, 29608}, {4359, 17397}, {4386, 30167}, {4461, 32830}, {4479, 7264}, {4671, 18135}, {4692, 24524}, {4980, 17389}, {5082, 5195}, {5100, 5564}, {6537, 27570}, {6542, 20432}, {7763, 17740}, {7799, 27187}, {10009, 20891}, {11679, 21587}, {14829, 21594}, {16705, 17147}, {17033, 24254}, {17135, 17141}, {17137, 17164}, {17163, 20242}, {17206, 32939}, {17248, 21816}, {17322, 27785}, {17346, 17746}, {17495, 27162}, {17886, 20538}, {19804, 29603}, {20541, 30149}, {20963, 31317}, {21327, 27634}, {21385, 21612}, {21605, 29605}

X(33935) = {X(76),X(20911)}-harmonic conjugate of X(33934)


X(33936) =  X(1)X(20911)∩X(2)X(14210)

Barycentrics    b*c*(-a^2 + a*b + b^2 + a*c + c^2) : :

X(33936) lies on these lines: {1, 20911}, {2, 14210}, {6, 8682}, {8, 150}, {10, 304}, {22, 18617}, {69, 758}, {75, 519}, {76, 4485}, {85, 3671}, {141, 3735}, {183, 5977}, {239, 26634}, {274, 4658}, {305, 21085}, {312, 6381}, {314, 17861}, {321, 3761}, {514, 27474}, {740, 24293}, {760, 3416}, {986, 16887}, {1111, 4441}, {1125, 18156}, {1231, 1448}, {1323, 7182}, {1330, 33867}, {1441, 10447}, {2271, 30127}, {2795, 5695}, {3125, 30945}, {3212, 10449}, {3263, 3679}, {3661, 26589}, {3673, 4673}, {3684, 30108}, {3687, 21621}, {3702, 3760}, {3704, 3933}, {3766, 23888}, {3959, 21240}, {3976, 24166}, {4095, 29697}, {4167, 17046}, {4251, 16822}, {4359, 16834}, {4376, 5291}, {4385, 16284}, {4388, 5195}, {4650, 6629}, {4680, 20553}, {4717, 20925}, {5011, 24586}, {5088, 32932}, {5224, 20932}, {5697, 17152}, {5883, 30962}, {5902, 30941}, {5903, 17137}, {8897, 11679}, {11520, 20880}, {16583, 30110}, {16600, 21216}, {16703, 32860}, {16739, 17592}, {17048, 29748}, {17231, 21331}, {17270, 20336}, {17489, 26759}, {18359, 30635}, {20629, 33677}, {24170, 24440}

X(33936) = {X(8),X(1930)}-harmonic conjugate of X(33937)


X(33937) =  X(1)X(3263)∩X(2)X(28594)

Barycentrics    b*c*(a^2 - a*b + b^2 - a*c + c^2) : :

X(33937) lies on these lines: {1, 3263}, {2, 28594}, {6, 30133}, {8, 150}, {10, 75}, {37, 30107}, {85, 4737}, {86, 30145}, {145, 14210}, {169, 3729}, {192, 16600}, {304, 519}, {305, 24211}, {312, 3008}, {321, 3294}, {335, 24190}, {536, 16583}, {712, 3959}, {758, 21281}, {982, 24170}, {1089, 4441}, {1125, 30758}, {1278, 16611}, {1698, 26234}, {1722, 17151}, {2140, 21067}, {2241, 24358}, {2329, 30108}, {2901, 3875}, {3061, 4568}, {3244, 18156}, {3266, 33120}, {3679, 20911}, {3681, 21415}, {3701, 3760}, {3730, 17755}, {3761, 4696}, {3765, 20432}, {3802, 16825}, {3881, 30962}, {3970, 29966}, {3992, 7264}, {4056, 20553}, {4090, 21590}, {4119, 17046}, {4359, 17308}, {4372, 5291}, {4561, 30144}, {4686, 16605}, {4723, 26563}, {4738, 25278}, {4872, 5100}, {4911, 32850}, {4968, 32092}, {5088, 9369}, {5271, 19835}, {5283, 24326}, {5692, 17152}, {5902, 17141}, {5904, 17137}, {6604, 12432}, {6757, 20437}, {8024, 33117}, {9055, 20255}, {10447, 10889}, {16589, 24357}, {16720, 16975}, {16777, 30126}, {17050, 21101}, {17200, 17716}, {17671, 20495}, {17736, 24602}, {17753, 21416}, {18743, 31191}, {19804, 29604}, {20235, 20895}, {20602, 32933}, {20606, 29069}, {20898, 33074}, {20907, 23100}, {20924, 24524}, {21232, 29697}, {21432, 30806}, {24166, 24174}, {26965, 31087}, {27091, 33891}, {27096, 30730}, {30110, 30748}, {30615, 30617}

X(33937) = {X(1),X(3263)}-harmonic conjugate of X(33942)
X(33937) = {X(8),X(1930)}-harmonic conjugate of X(33936)


X(33938) =  X(1)X(20947)∩X(2)X(21021)

Barycentrics    b*c*(a^2 - a*b + b^2 - a*c + b*c + c^2) : :

X(33938) lies on these lines: {1, 20947}, {2, 21021}, {8, 7261}, {10, 75}, {83, 30133}, {85, 11237}, {190, 3496}, {239, 312}, {274, 4692}, {304, 4737}, {319, 21276}, {321, 3975}, {335, 20255}, {350, 3701}, {536, 25994}, {594, 26558}, {668, 1930}, {1031, 17788}, {1089, 4986}, {1369, 20934}, {1655, 24326}, {1909, 3263}, {1925, 6386}, {3681, 22296}, {3703, 7019}, {3765, 17789}, {3797, 20691}, {3807, 33299}, {3952, 17152}, {3991, 17264}, {3992, 18140}, {4095, 17755}, {4361, 26687}, {4676, 12194}, {4723, 20911}, {5291, 30167}, {5295, 5564}, {7264, 18145}, {9055, 21025}, {16720, 21226}, {16830, 30758}, {17023, 18743}, {17034, 18137}, {18040, 30173}, {18055, 30036}, {18159, 31130}, {19804, 29610}, {20483, 33841}, {20715, 21281}, {21067, 30109}, {21101, 30030}, {23903, 27570}, {24357, 27269}, {25497, 30141}, {27040, 28598}, {29614, 30829}, {29633, 30963}

X(33938) = {X(75),X(6376)}-harmonic conjugate of X(33944)
X(33938) = {X(1909),X(3263)}-harmonic conjugate of X(33943)


X(33939) =  X(10)X(17762)∩X(37)X(27274)

Barycentrics    b*c*(-a^2 + b^2 + b*c + c^2) : :

X(33939) lies on these lines: {1, 33931}, {10, 17762}, {37, 27274}, {39, 3797}, {72, 33297}, {75, 1125}, {76, 85}, {99, 7283}, {190, 17206}, {274, 321}, {279, 32836}, {306, 21587}, {313, 502}, {314, 943}, {316, 7270}, {319, 3678}, {325, 3695}, {335, 22036}, {345, 7763}, {346, 3926}, {348, 32833}, {350, 1930}, {538, 7187}, {668, 3701}, {693, 29224}, {894, 1509}, {1043, 4561}, {1089, 1909}, {1231, 4554}, {1914, 30167}, {1921, 18050}, {1978, 18359}, {2140, 27487}, {2901, 33296}, {3159, 16887}, {3175, 16712}, {3263, 3702}, {3596, 20570}, {3807, 4006}, {3954, 31027}, {3992, 25280}, {3995, 16705}, {4037, 16720}, {4043, 18157}, {4135, 24215}, {4358, 17292}, {4359, 29609}, {4385, 18156}, {4417, 21594}, {4568, 18035}, {4671, 29569}, {4692, 25303}, {4872, 7768}, {5074, 7112}, {6381, 20955}, {6382, 30022}, {7035, 11607}, {7757, 25918}, {7769, 32851}, {7796, 17181}, {7799, 16577}, {10009, 20923}, {17137, 25253}, {17141, 29824}, {17147, 27162}, {17200, 30939}, {17322, 27784}, {18061, 29960}, {18135, 29587}, {18145, 26563}, {18146, 20942}, {18743, 29604}, {20179, 30130}, {20541, 30173}, {20951, 21081}, {28605, 29592}, {28808, 32832}, {30168, 30940}

X(33939) = isotomic conjugate of X(2160)
X(33939) = {X(1),X(33931)}-harmonic conjugate of X(33941)
X(33939) = {X(350),X(1930)}-harmonic conjugate of X(33940)


X(33940) =  X(1)X(20924)∩X(2)X(20432)

Barycentrics    b*c*(a^2 + b^2 - b*c + c^2) : :

X(33940) lies on these lines: {1, 20924}, {2, 20432}, {7, 315}, {10, 75}, {21, 99}, {39, 33891}, {63, 19805}, {83, 894}, {85, 10106}, {115, 27966}, {190, 17681}, {239, 7760}, {312, 29596}, {316, 4911}, {320, 3874}, {321, 10159}, {350, 1930}, {474, 26240}, {519, 20955}, {668, 26563}, {742, 17034}, {903, 17677}, {1015, 7187}, {1078, 1447}, {1086, 6656}, {1111, 1909}, {1125, 20893}, {2064, 19786}, {3096, 3662}, {3261, 21201}, {3263, 18140}, {3598, 3785}, {3701, 18145}, {3705, 7796}, {3735, 33890}, {3743, 17320}, {3758, 7878}, {3759, 7894}, {3946, 17788}, {3954, 31004}, {4000, 7803}, {4202, 30893}, {4359, 16815}, {4361, 7754}, {4363, 7770}, {4396, 30167}, {4660, 9941}, {4972, 20969}, {4986, 25280}, {5254, 7263}, {7179, 7752}, {7232, 7879}, {7762, 17365}, {7794, 30179}, {7859, 16600}, {7877, 17364}, {11185, 31995}, {16720, 26959}, {17023, 17789}, {17137, 20247}, {17140, 20556}, {17141, 20347}, {17143, 20911}, {17288, 32027}, {17302, 20234}, {17380, 20444}, {17669, 31129}, {17760, 18061}, {18054, 25959}, {18135, 31130}, {20271, 24190}, {20934, 29654}, {21208, 24170}, {24326, 27020}, {24357, 27255}, {24403, 27097}, {24993, 25965}, {25237, 27109}, {25368, 27274}, {25928, 26665}, {26100, 31087}, {26273, 33828}, {27040, 31077}, {28605, 29591}, {31083, 33836}, {33146, 33736}

X(33940) = {X(75),X(76)}-harmonic conjugate of X(33941)
X(33940) = {X(350),X(1930)}-harmonic conjugate of X(33939)


X(33941) =  X(8)X(315)∩X(10)X(75)

Barycentrics    b*c*(a^2 + b^2 + b*c + c^2) : :

X(33941) lies on these lines: {1, 33931}, {8, 315}, {10, 75}, {83, 213}, {99, 7061}, {172, 30167}, {257, 712}, {274, 1390}, {312, 17023}, {316, 5015}, {319, 4911}, {335, 21240}, {350, 1089}, {518, 33297}, {519, 17762}, {594, 6656}, {596, 24170}, {626, 30179}, {668, 4696}, {742, 17499}, {894, 7760}, {1078, 7081}, {1125, 20947}, {1500, 3797}, {1909, 1930}, {2345, 7803}, {2481, 6540}, {2901, 4360}, {3096, 3661}, {3496, 3729}, {3701, 18140}, {3702, 33775}, {3705, 7752}, {3758, 7894}, {3759, 7878}, {3785, 7172}, {3923, 12194}, {3934, 33891}, {4358, 29614}, {4359, 29610}, {4361, 7770}, {4363, 7754}, {4399, 7745}, {4445, 7879}, {4647, 4986}, {4665, 5254}, {7179, 7796}, {7762, 17362}, {7812, 29617}, {7859, 17289}, {7877, 17363}, {7883, 29615}, {9055, 21024}, {9902, 24293}, {10159, 17291}, {11185, 32087}, {14210, 25303}, {17137, 17165}, {17141, 17751}, {17163, 20556}, {17233, 33838}, {17287, 32027}, {17319, 27569}, {17750, 31317}, {17752, 24254}, {17758, 27487}, {18061, 30038}, {20179, 30133}, {21021, 27020}, {21101, 29960}, {22011, 30109}, {24326, 25264}, {24549, 32920}, {24995, 33162}, {26035, 31087}, {26978, 31077}, {31623, 31926}

X(33941) = {X(1),X(33931)}-harmonic conjugate of X(33939)
X(33941) = {X(75),X(76)}-harmonic conjugate of X(33940)
X(33941) = {X(75),X(6376)}-harmonic conjugate of X(33945)


X(33942) =  X(1)X(3263)∩X(2)X(1930)

Barycentrics    b*c*(-a^2 - a*b + b^2 - a*c + c^2) : :

X(33942) lies on these lines: {1, 3263}, {2, 1930}, {6, 30130}, {8, 14210}, {10, 304}, {32, 24358}, {37, 30110}, {69, 3678}, {75, 1125}, {76, 20947}, {85, 3947}, {86, 30142}, {145, 4986}, {305, 29653}, {312, 20888}, {321, 16831}, {325, 30172}, {344, 25065}, {345, 25583}, {519, 18156}, {712, 20271}, {975, 10436}, {984, 16887}, {986, 24170}, {1111, 18135}, {1698, 20911}, {1759, 24602}, {3061, 30109}, {3266, 29643}, {3314, 30173}, {3616, 31130}, {3624, 26234}, {3664, 3718}, {3673, 18743}, {3701, 3761}, {3702, 32104}, {3735, 20255}, {3754, 24282}, {3760, 4358}, {3836, 4920}, {3874, 30962}, {3878, 21281}, {3905, 30117}, {3932, 3933}, {3954, 30945}, {3971, 24214}, {4009, 4059}, {4253, 17755}, {4359, 25585}, {4360, 30148}, {4376, 5277}, {4561, 22836}, {4871, 24172}, {5282, 29473}, {5283, 16720}, {5552, 17880}, {5692, 17137}, {5904, 30941}, {6376, 20924}, {7822, 17279}, {8024, 29854}, {10481, 21609}, {14377, 17738}, {16502, 30133}, {16611, 21216}, {16703, 17210}, {16777, 30129}, {16998, 30167}, {17063, 24166}, {17141, 18398}, {17143, 24331}, {17165, 17169}, {17175, 32771}, {17181, 29641}, {17205, 24068}, {17211, 25957}, {17321, 27784}, {17753, 19582}, {17760, 29968}, {17776, 23581}, {17789, 30830}, {17861, 20629}, {19815, 24781}, {20435, 29982}, {20923, 21443}, {21232, 29400}, {24549, 30115}, {25599, 28606}, {27097, 31087}, {27248, 28594}, {27299, 30791}, {27514, 28410}, {30107, 30748}, {30636, 30690}

X(33942) = {X(1),X(3263)}-harmonic conjugate of X(33937)
X(33942) = {X(2),X(1930)}-harmonic conjugate of X(33945)


X(33943) =  X(1)X(75)∩X(2)X(16720)

Barycentrics    b*c*(-a^2 - a*b + b^2 - a*c - b*c + c^2) : :

X(33943) lies on these lines: {1, 75}, {2, 16720}, {10, 20924}, {12, 85}, {72, 320}, {76, 20947}, {92, 31916}, {142, 17760}, {257, 20255}, {312, 17244}, {321, 29569}, {344, 25242}, {350, 20880}, {384, 24358}, {742, 16827}, {764, 20949}, {1001, 32117}, {1107, 7187}, {1111, 18140}, {1125, 20893}, {1909, 3263}, {2140, 18061}, {3673, 30963}, {3735, 24190}, {3739, 17788}, {4372, 16998}, {4376, 16915}, {4406, 5592}, {4568, 17758}, {4687, 25499}, {4751, 20444}, {4986, 7278}, {6051, 17320}, {6646, 21879}, {7200, 21226}, {7760, 30130}, {7794, 30173}, {7796, 30172}, {16601, 17263}, {16604, 33891}, {16826, 20432}, {17141, 17169}, {17367, 19804}, {17673, 25345}, {18055, 30949}, {18743, 25525}, {20271, 33890}, {20925, 20943}, {21432, 26234}, {21604, 27706}, {21608, 30054}, {21613, 23807}, {25083, 33116}, {25263, 26978}, {25280, 30806}, {27487, 29960}

X(33943) = {X(2),X(33930)}-harmonic conjugate of X(33944)
X(33943) = {X(1909),X(3263)}-harmonic conjugate of X(33938)


X(33944) =  X(1)X(20955)∩X(2)X(16720)

Barycentrics    b*c*(a^2 + a*b + b^2 + a*c - b*c + c^2) : :

X(33944) lies on these lines: {1, 20955}, {2, 16720}, {10, 75}, {56, 85}, {257, 21138}, {261, 16709}, {274, 1111}, {304, 29637}, {312, 17292}, {320, 942}, {321, 29591}, {350, 3702}, {1086, 26558}, {1089, 18145}, {1107, 33891}, {1125, 20924}, {1909, 5484}, {1930, 18140}, {3634, 20893}, {3662, 20271}, {3721, 31004}, {3739, 25994}, {3846, 18208}, {3931, 17320}, {3975, 4359}, {4363, 26687}, {4372, 16997}, {4376, 16916}, {4657, 17788}, {4812, 17238}, {5745, 30854}, {6537, 21431}, {6625, 26806}, {7187, 16604}, {7264, 17143}, {7535, 20914}, {16583, 16706}, {16739, 18021}, {16815, 17595}, {16887, 21208}, {16918, 24358}, {17202, 18189}, {17256, 30892}, {17324, 21442}, {17326, 20234}, {17400, 20444}, {17489, 26100}, {17673, 25357}, {18743, 29596}, {18834, 26191}, {20349, 26842}, {20432, 29610}, {20894, 28611}, {20954, 21201}, {21604, 27966}, {24326, 26752}, {24403, 26759}, {24589, 30577}, {25303, 30806}, {25345, 33834}, {26801, 27918}, {27487, 29968}, {27912, 27954}

X(33944) = {X(2),X(33930)}-harmonic conjugate of X(33943)
X(33944) = {X(75),X(6376)}-harmonic conjugate of X(33938)


X(33945) =  X(1)X(20911)∩X(2)X(1930)

Barycentrics    b*c*(a^2 + a*b + b^2 + a*c + c^2) : :

X(33945) lies on these lines: {1, 20911}, {2, 1930}, {7, 1330}, {8, 20247}, {10, 75}, {58, 274}, {63, 169}, {69, 3874}, {85, 4298}, {101, 16822}, {192, 28594}, {304, 1125}, {312, 29604}, {321, 3760}, {551, 18156}, {742, 17750}, {982, 16739}, {1089, 18135}, {1111, 20345}, {1500, 24357}, {1698, 3263}, {1722, 25590}, {2176, 24254}, {3008, 17789}, {3290, 30110}, {3616, 14210}, {3617, 4986}, {3634, 30758}, {3739, 16583}, {3741, 24172}, {3743, 17321}, {3754, 21281}, {3757, 26236}, {3761, 4968}, {3846, 4920}, {3878, 24282}, {3905, 30115}, {4095, 29400}, {4253, 24631}, {4360, 30145}, {4361, 30133}, {4372, 5277}, {4388, 33865}, {4441, 4647}, {4456, 28287}, {4688, 16605}, {4699, 16611}, {4850, 25599}, {4894, 20553}, {5275, 30130}, {5902, 17137}, {5903, 17152}, {5904, 17141}, {7182, 10481}, {9780, 31130}, {9941, 33076}, {10447, 17863}, {10479, 24204}, {10527, 17880}, {15668, 30126}, {16478, 17200}, {16703, 17175}, {16997, 30167}, {17030, 33891}, {17048, 29455}, {17211, 25760}, {17352, 20933}, {17499, 31317}, {17760, 29991}, {18398, 30941}, {20271, 21240}, {20518, 23100}, {20898, 26061}, {20924, 31997}, {21070, 27474}, {21432, 24589}, {24165, 24214}, {24170, 24174}, {24549, 30117}, {26181, 26191}, {26274, 27248}, {27026, 31087}

X(33945) = {X(2),X(1930)}-harmonic conjugate of X(33942)
X(33945) = {X(75),X(6376)}-harmonic conjugate of X(33941)


X(33946) =  X(2)X(21138)∩X(75)X(2170)

Barycentrics    (a - b)*(a - c)*(b^2 - b*c + c^2) : :

X(33946) lies on these lines: {2, 21138}, {75, 2170}, {85, 18055}, {99, 163}, {150, 30225}, {190, 644}, {194, 17475}, {257, 16720}, {304, 20642}, {335, 7200}, {514, 668}, {698, 19565}, {835, 29075}, {932, 4367}, {1111, 18061}, {1909, 4876}, {1959, 17789}, {2275, 33890}, {3212, 19593}, {3570, 3732}, {3644, 17460}, {3721, 7187}, {3729, 4919}, {3808, 3888}, {3865, 16889}, {4554, 27805}, {4595, 21272}, {4639, 7260}, {7847, 33870}, {7985, 24349}, {9055, 9263}, {17464, 18156}, {18159, 21139}, {20535, 21281}, {20955, 33299}, {20982, 21431}, {21208, 27195}, {30790, 31640}

X(33946) = anticomplement of X(21138)
X(33946) = {X(3721),X(7187)}-harmonic conjugate of X(33947)


X(33947) =  X(1)X(16712)∩X(2)X(4754)

Barycentrics    (a + b)*(a + c)*(b^2 - b*c + c^2) : :

X(33947) lies on these lines: {1, 16712}, {2, 4754}, {6, 33826}, {7, 21}, {8, 16711}, {10, 274}, {69, 16714}, {81, 21997}, {85, 1393}, {99, 28574}, {145, 18600}, {190, 27097}, {194, 30945}, {257, 7200}, {310, 6384}, {314, 1266}, {320, 1193}, {333, 16752}, {335, 16720}, {350, 24214}, {849, 1509}, {1086, 26801}, {1125, 17180}, {1475, 16706}, {2275, 3662}, {3570, 33828}, {3624, 17175}, {3632, 33297}, {3670, 20924}, {3721, 7187}, {3794, 7185}, {3834, 16696}, {4352, 30962}, {4415, 26113}, {4442, 30660}, {4871, 31008}, {4921, 29590}, {5224, 17674}, {5235, 24183}, {5333, 16047}, {7760, 29473}, {7799, 25645}, {16604, 31004}, {16709, 17250}, {16726, 16744}, {16737, 18299}, {16742, 18172}, {16750, 26015}, {16827, 24690}, {16975, 24190}, {17033, 24691}, {17178, 26835}, {17206, 33295}, {17207, 17304}, {17230, 30965}, {17274, 21214}, {17276, 24652}, {17283, 27109}, {17290, 18198}, {17300, 33021}, {17378, 19767}, {18055, 25918}, {20072, 27644}, {20255, 21226}, {20943, 28660}, {20955, 24443}, {24663, 24803}, {25350, 26752}, {26959, 30997}, {30811, 32821}, {30940, 33149}, {33120, 33730}

X(33947) = {X(3721),X(7187)}-harmonic conjugate of X(33946)


X(33948) =  X(8)X(33775)∩X(72)X(33297)

Barycentrics    (a - b)*(a - c)*(a*b + b^2 + a*c + b*c + c^2) : :

X(33948) lies on these lines: {8, 33775}, {72, 33297}, {75, 10176}, {76, 21403}, {99, 101}, {315, 1265}, {316, 16086}, {319, 4134}, {664, 6540}, {668, 891}, {758, 20947}, {789, 29071}, {815, 839}, {1015, 33888}, {1018, 3807}, {1305, 29337}, {3159, 33296}, {3678, 17762}, {4103, 4595}, {4518, 5977}, {4717, 5564}, {9059, 29059}, {16827, 22036}, {17143, 25253}, {17755, 18061}, {24282, 27538}


X(33949) =  X(1)X(4056)∩X(2)X(5244)

Barycentrics    (a + b - c)*(a - b + c)*(a*b + b^2 + a*c + b*c + c^2) : :

X(33949) lies on these lines: {1, 4056}, {2, 5244}, {3, 33865}, {7, 21}, {12, 3212}, {35, 33866}, {37, 27129}, {55, 33867}, {57, 17095}, {65, 7179}, {76, 85}, {279, 1255}, {388, 664}, {942, 17181}, {1088, 18651}, {1447, 11375}, {1565, 6147}, {1996, 14256}, {3218, 27187}, {3295, 5195}, {3487, 14828}, {3671, 9436}, {3673, 12047}, {3782, 4352}, {3876, 5224}, {3926, 32939}, {4059, 7185}, {4080, 4624}, {4315, 25723}, {4417, 20911}, {4454, 32840}, {4654, 17078}, {4955, 24798}, {5290, 9312}, {6604, 17152}, {7176, 10404}, {7196, 30964}, {7264, 18393}, {9650, 24281}, {10030, 29990}, {11036, 14548}, {11680, 20247}, {16062, 17211}, {17234, 18055}, {18600, 33146}, {24215, 33103}, {26563, 31053}


X(33950) =  X(2)X(169)∩X(3)X(26690)

Barycentrics    a*(a - b - c)*(a^2 + b^2 - b*c + c^2) : :

X(33950) lies on these lines: {2, 169}, {3, 26690}, {5, 27068}, {6, 977}, {8, 9}, {10, 5540}, {19, 4200}, {21, 294}, {35, 24036}, {37, 33882}, {41, 3061}, {55, 25082}, {63, 5222}, {100, 25066}, {145, 17742}, {149, 21073}, {150, 26526}, {218, 3869}, {220, 3877}, {239, 3219}, {377, 5819}, {404, 910}, {519, 17744}, {594, 7300}, {644, 3057}, {672, 3496}, {673, 20880}, {758, 17745}, {894, 20605}, {960, 2348}, {1475, 3509}, {1565, 27006}, {1621, 16601}, {1729, 5826}, {1743, 12526}, {1752, 19843}, {1759, 3218}, {1760, 3618}, {1766, 20070}, {2170, 2329}, {2243, 33863}, {2297, 18594}, {2339, 5273}, {2478, 6554}, {3086, 26258}, {3101, 5294}, {3160, 7131}, {3177, 17691}, {3244, 5525}, {3305, 29611}, {3452, 28813}, {3661, 21373}, {3684, 4420}, {3693, 3871}, {3732, 17681}, {3794, 20229}, {3878, 5526}, {3885, 4513}, {3957, 3970}, {4051, 4390}, {4209, 27340}, {4254, 27396}, {4391, 18086}, {4512, 28043}, {4850, 9605}, {4857, 21090}, {4872, 33839}, {4936, 9819}, {5011, 16549}, {5046, 5179}, {5280, 17016}, {5282, 21384}, {5299, 7191}, {5305, 33133}, {5330, 6603}, {5332, 16974}, {5750, 16547}, {6919, 27541}, {7187, 33826}, {7283, 26770}, {7297, 17369}, {8074, 24982}, {11343, 24635}, {11344, 15288}, {16502, 26242}, {16503, 21808}, {16555, 29654}, {16583, 33854}, {16779, 28082}, {16823, 18785}, {17023, 20602}, {17046, 24712}, {17183, 27420}, {17261, 28598}, {17277, 20911}, {17292, 21383}, {17349, 21216}, {17368, 27059}, {17541, 25994}, {17671, 27132}, {17752, 20372}, {18228, 28795}, {21215, 26203}, {21372, 27003}, {25918, 33830}, {26279, 26959}


X(33951) =  X(75)X(5540)∩X(99)X(666)

Barycentrics    (a - b)*(a - c)*(a^2 + b^2 - b*c + c^2) : :

X(33951) lies on these lines: {75, 5540}, {99, 666}, {100, 6012}, {190, 646}, {274, 18785}, {304, 16550}, {514, 18047}, {894, 3125}, {1016, 21272}, {1111, 29479}, {1577, 29420}, {2503, 21431}, {3570, 4568}, {4737, 5541}, {7760, 17489}, {9318, 18061}, {16555, 20934}, {17332, 21711}, {17351, 21888}, {17744, 20955}, {17789, 20602}, {20096, 30225}, {20933, 21378}, {26273, 27195}


X(33952) =  X(35)X(17760)∩X(99)X(163)

Barycentrics    (a - b)*(a - c)*(a^2 + a*b + b^2 + a*c + c^2) : :

X(33952) lies on these lines: {35, 17760}, {99, 163}, {100, 831}, {190, 646}, {304, 1759}, {595, 17489}, {712, 1914}, {835, 29063}, {894, 4424}, {1089, 17739}, {1111, 17738}, {1331, 2398}, {1724, 21216}, {1930, 3496}, {3125, 24358}, {3263, 5011}, {3509, 14210}, {3729, 4692}, {3735, 4376}, {3905, 7031}, {4400, 22036}, {4482, 21272}, {4781, 25272}, {4920, 30104}, {5540, 17755}, {6656, 33870}, {16788, 24282}, {17736, 18156}, {18061, 25532}, {26561, 33868}


X(33953) =  X(1)X(75)∩X(2)X(4251)

Barycentrics    (a + b)*(a + c)*(a^2 - a*b + b^2 - a*c + c^2) : :

X(33953) lies on these lines: {1, 75}, {2, 4251}, {6, 25497}, {21, 16887}, {32, 29473}, {41, 30110}, {58, 30941}, {69, 1724}, {81, 3912}, {99, 28574}, {100, 24170}, {101, 27097}, {141, 17540}, {325, 25645}, {333, 17284}, {595, 17137}, {894, 3970}, {1333, 29789}, {1434, 4234}, {1914, 21240}, {2170, 30128}, {2193, 18639}, {2280, 30107}, {2327, 28409}, {2329, 25536}, {3865, 4594}, {3954, 24358}, {4000, 4483}, {4184, 17208}, {4253, 33819}, {4256, 27162}, {4262, 33830}, {4357, 5259}, {4653, 16705}, {4754, 24275}, {4872, 17211}, {4911, 33124}, {5011, 26562}, {5235, 29596}, {5299, 27644}, {5333, 17023}, {6629, 16948}, {7031, 24586}, {7776, 30811}, {7787, 17232}, {8025, 17316}, {10479, 16992}, {11110, 17210}, {11115, 17169}, {13740, 14828}, {16050, 17742}, {16503, 16818}, {16552, 33821}, {16704, 29579}, {16738, 16788}, {16784, 30038}, {17046, 30104}, {17170, 17183}, {17353, 17745}, {17451, 30131}, {17499, 33816}, {17686, 17758}, {20911, 30117}, {21840, 30126}, {24211, 29656}, {24632, 30965}, {25507, 29598}, {25532, 26959}, {25669, 30761}, {26843, 27185}, {26860, 29583}, {28618, 29646}, {29637, 30966}, {29674, 33295}


X(33954) =  X(1)X(75)∩X(2)X(18755)

Barycentrics    (a + b)*(a + c)*(a^2 - a*b + b^2 - a*c + b*c + c^2) : :

X(33954) lies on these lines: {1, 75}, {2, 18755}, {6, 17688}, {8, 33295}, {10, 8298}, {21, 6626}, {58, 17731}, {69, 4195}, {81, 2295}, {99, 16887}, {141, 384}, {172, 31027}, {190, 3954}, {218, 17354}, {316, 3454}, {319, 5247}, {333, 3661}, {385, 21024}, {405, 2893}, {519, 17200}, {904, 7018}, {1213, 16912}, {1434, 30617}, {2238, 33816}, {3570, 27040}, {3619, 17691}, {3763, 33827}, {3797, 16519}, {4184, 23339}, {4234, 17206}, {4357, 12579}, {5235, 16047}, {5291, 29767}, {5293, 20947}, {5333, 29586}, {5337, 14829}, {6651, 21879}, {7928, 19667}, {8025, 29588}, {10449, 33745}, {11115, 17103}, {11320, 32782}, {11321, 17234}, {13588, 17798}, {13735, 17271}, {14012, 33171}, {16053, 17308}, {16065, 31330}, {16394, 17378}, {16911, 17245}, {16913, 17232}, {16914, 17238}, {16915, 30945}, {17139, 33867}, {17277, 33821}, {17283, 17682}, {17397, 24789}, {17499, 24275}, {18047, 26759}, {18134, 19281}, {19269, 25650}, {20179, 29960}, {20541, 30175}, {20955, 24291}, {24552, 30660}, {25787, 25866}, {27332, 28753}

X(33954) = crosspoint, wrt excentral or anticomplementary triangle, of X(1) and X(2896)


X(33955) =  X(1)X(75)∩X(2)X(3108)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - b*c + c^2) : :

X(33955) lies on these lines: {1, 75}, {2, 3108}, {21, 16712}, {60, 1509}, {76, 5192}, {81, 17367}, {83, 26978}, {99, 9109}, {194, 25497}, {320, 1203}, {538, 33816}, {754, 33831}, {764, 17212}, {894, 21802}, {1014, 7185}, {1078, 27162}, {3788, 17003}, {4202, 7768}, {4400, 27324}, {5007, 33826}, {5262, 20924}, {5299, 16706}, {5309, 33836}, {5333, 17244}, {6179, 33830}, {7757, 33819}, {7759, 16906}, {7765, 33820}, {7790, 26099}, {7801, 16905}, {7812, 16910}, {7827, 33839}, {7840, 16908}, {7855, 16991}, {7877, 26085}, {8025, 16752}, {11115, 16711}, {13741, 18145}, {16480, 17770}, {16705, 17588}, {16720, 30168}, {16726, 16735}, {16887, 33295}, {16992, 19273}, {17000, 25499}, {17103, 17200}, {17378, 33833}, {17392, 17670}, {17526, 32833}, {20179, 24790}


X(33956) =  X(1)X(5123)∩X(8)X(1319)

Barycentrics    4*a^4 - 5*a^3*b - 2*a^2*b^2 + 5*a*b^3 - 2*b^4 - 5*a^3*c + 14*a^2*b*c - 7*a*b^2*c - 2*a^2*c^2 - 7*a*b*c^2 + 4*b^2*c^2 + 5*a*c^3 - 2*c^4 : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29319.

X(33956) lies on these lines: {1, 5123}, {8, 1319}, {10, 25405}, {30, 511}, {36, 3632}, {145, 1837}, {355, 22835}, {484, 6762}, {496, 3244}, {944, 13528}, {956, 32760}, {1155, 3621}, {1317, 6735}, {1376, 5193}, {1483, 10915}, {2077, 3913}, {2136, 10085}, {3583, 26726}, {3625, 5126}, {3626, 6681}, {3633, 9614}, {3838, 5252}, {4511, 20586}, {5057, 20014}, {5080, 5225}, {5122, 24391}, {5183, 20053}, {5440, 7972}, {5690, 18857}, {5836, 10944}, {5881, 10912}, {6700, 33559}, {8666, 23961}, {10106, 10107}, {10950, 17615}, {11236, 16200}, {11256, 12531}, {11681, 33176}, {12629, 17857}, {12641, 17613}, {20054, 20067}, {24477, 31145}, {25416, 30384}, {27870, 33899}

X(33956) = crossdifference of every pair of points on line X(6)X(17424)


X(33957) =  X(15)X(1337)∩X(30)X(511)

Barycentrics    a^2*(b^2*(a^2 - b^2)*(Sqrt[3]*c^2 + 2*S)*(Sqrt[3]*(a^2 + b^2 - c^2) + 2*S) + c^2*(a^2 - c^2)*(Sqrt[3]*b^2 + 2*S)*(Sqrt[3]*(a^2 - b^2 + c^2) + 2*S)) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29319.

X(33957) lies on these lines: {15, 1337}, {30, 511}, {51, 15768}, {396, 15929}, {621, 10210}, {623, 33500}, {2979, 16259}, {3060, 30439}, {6671, 32223}, {8172, 25177}, {14178, 25225}, {14538, 18863}, {16267, 16461}, {25219, 25221}


X(33958) =  X(16)X(1338)∩X(30)X(511)

Barycentrics    a^2*(b^2*(a^2 - b^2)*(Sqrt[3]*c^2 - 2*S)*(Sqrt[3]*(a^2 + b^2 - c^2) - 2*S) + c^2*(a^2 - c^2)*(Sqrt[3]*b^2 - 2*S)*(Sqrt[3]*(a^2 - b^2 + c^2) - 2*S)) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29319.

X(33958) lies on these lines: {16, 1338}, {30, 511}, {51, 15769}, {395, 15930}, {624, 33498}, {2979, 16260}, {3060, 30440}, {6672, 32223}, {8173, 25182}, {14182, 25226}, {14539, 18864}, {16268, 16462}, {25220, 25222}


X(33959) =  X(15)X(22113)∩X(16)X(629)

Barycentrics    (a^2 - b^2)*(a^2 + b^2 - c^2 + 2*Sqrt[3]*S)*(3*a^2 + 3*b^2 - c^2 + 2*Sqrt[3]*S) + (a^2 - c^2)*(a^2 - b^2 + c^2 + 2*Sqrt[3]*S)*(3*a^2 - b^2 + 3*c^2 + 2*Sqrt[3]*S) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29319.

X(33959) lies on these lines: {15, 22113}, {16, 629}, {17, 622}, {30, 511}, {623, 627}, {624, 6673}, {5615, 16626}, {7684, 16629}, {14138, 33465}, {14369, 31939}, {14538, 22916}, {20429, 22832}, {22737, 22907}, {22901, 33518}


X(33960) =  X(15)X(630)∩X(16)X(22114)

Barycentrics    (a^2 - b^2)*(a^2 + b^2 - c^2 - 2*Sqrt[3]*S)*(3*a^2 + 3*b^2 - c^2 - 2*Sqrt[3]*S) + (a^2 - c^2)*(a^2 - b^2 + c^2 - 2*Sqrt[3]*S)*(3*a^2 - b^2 + 3*c^2 - 2*Sqrt[3]*S) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29319.

X(33960) lies on these lines: {15, 630}, {16, 22114}, {18, 621}, {30, 511}, {623, 6674}, {624, 628}, {5611, 16627}, {7685, 16628}, {14139, 33464}, {14368, 31940}, {14539, 22871}, {20428, 22831}, {22736, 22861}, {22855, 33517}


X(33961) =  X(11)X(14527)∩X(12)X(21)

Barycentrics    (a + c)*(a - b + c)*(c*(-a - b + c)^2*(b + c)^3 + a*(a + b)^3*(a - b - c)*(-a + b + c)) - (a + b)*(a + b - c)*(b*(-a + b - c)*(a - b + c)*(b + c)^3 - a*(a - b - c)*(a + c)^3*(-a + b + c)) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29319.

X(33961) lies on these lines: {11, 14527}, {12, 21}, {30, 511}, {36, 442}, {55, 15680}, {1319, 11281}, {2099, 14450}, {2475, 2886}, {3035, 27086}, {3419, 6763}, {3651, 30264}, {3814, 6668}, {4996, 15326}, {5057, 10543}, {5131, 11112}, {5176, 21677}, {5180, 6284}, {5426, 11113}, {5427, 6667}, {5428, 31659}, {5536, 6598}, {6175, 31157}, {7680, 13743}, {8666, 18407}, {11263, 18990}, {11491, 11827}, {15670, 31160}, {21155, 21161}, {22765, 26470}, {31254, 31260}, {31799, 32157}


X(33962) =  X(1)X(3325)∩X(3)X(111)

Barycentrics    a^2*(a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8 + a^6*c^2 - 14*a^4*b^2*c^2 + 10*a^2*b^4*c^2 + 7*b^6*c^2 + a^4*c^4 + 10*a^2*b^2*c^4 - 20*b^4*c^4 - a^2*c^6 + 7*b^2*c^6 - c^8) : :

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29319.

X(33962) lies on these lines: {1, 3325}, {3, 111}, {4, 10748}, {5, 126}, {20, 14654}, {26, 14657}, {30, 511}, {49, 3048}, {99, 12093}, {140, 6719}, {143, 22100}, {182, 14688}, {351, 19901}, {352, 9871}, {376, 14666}, {381, 10717}, {382, 10734}, {549, 9172}, {574, 10204}, {1151, 11835}, {1152, 11836}, {1351, 10765}, {1385, 11721}, {1482, 10704}, {1511, 9129}, {2493, 9177}, {5077, 7998}, {5640, 11159}, {5650, 20326}, {5971, 13168}, {6076, 6077}, {6093, 14514}, {6407, 11833}, {6408, 11834}, {7514, 15560}, {9734, 14662}, {10738, 10779}, {11171, 15921}, {11287, 33879}, {12006, 14135}, {33532, 33900}

X(33962) = isogonal conjugate of X(6093)
X(33962) = crossdifference of every pair of points on line X(6)X(9125)
X(33962) = X(30) of 4th anti-Brocard triangle


X(33963) =  ISOGONAL CONJUGATE OF X(6049)

Barycentrics    a^2 (a+b-3 c)^2 (a-b-c) (a-3 b+c)^2 : :

See Tran Viet Hung and Ercole Suppa, Hyacinthos 29320.

X(33963) lies on these lines: {11,6556}, {55,3445}, {200,2098}, {220,8163}, {1043,4345}, {1293,5204}, {3057,8056}, {3304,14261}, {7962,10563}, {12513,27834}, {16078,21453}

X(33963) = barycentric product of X(i) and X(j) for these {i,j}: {220,16078}, {346,16079}, {3445,6557}, {3680,8056}
X(33963) = barycentric quotient of X(i) and X(j) for these {i,j}: {6,6049}, {220,15519}, {657,4943}, {663,31182}, {3445,5435}, {3680,18743}, {16079,279}
X(33963) = trilinear product of X(i) and X(j) for these {i,j}: {200,16079}, {1253,16078}, {1253,16078}, {3445,3680}, {6556,16945}
X(33963) = trilinear quotient of X(i) and X(j) for these {i,j}: {1,6049}, {200,15519}, {3900,4943}


X(33964) =  X(1)X(16168)∩X(11)X(25641)

Barycentrics    (a+b-c) (a-b+c) (b+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)^2 : :

See Tran Viet Hung and Ercole Suppa, Hyacinthos 29320.

X(33964) lies on the incircle and these lines: {1,16168}, {11,25641}, {12,3258}, {30,3024}, {55,477}, {56,476}, {388,14731}, {496,18319}, {523,3028}, {1478,20957}, {3023,7286}, {3025,24470}, {3649,31522}, {5432,31379}, {5433,22104}, {5434,6027}, {7158,10149}, {12091,18447}, {12903,17511}, {12953,14989}

X(33964) = reflection of X(33965) in X(1)
X(33964) = incircle antipode of X(33965)
X(33964) = X(477)-of-Mandart-incircle-triangle


X(33965) =  X(1)X(16168)∩X(11)X(3258)

Barycentrics    (b+c-a) (b-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)^2 : :

See Tran Viet Hung and Ercole Suppa, Hyacinthos 29320.

X(33965) lies on the incircle and these lines: {1,16168}, {11,3258}, {12,25641}, {30,3028}, {55,476}, {56,477}, {495,18319}, {497,14731}, {523,3024}, {1479,20957}, {3027,5160}, {3058,6023}, {5432,22104}, {5433,31379}, {10543,31524}, {12091,18455}, {12904,17511}, {12943,14989}

X(33965) = reflection of X(33964) in X(1)
X(33965) = incircle antipode of X(33964)
X(33965) = X(476)-of-Mandart-incircle-triangle


X(33966) =  REFLECTION OF X(6025) IN X(1)

Barycentrics    (b-c)^2 (a-b+c) (a+b-c) (-a^3+a^2 b+a^2 c+b^2 c+b c^2)^2 : :
X(33966) = 2*X[1]-X[6025]

See Tran Viet Hung and Ercole Suppa, Hyacinthos 29320.

X(33966) lies on the incircle and these lines: {1,6025}, {11,25642}, {12,5513}, {56,675}, {544,1362}, {5433,31380}

X(33966) = reflection of X(6025) in X(1)


X(33967) =  COMPLEMENT OF X(14366)

Barycentrics    (b-c)^2 (b+c)^2 (-a^10 b^2+3 a^8 b^4-4 a^6 b^6+4 a^4 b^8-3 a^2 b^10+b^12-a^10 c^2+2 a^8 b^2 c^2-2 a^6 b^4 c^2+a^4 b^6 c^2+a^2 b^8 c^2-b^10 c^2+3 a^8 c^4-2 a^6 b^2 c^4-2 a^4 b^4 c^4+a^2 b^6 c^4+b^8 c^4-4 a^6 c^6+a^4 b^2 c^6+a^2 b^4 c^6-2 b^6 c^6+4 a^4 c^8+a^2 b^2 c^8+b^4 c^8-3 a^2 c^10-b^2 c^10+c^12) : :
X(33967) = 3*X[2]-X[14366]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29324.

X(33967) lies on these lines: {2,14366}, {3,30715}, {523,6328}, {868,5489}, {3767,6792}, {5007,23991}

X(33967) = complement of X(14366)


X(33968) =  X(520)X(647)∩X(525)X(14939)

Barycentrics    a^2 (b-c) (b+c) (a^2-b^2-c^2) (2 a^6-3 a^4 b^2+b^6-3 a^4 c^2+8 a^2 b^2 c^2-b^4 c^2-b^2 c^4+c^6) : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29328.

X(33968) lies on these lines: {520,647}, {525,14939}, {6587,14398}

X(33968) = barycentric product X(520)*X(1885)
X(33968) = barycentric quotient X(1885)/X(6528)


X(33969) =  X(650)X(663)∩X(3669)X(30574)

Barycentrics    a (a-b-c) (b-c) (a^4-2 a^2 b^2+b^4+4 a b^2 c-2 a^2 c^2+4 a b c^2-2 b^2 c^2+c^4) : :

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29328.

X(33969) lies on these lines: {650,663}, {3669,30574}, {9373,22091}

X(33969) = barycentric product X(4041)*X(24556)
X(33969) = barycentric quotient X(24556)/X(4625)
X(33969) = trilinear quotient X(3709)/X(24556)


X(33970) =  MIDPOINT OF X(11) AND X(105)

Barycentrics    2*a^8-4*(b+c)*a^7+(b^2+10*b*c+c^2)*a^6+2*(b+c)*(b^2-4*b*c+c^2)*a^5-(3*b^4+3*c^4-(9*b^2-10*b*c+9*c^2)*b*c)*a^4+(b^2-c^2)*(b-c)*(4*b^2-13*b*c+4*c^2)*a^3-(b^4+c^4-(9*b^2+2*b*c+9*c^2)*b*c)*(b-c)^2*a^2-(b^2-c^2)*(b-c)*(2*b^4+2*c^4+3*(b-c)^2*b*c)*a+(b^4-c^4)*(b^2-c^2)*(b-c)^2 : :
X(33970) = 3*X(11)-X(10773), 3*X(105)+X(10773), X(1292)-3*X(21154), X(5540)+3*X(16173), X(10743)-3*X(23513), X(20344)-5*X(31272)

See Tran Viet Hung and César Lozada, Hyacinthos 29332.

X(33970) lies on these lines: {2, 11}, {676, 2826}, {952, 11716}, {1292, 21154}, {1387, 2809}, {2829, 5511}, {3756, 11219}, {5540, 16173}, {6713, 28915}, {10743, 23513}

X(33970) = midpoint of X(11) and X(105)
X(33970) = reflection of X(i) in X(j) for these (i,j): (120, 6667), (3035, 6714)


X(33971) =  REFLECTION OF X(4) IN X(53)

Barycentrics    (a^2+b^2-c^2)^2 (a^2-b^2+c^2)^2 (a^4-a^2 b^2-a^2 c^2-2 b^2 c^2) : :
Barycentrics    (4 R^2 SB+4 R^2 SC+SB SC-SB SW-SC SW)S^2 - 4 R^2 SB SC SW+SB SC SW^2 : :
X(33971) = 2*X[389]-X[6751]

See Kadir Altintas and Ercole Suppa, Hyacinthos 29333.

X(33971) lies on these lines: {2,26870}, {3,95}, {4,6}, {5,17907}, {22,324}, {24,157}, {25,98}, {54,19212}, {154,436}, {182,458}, {186,2453}, {232,13860}, {275,11402}, {297,1352}, {317,3564}, {340,11898}, {389,6751}, {403,16324}, {427,9744}, {428,14495}, {467,11442}, {511,9308}, {648,1351}, {917,32704}, {930,23233}, {1093,1598}, {1141,23232}, {1300,30247}, {1593,11257}, {1594,23333}, {1597,11169}, {1896,4186}, {1948,24320}, {1993,19174}, {2871,6403}, {2980,10594} ,{3168,17810}, {3172,12110}, {4230,15928}, {4994,11423}, {5020,15466}, {5094,14165}, {5198,14249}, {5422,30506}, {5890,9792}, {6524,6995}, {6525,7714}, {6528,12188}, {6747,11550}, {6750,18381}, {6755,11245}, {6759,8887}, {6820,14826}, {9753,16318}, {9755,10311}, {10519,32000}, {11331,24206}, {11412,19197}, {13200,15356}, {15087,19177}, {16263,17983}, {17984,18027}, {18916,18953}, {19128,19156}, {19544,31623}

X(33971) = reflection of X(i) in X(j) for these {i,j}: {4,53}, {6751,389}, {18437,5}, {20477,3}
X(33971) = X(6)-of-circumorthic-triangle
X(33971) = X(3751)-of-orthic-triangle if ABC is acute
X(33971) = barycentric product of X(i) and X(j) for these {i,j}: {4,458}, {107,23878}, {182,2052}, {183,393}, {264,10311}, {1096,3403}, {2207,20023}, {3288,6528}
X(33971) = barycentric quotient of X(i) and X(j) for these {i,j}: {182,394}, {183,3926}, {393,262}, {458,69}, {1096,2186}, {2052,327}, {2207,263}, {3288,520}, {6784,3269}, {10311,3}, {20031,6037}, {23878,3265}, {32713,26714}
X(33971) = trilinear product of X(i) and X(j) for these {i,j}: {19,458}, {19,458}, {92,10311}, {158,182}, {158,182}, {183,1096}, {183,1096}, {823,3288}, {823,3288}, {2207,3403}, {2207,3403}, {6784,23999}, {6784,23999}, {23878,24019}
X(33971) = trilinear quotient of X(i) and X(j) for these {i,j}: {158,262}, {183,326}, {393,2186}, {2207,3402}, {3403,3926}, {24019,26714}
X(33971) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {4,393,6530}, {4,1249,14853}, {4,14912,3087}, {1629,2052,25}, {3087,15258,14912}, {6530,16264,4}, {8795,8884,19189}, {20477,20792,3}


X(33972) =  X(3)X(543)∩X(351)X(8723)

Barycentrics    a^2*(a^10 - 6*a^8*b^2 + 11*a^6*b^4 - 11*a^4*b^6 + 6*a^2*b^8 - b^10 - 6*a^8*c^2 + 19*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 12*a^2*b^6*c^2 + b^8*c^2 + 11*a^6*c^4 - 6*a^4*b^2*c^4 + 8*b^6*c^4 - 11*a^4*c^6 - 12*a^2*b^2*c^6 + 8*b^4*c^6 + 6*a^2*c^8 + b^2*c^8 - c^10) : :

X(33972) lies on the cubic K1116 and these lines: {3, 543}, {351, 8723}, {511, 9145}, {574, 3124}, {2482, 33929}


X(33973) =  X(6)X(23)∩X(1350)X(6233)

Barycentrics    a^2*(4*a^8 - 18*a^6*b^2 + 4*a^4*b^4 + 6*a^2*b^6 + 4*b^8 - 18*a^6*c^2 + a^4*b^2*c^2 + 13*a^2*b^4*c^2 + 6*b^6*c^2 + 4*a^4*c^4 + 13*a^2*b^2*c^4 - 8*b^4*c^4 + 6*a^2*c^6 + 6*b^2*c^6 + 4*c^8) : :

X(33973) lies on the cubics K1116 and K1124 and these lines: {6, 23}, {1350, 6233}, {5210, 6323}, {8667, 9830}


X(33974) =  X(3)X(13468)∩X(6)X(1196)

Barycentrics    a^2*(a^8 - 6*a^6*b^2 + 6*a^2*b^6 - b^8 - 6*a^6*c^2 + 24*a^4*b^2*c^2 - 6*a^2*b^4*c^2 + 12*b^6*c^2 - 6*a^2*b^2*c^4 - 38*b^4*c^4 + 6*a^2*c^6 + 12*b^2*c^6 - c^8) : :

X(33974) lies on the cubic K1120 and these lines: {3, 13468}, {6, 1196}, {7484, 9723}, {7669, 9909}, {20850, 33582}


X(33975) =  (name pending)

Barycentrics    a^2*(a^10 - 7*a^8*b^2 + 8*a^6*b^4 - 8*a^4*b^6 + 7*a^2*b^8 - b^10 - 7*a^8*c^2 + 36*a^6*b^2*c^2 - 8*a^4*b^4*c^2 - 36*a^2*b^6*c^2 - b^8*c^2 + 8*a^6*c^4 - 8*a^4*b^2*c^4 - 22*a^2*b^4*c^4 + 34*b^6*c^4 - 8*a^4*c^6 - 36*a^2*b^2*c^6 + 34*b^4*c^6 + 7*a^2*c^8 - b^2*c^8 - c^10) : :

X(33975) lies on the cubic K1120 and these lines: {3, 13468}


X(33976) =  X(6)X(22)∩X(826)X(3534)

Barycentrics    a^2*(b^2 + c^2)*(7*a^6 + 2*a^4*b^2 - 5*a^2*b^4 - 4*b^6 + 2*a^4*c^2 - 3*a^2*b^2*c^2 - b^4*c^2 - 5*a^2*c^4 - b^2*c^4 - 4*c^6) : :

X(33976) lies on the cubics K1120 and K1124,and these lines: {6, 22}, {826, 3534}, {1350, 29011}


X(33977) =  X(3)X(9740)∩X(6)X(5646)

Barycentrics    a^2*(a^8 + 14*a^6*b^2 - 14*a^2*b^6 - b^8 + 14*a^6*c^2 + 144*a^4*b^2*c^2 - 66*a^2*b^4*c^2 - 28*b^6*c^2 - 66*a^2*b^2*c^4 - 198*b^4*c^4 - 14*a^2*c^6 - 28*b^2*c^6 - c^8) : :

X(33977) lies on the cubic K1121 and these lines: {3, 9740}, {6, 5646}, {1995, 30698}


X(33978) =  X(3)X(9740)∩X(574)X(5646)

Barycentrics    a^2*(a^10 + 3*a^8*b^2 - 142*a^6*b^4 + 142*a^4*b^6 - 3*a^2*b^8 - b^10 + 3*a^8*c^2 + 316*a^6*b^2*c^2 - 78*a^4*b^4*c^2 - 516*a^2*b^6*c^2 + 19*b^8*c^2 - 142*a^6*c^4 - 78*a^4*b^2*c^4 - 882*a^2*b^4*c^4 + 494*b^6*c^4 + 142*a^4*c^6 - 516*a^2*b^2*c^6 + 494*b^4*c^6 - 3*a^2*c^8 + 19*b^2*c^8 - c^10) : :

X(33978) lies on the cubic K1121 and these lines: {3, 9740}, {574, 5646}


X(33979) =  X(6)X(373)∩X(111)X(1350)

Barycentrics    a^2*(5*a^4 - 14*a^2*b^2 - 7*b^4 - 14*a^2*c^2 + 46*b^2*c^2 - 7*c^4) : :

X(33979) lies on the cubics K1121 and K1124 and these lines: {6, 373}, {111, 1350}, {154, 2502}, {352, 11477}, {353, 5085}, {574, 5646}, {599, 16317}, {3231, 31860}, {3787, 11173}, {5210, 9486}, {6791, 15533}


X(33980) =  X(3)X(3849)∩X(6)X(23)

Barycentrics    a^2*(4*a^8 - 4*a^6*b^2 + 4*a^2*b^6 - 4*b^8 - 4*a^6*c^2 - 9*a^4*b^2*c^2 - 9*a^2*b^4*c^2 + 8*b^6*c^2 - 9*a^2*b^2*c^4 - 12*b^4*c^4 + 4*a^2*c^6 + 8*b^2*c^6 - 4*c^8) : :

X(33980) lies on the cubic K1123 and these lines: {3, 3849}, {6, 23}, {1995, 7669}, {7492, 11163}


X(33981) =  (name pending)

Barycentrics    a^2*(a^2 - 2*b^2 - 2*c^2)*(4*a^8 - 10*a^6*b^2 + 12*a^4*b^4 - 8*a^2*b^6 + 2*b^8 - 10*a^6*c^2 + 9*a^4*b^2*c^2 + 15*a^2*b^4*c^2 - 10*b^6*c^2 + 12*a^4*c^4 + 15*a^2*b^2*c^4 + 12*b^4*c^4 - 8*a^2*c^6 - 10*b^2*c^6 + 2*c^8) : :

X(33981) lies on the cubic K1123 and these lines: {3, 3849}


X(33982) =  X(6)X(14002)∩X(1350)X(8600)

Barycentrics    a^2*(80*a^8 - 196*a^6*b^2 + 184*a^4*b^4 - 20*a^2*b^6 - 48*b^8 - 196*a^6*c^2 + 133*a^4*b^2*c^2 - 71*a^2*b^4*c^2 + 140*b^6*c^2 + 184*a^4*c^4 - 71*a^2*b^2*c^4 - 164*b^4*c^4 - 20*a^2*c^6 + 140*b^2*c^6 - 48*c^8) : :

X(33982) lies on the cubics K1123 and K1124 and these lines: {6, 14002}, {1350, 8600}


X(33983) =  X(3)X(76)∩X(6)X(6784)

Barycentrics    a^2*(a^8*b^4 - a^4*b^8 + 3*a^8*b^2*c^2 - 3*a^6*b^4*c^2 + a^4*b^6*c^2 - 3*a^2*b^8*c^2 + a^8*c^4 - 3*a^6*b^2*c^4 - 3*a^4*b^4*c^4 + 5*a^2*b^6*c^4 - 3*b^8*c^4 + a^4*b^2*c^6 + 5*a^2*b^4*c^6 + 6*b^6*c^6 - a^4*c^8 - 3*a^2*b^2*c^8 - 3*b^4*c^8) : :

X(33983) lies on the cubic K1119 and these lines: {3, 76}, {6, 6784}, {385, 9512}, {1634, 15271}, {5201, 33900}

X(33983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 33758, 183}, {183, 9149, 3511}


X(33984) =  X(6)X(160)∩X(99)X(1350)

Barycentrics    a^2*(2*a^8*b^4 + 4*a^6*b^6 - 6*a^4*b^8 + 5*a^8*b^2*c^2 + 11*a^6*b^4*c^2 - 9*a^4*b^6*c^2 - 7*a^2*b^8*c^2 + 2*a^8*c^4 + 11*a^6*b^2*c^4 - 12*a^4*b^4*c^4 - 5*a^2*b^6*c^4 - 2*b^8*c^4 + 4*a^6*c^6 - 9*a^4*b^2*c^6 - 5*a^2*b^4*c^6 + 4*b^6*c^6 - 6*a^4*c^8 - 7*a^2*b^2*c^8 - 2*b^4*c^8) : :

X(33984) lies on the cubics K1119 and K1124, and on these lines: {6, 160}, {99, 1350}


X(33985) =  X(6)X(18191)∩X(75)X(100)

Barycentrics    a*(a^7*b^2 - a^3*b^6 + 2*a^7*b*c - a^6*b^2*c - 2*a^5*b^3*c + 2*a^4*b^4*c - a^2*b^6*c + a^7*c^2 - a^6*b*c^2 - a^4*b^3*c^2 - a^3*b^4*c^2 - 2*a*b^6*c^2 - 2*a^5*b*c^3 - a^4*b^2*c^3 + 3*a^2*b^4*c^3 + 2*a*b^5*c^3 - 2*b^6*c^3 + 2*a^4*b*c^4 - a^3*b^2*c^4 + 3*a^2*b^3*c^4 + 2*b^5*c^4 + 2*a*b^3*c^5 + 2*b^4*c^5 - a^3*c^6 - a^2*b*c^6 - 2*a*b^2*c^6 - 2*b^3*c^6) : :

X(33985) lies on the cubic K1122 and these lines: {6, 18191}, {75, 100}, {4557, 29828}


X(33986) =  X(574)X(33846)∩X(20470)X(33845)

Barycentrics    a^2*(2*a^6*b^4 - 2*a^4*b^6 - a^6*b^3*c - a^5*b^4*c + a^4*b^5*c + a^3*b^6*c - 6*a^6*b^2*c^2 - 3*a^5*b^3*c^2 + a^4*b^4*c^2 + 3*a^3*b^5*c^2 + 9*a^2*b^6*c^2 - a^6*b*c^3 - 3*a^5*b^2*c^3 - 4*a^4*b^3*c^3 - 2*a*b^6*c^3 + 2*a^6*c^4 - a^5*b*c^4 + a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*a*b^5*c^4 - 8*b^6*c^4 + a^4*b*c^5 + 3*a^3*b^2*c^5 - 2*a*b^4*c^5 - 2*a^4*c^6 + a^3*b*c^6 + 9*a^2*b^2*c^6 - 2*a*b^3*c^6 - 8*b^4*c^6) : :

X(33986) lies on the cubic K1122 and these lines: {574, 33846}, {20470, 33845}


X(33987) =  X(6)X(512)∩X(74)X(1296)

Barycentrics    a^2*(2*a^10 - 7*a^8*b^2 - 7*a^6*b^4 + 5*a^4*b^6 + 5*a^2*b^8 + 2*b^10 - 7*a^8*c^2 + 44*a^6*b^2*c^2 - 18*a^4*b^4*c^2 + 8*a^2*b^6*c^2 - 19*b^8*c^2 - 7*a^6*c^4 - 18*a^4*b^2*c^4 - 18*a^2*b^4*c^4 + 17*b^6*c^4 + 5*a^4*c^6 + 8*a^2*b^2*c^6 + 17*b^4*c^6 + 5*a^2*c^8 - 19*b^2*c^8 + 2*c^10) : :
X(33987) = 3 X[5085] - 2 X[33928]

X(33987) lies on the cubic K1124 and these lines: {6, 512}, {74, 1296}, {154, 2502}, {2715, 9136}, {5085, 33928}, {5210, 7669}, {8667, 9830}


X(33988) =  X(6)X(647)∩X(22)X(110)

Barycentrics    a^2*(2*a^12 - 3*a^10*b^2 - 2*a^8*b^4 + 2*a^6*b^6 + 6*a^4*b^8 - 7*a^2*b^10 + 2*b^12 - 3*a^10*c^2 + 10*a^8*b^2*c^2 - 3*a^6*b^4*c^2 - 3*a^4*b^6*c^2 - 2*a^2*b^8*c^2 + b^10*c^2 - 2*a^8*c^4 - 3*a^6*b^2*c^4 - 6*a^4*b^4*c^4 + 9*a^2*b^6*c^4 + 2*b^8*c^4 + 2*a^6*c^6 - 3*a^4*b^2*c^6 + 9*a^2*b^4*c^6 - 10*b^6*c^6 + 6*a^4*c^8 - 2*a^2*b^2*c^8 + 2*b^4*c^8 - 7*a^2*c^10 + b^2*c^10 + 2*c^12) : :

X(33988) lies on the cubic K1124 and these lines: {6, 647}, {22, 110}, {511, 5502}, {5085, 33927}, {5967, 10190}, {14355, 17809}


X(33989) =  X(6)X(523)∩X(99)X(1350)

Barycentrics    3*a^12*b^2 - 6*a^10*b^4 + 10*a^8*b^6 - 6*a^6*b^8 - a^4*b^10 + 3*a^12*c^2 - 6*a^10*b^2*c^2 - a^8*b^4*c^2 + 7*a^6*b^6*c^2 - 6*a^4*b^8*c^2 + 3*a^2*b^10*c^2 - 6*a^10*c^4 - a^8*b^2*c^4 - 8*a^6*b^4*c^4 + 7*a^4*b^6*c^4 - 2*a^2*b^8*c^4 + 4*b^10*c^4 + 10*a^8*c^6 + 7*a^6*b^2*c^6 + 7*a^4*b^4*c^6 - 2*a^2*b^6*c^6 - 4*b^8*c^6 - 6*a^6*c^8 - 6*a^4*b^2*c^8 - 2*a^2*b^4*c^8 - 4*b^6*c^8 - a^4*c^10 + 3*a^2*b^2*c^10 + 4*b^4*c^10 : :

X(33989) lies on the cubic K1124 and these lines: {6, 523}, {99, 1350}, {154, 8667}, {15271, 33928}


X(33990) =  X(6)X(526)∩X(154)X(33928)

Barycentrics    a^2*(2*a^18 - 6*a^16*b^2 + 5*a^14*b^4 + a^12*b^6 - 6*a^10*b^8 + 6*a^8*b^10 + a^6*b^12 - 3*a^4*b^14 - 2*a^2*b^16 + 2*b^18 - 6*a^16*c^2 + 20*a^14*b^2*c^2 - 21*a^12*b^4*c^2 + 18*a^10*b^6*c^2 - 26*a^8*b^8*c^2 + 26*a^6*b^10*c^2 - 21*a^4*b^12*c^2 + 20*a^2*b^14*c^2 - 10*b^16*c^2 + 5*a^14*c^4 - 21*a^12*b^2*c^4 + 6*a^10*b^4*c^4 + 14*a^8*b^6*c^4 - 14*a^6*b^8*c^4 + 6*a^4*b^10*c^4 - 9*a^2*b^12*c^4 + 13*b^14*c^4 + a^12*c^6 + 18*a^10*b^2*c^6 + 14*a^8*b^4*c^6 - 24*a^6*b^6*c^6 + 18*a^4*b^8*c^6 - 14*a^2*b^10*c^6 - 11*b^12*c^6 - 6*a^10*c^8 - 26*a^8*b^2*c^8 - 14*a^6*b^4*c^8 + 18*a^4*b^6*c^8 + 10*a^2*b^8*c^8 + 6*b^10*c^8 + 6*a^8*c^10 + 26*a^6*b^2*c^10 + 6*a^4*b^4*c^10 - 14*a^2*b^6*c^10 + 6*b^8*c^10 + a^6*c^12 - 21*a^4*b^2*c^12 - 9*a^2*b^4*c^12 - 11*b^6*c^12 - 3*a^4*c^14 + 20*a^2*b^2*c^14 + 13*b^4*c^14 - 2*a^2*c^16 - 10*b^2*c^16 + 2*c^18) : :

X(33990) lies on the cubic K1124 and these lines: {6, 526}, {154, 33928}, {691, 1350}


X(33991) =  X(6)X(669)∩X(98)X(1350)

Barycentrics    a^2*(2*a^10*b^6 + 4*a^8*b^8 - 6*a^6*b^10 - 3*a^10*b^4*c^2 - a^8*b^6*c^2 - 5*a^6*b^8*c^2 + a^4*b^10*c^2 - 3*a^10*b^2*c^4 + 8*a^8*b^4*c^4 - 4*a^6*b^6*c^4 + 20*a^4*b^8*c^4 + 5*a^2*b^10*c^4 + 2*a^10*c^6 - a^8*b^2*c^6 - 4*a^6*b^4*c^6 - 16*a^4*b^6*c^6 - 9*a^2*b^8*c^6 - 2*b^10*c^6 + 4*a^8*c^8 - 5*a^6*b^2*c^8 + 20*a^4*b^4*c^8 - 9*a^2*b^6*c^8 + 4*b^8*c^8 - 6*a^6*c^10 + a^4*b^2*c^10 + 5*a^2*b^4*c^10 - 2*b^6*c^10) : :

X(33991) lies on the cubic K1124 and these lines: {6, 669}, {98, 1350}


X(33992) =  X(39)X(16040)∩X(231)X(3054)

Barycentrics    4 a^12-8 a^10 b^2-5 a^8 b^4+21 a^6 b^6-13 a^4 b^8-a^2 b^10+2 b^12-8 a^10 c^2-2 a^8 b^2 c^2+15 a^6 b^4 c^2+3 a^4 b^6 c^2-3 a^2 b^8 c^2-5 b^10 c^2-5 a^8 c^4+15 a^6 b^2 c^4+20 a^4 b^4 c^4+4 a^2 b^6 c^4+2 b^8 c^4+21 a^6 c^6+3 a^4 b^2 c^6+4 a^2 b^4 c^6+2 b^6 c^6-13 a^4 c^8-3 a^2 b^2 c^8+2 b^4 c^8-a^2 c^10-5 b^2 c^10+2 c^12 : :
Barycentrics    (144 R^4-30 R^2 SB-30 R^2 SC-5 SB SC-96 R^2 SW+12 SB SW+12 SC SW+15 SW^2)S^2 + 3 S^4+4 R^2 SB SC SW-SB SC SW^2 : :

See Thanassis Gakopoulos, Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29350.

X(33992) lies on these lines: {39,16040}, {231,3054}, {550,10610}


X(33993) =  X(2)X(955)∩X(4)X(3601)

Barycentrics    3 a^6-8 a^5 b+a^4 b^2+12 a^3 b^3-7 a^2 b^4-4 a b^5+3 b^6-8 a^5 c+6 a^4 b c+4 a^3 b^2 c+4 a b^4 c-6 b^5 c+a^4 c^2+4 a^3 b c^2+14 a^2 b^2 c^2-3 b^4 c^2+12 a^3 c^3+12 b^3 c^3-7 a^2 c^4+4 a b c^4-3 b^2 c^4-4 a c^5-6 b c^5+3 c^6 : :

See Thanassis Gakopoulos, Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29350.

X(33993) lies on these lines: {2,955}, {4,3601}, {11,3488}, {65,3085}, {72,18231}, {100,954}, {165,226}, {405,5328}, {442,5703}, {498,18397}, {950,7988}, {2550,3158}, {3475,5659}, {3651,5217}, {5226,7580}, {5308,15252}, {5316,16845}, {5660,5817}, {5748,13615}, {6843,24929}, {6908,11374}, {8164,18446}, {10393,10588}, {10578,33108}, {11041,31397}

X(33993) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {226,5218,5759}


X(33994) =  X(2)X(12915)∩X(57)X(8166)

Barycentrics    3 a^6-4 a^5 b-7 a^4 b^2+12 a^3 b^3+a^2 b^4-8 a b^5+3 b^6-4 a^5 c+22 a^4 b c-12 a^3 b^2 c-32 a^2 b^3 c+32 a b^4 c-6 b^5 c-7 a^4 c^2-12 a^3 b c^2+62 a^2 b^2 c^2-24 a b^3 c^2-3 b^4 c^2+12 a^3 c^3-32 a^2 b c^3-24 a b^2 c^3+12 b^3 c^3+a^2 c^4+32 a b c^4-3 b^2 c^4-8 a c^5-6 b c^5+3 c^6 : :

See Thanassis Gakopoulos, Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29350.

X(33994) lies on these lines: {2,12915}, {57,8166}, {165,497}, {392,18231}, {944,1210}, {956,5704}, {1317,18391}, {1864,5658}, {3057,3086}, {3158,11019}, {3651,5204}, {4000,7658}, {5083,5660}, {5274,17613}, {5603,12736}, {8732,11575}, {14986,20789}


X(33995) =  X(57)X(5658)∩X(165)X(15299)

Barycentrics    a (a^8-2 a^7 b-2 a^6 b^2+6 a^5 b^3-6 a^3 b^5+2 a^2 b^6+2 a b^7-b^8-2 a^7 c-4 a^6 b c+18 a^5 b^2 c-8 a^4 b^3 c-14 a^3 b^4 c+12 a^2 b^5 c-2 a b^6 c-2 a^6 c^2+18 a^5 b c^2-48 a^4 b^2 c^2+20 a^3 b^3 c^2+46 a^2 b^4 c^2-38 a b^5 c^2+4 b^6 c^2+6 a^5 c^3-8 a^4 b c^3+20 a^3 b^2 c^3-120 a^2 b^3 c^3+38 a b^4 c^3-14 a^3 b c^4+46 a^2 b^2 c^4+38 a b^3 c^4-6 b^4 c^4-6 a^3 c^5+12 a^2 b c^5-38 a b^2 c^5+2 a^2 c^6-2 a b c^6+4 b^2 c^6+2 a c^7-c^8) : :

See Thanassis Gakopoulos, Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29350.

X(33995) lies on these lines: {57,5658}, {165,15299}, {1058,1210}, {3086,7160}, {3651,10396}, {5219,6983}, {5704,18231}, {7966,18391}, {15285,16610}


X(33996) =  X(376)X(3017)∩X(551)X(4906)

Barycentrics    4 a^6-a^4 b^2+9 a^3 b^3+3 a^2 b^4-a b^5+2 b^6+6 a^4 b c+3 a^3 b^2 c+3 a^2 b^3 c+5 a b^4 c-b^5 c-a^4 c^2+3 a^3 b c^2+4 a^2 b^2 c^2-4 a b^3 c^2-2 b^4 c^2+9 a^3 c^3+3 a^2 b c^3-4 a b^2 c^3+2 b^3 c^3+3 a^2 c^4+5 a b c^4-2 b^2 c^4-a c^5-b c^5+2 c^6 : :

See Thanassis Gakopoulos, Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29350.

X(33996) lies on these lines: {376,3017}, {551,4906}, {3752,14838}, {14829,31168}


X(33997) =  X(3)X(76)∩X(23)X(6038)

Barycentrics    a^12 - 6*a^10*b^2 + 5*a^8*b^4 - 5*a^6*b^6 + 6*a^4*b^8 - a^2*b^10 - 6*a^10*c^2 + a^8*b^2*c^2 + 6*a^6*b^4*c^2 - 3*a^4*b^6*c^2 + 10*a^2*b^8*c^2 + 5*a^8*c^4 + 6*a^6*b^2*c^4 - 13*a^2*b^6*c^4 + 6*b^8*c^4 - 5*a^6*c^6 - 3*a^4*b^2*c^6 - 13*a^2*b^4*c^6 - 12*b^6*c^6 + 6*a^4*c^8 + 10*a^2*b^2*c^8 + 6*b^4*c^8 - a^2*c^10 : :

X(33997) lies on the cubic K1126 and these lines: {3,76}, {23,6038}, {147,3815}, {524,5999}, {542,11163}, {1350,14931}, {1916,11477}, {3090,9478}, {5085,8289}, {5984,7774}, {7770,11623}, {7792,14651}, {9772,15271}, {11174,12177}, {11285,14981}, {11676,12243}

X(33997) = midpoint of X(5984) and X(7774)
X(33997) = reflection of X(i) in X(j) for these {i,j}: {147, 3815}, {183, 98}


X(33998) =  X(3)X(9172)∩X(22)X(11643)

Barycentrics    a^2*(a^10 - 6*a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 + 6*a^2*b^8 - b^10 - 6*a^8*c^2 + 55*a^6*b^2*c^2 - 24*a^4*b^4*c^2 - 75*a^2*b^6*c^2 + 10*b^8*c^2 - 7*a^6*c^4 - 24*a^4*b^2*c^4 + 126*a^2*b^4*c^4 - b^6*c^4 + 7*a^4*c^6 - 75*a^2*b^2*c^6 - b^4*c^6 + 6*a^2*c^8 + 10*b^2*c^8 - c^10) : :

X(33998) lies on the cubic K1126 and these lines: {3,9172}, {22,11643}, {25,2930}, {99,1995}, {5104,20998}

X(33998) = circumcircle-inverse of X(9172)


X(33999) =  X(524)X(5999)∩X(5104)X(20998)

Barycentrics    a^2*(a^12 - 8*a^10*b^2 + 14*a^8*b^4 - 48*a^6*b^6 + 40*a^4*b^8 + 2*a^2*b^10 - b^12 - 8*a^10*c^2 + 58*a^8*b^2*c^2 - 54*a^6*b^4*c^2 + 46*a^4*b^6*c^2 - 44*a^2*b^8*c^2 + 6*b^10*c^2 + 14*a^8*c^4 - 54*a^6*b^2*c^4 + 69*a^4*b^4*c^4 - 28*a^2*b^6*c^4 - 18*b^8*c^4 - 48*a^6*c^6 + 46*a^4*b^2*c^6 - 28*a^2*b^4*c^6 + 58*b^6*c^6 + 40*a^4*c^8 - 44*a^2*b^2*c^8 - 18*b^4*c^8 + 2*a^2*c^10 + 6*b^2*c^10 - c^12) : :

X(33999) lies on the cubic K1126 and these lines: {524,5999}, {5104,20998}, {31884,33928}

X(33999) = Thomson-isogonal conjugate of X(12243)


X(34000) =  X(3)X(33707)∩X(99)X(5201)

Barycentrics    a^2*(a^8*b^2 + 7*a^6*b^4 - 7*a^4*b^6 - a^2*b^8 + a^8*c^2 + 24*a^6*b^2*c^2 + 16*a^4*b^4*c^2 - 20*a^2*b^6*c^2 - b^8*c^2 + 7*a^6*c^4 + 16*a^4*b^2*c^4 - 8*a^2*b^4*c^4 - 3*b^6*c^4 - 7*a^4*c^6 - 20*a^2*b^2*c^6 - 3*b^4*c^6 - a^2*c^8 - b^2*c^8 - Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2]*(5*a^6*b^2 - 5*a^2*b^6 + 5*a^6*c^2 + 32*a^4*b^2*c^2 - 12*a^2*b^4*c^2 - 5*b^6*c^2 - 12*a^2*b^2*c^4 + 2*b^4*c^4 - 5*a^2*c^6 - 5*b^2*c^6)) : :

X(34000) lies on the cubic K1126 and these lines: {3,33707}, {99,5201}



This is the end of PART 17: Centers X(32001) - X(34000)

Introduction and Centers X(1) - X(1000) Centers X(1001) - X(3000) Centers X(3001) - X(5000)
Centers X(5001) - X(7000) Centers X(7001) - X(10000) Centers X(10001) - X(12000)
Centers X(12001) - X(14000) Centers X(14001) - X(16000) Centers X(16001) - X(18000)
Centers X(18001) - X(20000) Centers X(20001) - X(22000) Centers X(22001) - X(24000)
Centers X(24001) - X(26000) Centers X(26001) - X(28000) Centers X(28001) - X(30000)
Centers X(30001) - X(32000) Centers X(32001) - X(34000) Centers X(34001) - X(36000)
Centers X(36001) - X(38000) Centers X(38001) - X(40000) Centers X(40001) - X(42000)
Centers X(42001) - X(44000) Centers X(44001) - X(46000) Centers X(46001) - X(48000)
Centers X(48001) - X(50000) Centers X(50001) - X(52000) Centers X(52001) - X(54000)
Centers X(54001) - X(56000) Centers X(56001) - X(58000) Centers X(58001) - X(60000)
Centers X(60001) - X(62000) Centers X(62001) - X(64000) Centers X(64001) - X(66000)
Centers X(66001) - X(68000) Centers X(68001) - X(70000) Centers X(70001) - X(72000)