X(45186) = X(3)X(51)∩X(4)X(69)
Barycentrics a^2 (a^6 b^2-3 a^4 b^4+3 a^2 b^6-b^8+a^6 c^2-6 a^4 b^2 c^2+a^2 b^4 c^2+4 b^6 c^2-3 a^4 c^4+a^2 b^2 c^4-6 b^4 c^4+3 a^2 c^6+4 b^2 c^6-c^8) : :Barycentrics (SB+SC) (S^2-4 R^2 SA+SB SC) : :
X(45186) = 3*X(2)-4*X(10110),2*X(3)-3*X(51),3*X(3)-4*X(5462),5*X(3)-6*X(5892),4*X(3)-3*X(36987),3*X(4)-2*X(5907),3*X(4)-X(11412),5*X(4)-3*X(11459),4*X(4)-3*X(15030),7*X(4)-5*X(15058),4*X(5)-3*X(3917),3*X(5)-2*X(10627),5*X(5)-4*X(32142),X(20)-3*X(3060),3*X(20)-5*X(10574),3*X(51)-4*X(5446),9*X(51)-8*X(5462),5*X(51)-4*X(5892),3*X(52)-2*X(6102),3*X(52)-X(10575),5*X(52)-2*X(13491),3*X(52)-4*X(14449),4*X(52)-3*X(14831),2*X(52)-3*X(21969),X(64)-3*X(34751),8*X(140)-9*X(373),4*X(143)-3*X(9730),3*X(185)-4*X(6102),X(185)-4*X(10263),3*X(185)-2*X(10575),5*X(185)-4*X(13491),3*X(185)-8*X(14449),2*X(185)-3*X(14831),X(185)-3*X(21969),3*X(376)-5*X(3567),3*X(376)-4*X(9729),2*X(376)-3*X(16226),3*X(381)-2*X(1216),3*X(381)-X(37484),2*X(382)+X(14531),3*X(382)-X(18439),2*X(389)-3*X(3060),6*X(389)-5*X(10574),4*X(546)-3*X(5891),2*X(548)-3*X(5946),3*X(549)-4*X(10095),2*X(550)-3*X(9730),3*X(568)-X(1657),3*X(568)-2*X(40647),4*X(576)-3*X(40673),5*X(631)-6*X(5943),5*X(631)-7*X(9781),5*X(631)-4*X(13348),5*X(632)-6*X(13364),4*X(1112)-3*X(16223),3*X(1351)-2*X(32284),5*X(1656)-4*X(5447),10*X(1656)-9*X(5650),5*X(1656)-8*X(12002),5*X(1656)-3*X(13340),5*X(1843)-4*X(41714),3*X(2979)-5*X(3091),3*X(2979)-4*X(11793),9*X(3060)-5*X(10574),7*X(3090)-6*X(3819),5*X(3091)-4*X(11793),5*X(3522)-9*X(11002),5*X(3522)-7*X(15043),5*X(3522)-6*X(16836),7*X(3523)-9*X(5640),7*X(3523)-8*X(11695),7*X(3528)-9*X(15045),7*X(3528)-8*X(17704),X(3529)-3*X(5890),X(3529)-4*X(16625),2*X(3530)-3*X(13451),4*X(3530)-5*X(15026),3*X(3534)-5*X(37481),3*X(3543)-X(12111),3*X(3543)-2*X(13474),9*X(3545)-7*X(7999),5*X(3567)-4*X(9729),10*X(3567)-9*X(16226),5*X(3567)-6*X(21849),3*X(3574)-2*X(12363),4*X(3627)-3*X(32062),3*X(3627)-2*X(32137),8*X(3628)-9*X(14845),3*X(3830)-X(18436),7*X(3832)-5*X(11444),7*X(3832)-4*X(15606),9*X(3839)-7*X(15056),5*X(3843)-3*X(23039),3*X(3845)-2*X(11591),4*X(3850)-3*X(15067),7*X(3851)-6*X(10170),4*X(3853)-3*X(16194),5*X(3858)-4*X(14128),4*X(3861)-3*X(15060),3*X(3917)-2*X(10625),9*X(3917)-8*X(10627),X(5059)-4*X(13382),X(5059)-3*X(15072),X(5059)-9*X(16981),5*X(5076)-3*X(18435),3*X(5102)-2*X(32366),3*X(5446)-2*X(5462),5*X(5446)-3*X(5892),8*X(5446)-3*X(36987),8*X(5447)-9*X(5650),4*X(5447)-3*X(13340),10*X(5462)-9*X(5892),3*X(5562)-4*X(5907),3*X(5562)-2*X(11412),5*X(5562)-6*X(11459),X(5562)-4*X(13598),2*X(5562)-3*X(15030),7*X(5562)-10*X(15058),9*X(5640)-8*X(11695),3*X(5650)-2*X(13340),3*X(5657)-4*X(23841),2*X(5876)-3*X(16194),3*X(5890)-4*X(16625),3*X(5891)-2*X(6101),8*X(5892)-5*X(36987),10*X(5907)-9*X(11459),X(5907)-3*X(13598),8*X(5907)-9*X(15030),6*X(5943)-7*X(9781),3*X(5943)-2*X(13348),X(6102)-3*X(10263),5*X(6102)-3*X(13491),8*X(6102)-9*X(14831),4*X(6102)-9*X(21969),2*X(6243)+X(11381),3*X(6243)+X(18439),3*X(6467)-4*X(32284),4*X(6759)-3*X(34750),3*X(8703)-4*X(12006),8*X(9729)-9*X(16226),2*X(9729)-3*X(21849),7*X(9781)-4*X(13348),4*X(9822)-3*X(10519),6*X(10263)-X(10575),5*X(10263)-X(13491),3*X(10263)-2*X(14449),8*X(10263)-3*X(14831),4*X(10263)-3*X(21969),5*X(10575)-6*X(13491),X(10575)-4*X(14449),4*X(10575)-9*X(14831),2*X(10575)-9*X(21969),3*X(10625)-4*X(10627),5*X(10625)-8*X(32142),5*X(10627)-6*X(32142),9*X(11002)-7*X(15043),3*X(11002)-2*X(16836),8*X(11017)-9*X(23046),3*X(11381)-2*X(18439),5*X(11412)-9*X(11459),X(11412)-6*X(13598),4*X(11412)-9*X(15030),5*X(11444)-4*X(15606),3*X(11459)-10*X(13598),4*X(11459)-5*X(15030),9*X(11539)-8*X(11592),2*X(11574)-3*X(14853),4*X(11746)-3*X(38727),8*X(12002)-3*X(13340),6*X(12099)-5*X(38729),2*X(12162)-3*X(32062),3*X(12162)-4*X(32137),X(12290)-3*X(15682),2*X(12362)-3*X(16657),4*X(12811)-3*X(44324),9*X(13321)-5*X(15696),6*X(13363)-5*X(15712),4*X(13382)-3*X(15072),4*X(13382)-9*X(16981),2*X(13419)-3*X(34603),4*X(13446)-3*X(37943),6*X(13451)-5*X(15026),3*X(13491)-10*X(14449),8*X(13598)-3*X(15030),4*X(13630)-3*X(14855),8*X(14449)-9*X(21969),X(14516)-3*X(34603),3*X(14531)+2*X(18439),2*X(14689)-3*X(16225),3*X(14855)-2*X(15704),3*X(14855)-8*X(16982),7*X(14869)-8*X(32205),8*X(15012)-5*X(17538),3*X(15035)-4*X(41671),7*X(15043)-6*X(16836),9*X(15045)-8*X(17704),X(15072)-3*X(16981),3*X(15305)-5*X(17578),X(15704)-4*X(16982),3*X(15800)-X(22815),2*X(16163)-3*X(16223),3*X(16222)-2*X(38726),3*X(16226)-4*X(21849),X(16659)-3*X(34613),2*X(17712)-3*X(43573),3*X(20423)-2*X(44479),2*X(22815)-3*X(43581),4*X(30531)-3*X(44325),9*X(32062)-8*X(32137),2*X(34782)-3*X(41580),3*X(36518)-2*X(41673)
See Antreas Hatzipolakis and Ercole Suppa, euclid 2736.
X(45186) lies on these lines: {2,10110}, {3,51}, {4,69}, {5,3917}, {6,10984}, {20,389}, {22,578}, {23,10282}, {24,13346}, {25,1092}, {26,13352}, {30,52}, {49,5899}, {54,12088}, {64,34751}, {68,11550}, {74,11800}, {110,11807}, {125,23335}, {140,373}, {143,550}, {155,18534}, {181,601}, {182,10323}, {184,7387}, {186,15010}, {193,34781}, {195,37924}, {235,1568}, {343,1595}, {376,3567}, {381,1216}, {382,6243}, {394,1598}, {500,7420}, {517,16980}, {524,16621}, {542,16659}, {546,5891}, {548,5946}, {549,10095}, {567,13564}, {568,1657}, {569,22352}, {576,7592}, {602,3271}, {631,5943}, {632,13364}, {674,14872}, {970,6906}, {1012,5752}, {1064,10475}, {1112,16163}, {1147,1495}, {1154,3627}, {1181,1351}, {1199,5097}, {1204,12085}, {1350,7395}, {1370,39571}, {1498,2393}, {1519,35631}, {1532,37536}, {1533,2883}, {1593,17834}, {1614,34986}, {1656,5447}, {1899,34938}, {1907,11576}, {1941,8884}, {1986,16879}, {1993,6759}, {1994,12087}, {2070,12038}, {2777,21649}, {2781,41362}, {2794,39817}, {2807,41869}, {2937,18475}, {2979,3091}, {3090,3819}, {3098,7509}, {3133,23217}, {3146,5889}, {3149,37482}, {3199,3289}, {3292,7530}, {3313,5480}, {3448,14864}, {3515,37497}, {3517,35602}, {3518,43574}, {3522,11002}, {3523,5640}, {3524,15024}, {3525,6688}, {3528,15045}, {3529,5890}, {3530,13451}, {3534,37481}, {3538,18928}, {3543,12111}, {3545,7999}, {3560,22076}, {3564,16655}, {3574,12363}, {3580,20299}, {3628,14845}, {3796,11426}, {3830,18436}, {3832,11444}, {3839,15056}, {3843,23039}, {3845,11591}, {3850,15067}, {3851,10170}, {3853,5876}, {3855,13570}, {3858,14128}, {3861,15060}, {3937,37532}, {4297,31757}, {5012,37505}, {5056,7998}, {5059,13382}, {5068,33884}, {5073,14915}, {5076,18435}, {5092,43651}, {5102,32366}, {5188,27375}, {5198,17814}, {5422,37515}, {5448,11799}, {5651,7529}, {5657,23841}, {5663,13421}, {5706,37516}, {5709,26892}, {5751,9122}, {5925,31978}, {5965,16658}, {6153,12307}, {6193,31383}, {6241,33703}, {6515,14216}, {6636,13434}, {6642,34417}, {6823,9967}, {6834,37521}, {6907,18180}, {6950,15489}, {6979,33852}, {7330,26893}, {7383,14561}, {7391,18381}, {7400,11574}, {7404,43653}, {7409,33523}, {7488,11430}, {7500,9833}, {7506,44106}, {7512,15033}, {7525,37513}, {7526,37478}, {7527,7691}, {7555,10610}, {8276,9686}, {8541,44492}, {8703,12006}, {8718,15032}, {9019,12233}, {9306,10594}, {9545,26881}, {9715,11425}, {9777,37198}, {9786,21312}, {9818,37486}, {9820,37971}, {9822,10519}, {9909,19357}, {9914,34777}, {9927,11572}, {9973,15811}, {10018,32223}, {10112,29012}, {10303,11451}, {10531,35645}, {10540,41597}, {10564,37814}, {10619,43595}, {10628,10733}, {11017,23046}, {11064,21841}, {11250,32110}, {11387,14826}, {11413,11438}, {11456,37517}, {11479,33878}, {11539,11592}, {11557,12121}, {11692,18859}, {11746,38727}, {11806,20127}, {11826,22300}, {12022,29317}, {12058,18390}, {12083,13366}, {12084,21663}, {12099,38729}, {12102,31834}, {12103,16881}, {12107,43394}, {12163,12235}, {12164,34382}, {12225,13403}, {12236,16111}, {12237,12256}, {12238,12257}, {12239,42258}, {12240,42259}, {12241,19161}, {12280,13433}, {12290,15682}, {12295,21650}, {12359,41586}, {12362,16657}, {12811,44324}, {12897,18563}, {13321,15696}, {13358,14677}, {13363,15712}, {13417,17702}, {13419,14516}, {13446,37943}, {13621,37496}, {13630,14855}, {13851,18569}, {14110,42450}, {14520,36012}, {14627,44111}, {14641,17800}, {14689,16225}, {14788,19130}, {14869,32205}, {14984,15063}, {15004,35243}, {15012,17538}, {15028,15717}, {15035,41671}, {15038,37471}, {15073,34621}, {15305,17578}, {15472,22109}, {15559,21243}, {15705,40284}, {15800,22815}, {15801,43605}, {16197,37649}, {16222,38726}, {16386,32411}, {16654,34380}, {16661,34545}, {17080,34956}, {17712,43573}, {17928,37480}, {18281,32225}, {18378,22115}, {18483,31738}, {18925,34608}, {19124,37488}, {19467,31305}, {19925,31737}, {20423,44479}, {22416,33843}, {23154,24474}, {23698,39846}, {25739,43896}, {26882,32237}, {28150,31728}, {28164,31732}, {30531,44325}, {31074,32767}, {31304,34785}, {31730,31760}, {31810,44544}, {31817,31871}, {32171,37936}, {34565,36753}, {34782,41580}, {36518,41673}, {36742,40952}, {36978,42147}, {36979,42432}, {36980,42148}, {36981,42431}, {37200,41365}, {37406,39271}, {37437,41723}, {37474,40954}, {38281,44436}, {38738,39835}, {38749,39806}, {44076,44407}, {44102,44469}
X(45186) = midpoint of X(i) and X(j) for these {i,j}: {382,6243}, {3146,5889}, {5073,34783}, {6241,33703}, {11381,14531}
X(45186) = reflection of X(i) in X(j) for these (i,j): (3,5446), (4,13598), (20,389), (52,10263), (74,11800), (110,11807), (185,52), (376,21849), (550,143), (1350,9969), (1657,40647), (3313,5480), (4297,31757), (5188,27375), (5447,12002), (5562,4), (5876,3853), (5925,31978), (6101,546), (6102,14449), (6146,13142), (6467,1351), (7691,11808), (9967,21850), (10575,6102), (10625,5), (11381,382), (11412,5907), (11750,12370), (11826,22300), (12058,18390), (12103,16881), (12111,13474), (12121,11557), (12162,3627), (12163,12235), (12225,13403), (12256,12237), (12257,12238), (12280,13433), (12294,31670), (12307,6153), (13630,16982), (14110,42450), (14516,13419), (14531,6243), (14677,13358), (14831,21969), (15063,16105), (15644,10110), (15704,13630), (16111,12236), (16163,1112), (16386,32411), (17800,14641), (18563,12897), (18859,11692), (20127,11806), (21650,12295), (23154,24474), (31730,31760), (31737,19925), (31738,18483), (31817,31871), (31834,12102), (34224,10112), (36987,51), (37484,1216), (38738,39835), (38749,39806), (43581,15800)
X(45186) = anticomplement of X(15644)
X(45186) = crosssum of X(3)and X(11411)
X(45186) = barycentric product X(343)*X(19173)
X(45186) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,3527,10601),(3,5446,51),(3,44413,11424),(4,5562,15030),(4,11412,5907),(5,10625,3917),(6,11414,10984),(20,3060,389),(23,34148,10282),(25,37498,1092),(26,13352,13367),(52,185,14831),(52,10263,21969),(52,10575,6102),(143,550,9730),(155,18534,26883),(185,21969,52),(376,3567,9729),(376,21849,16226),(381,37484,1216),(546,6101,5891),(568,1657,40647),(631,9781,5943),(1112,16163,16223),(1147,7517,1495),(1351,39568,1181),(1498,11477,12160),(1656,5447,5650),(1656,13340,5447),(1993,6759,43844),(2070,37495,12038),(2937,37472,18475),(2979,3091,11793),(3522,11002,15043),(3522,15043,16836),(3523,5640,11695),(3528,15045,17704),(3530,13451,15026),(3543,12111,13474),(3567,9729,16226),(3627,12162,32062),(3853,5876,16194),(5650,27355,1656),(5907,11412,5562),(5943,13348,631),(6102,10263,14449),(6102,10575,185),(6102,14449,52),(6642,37483,43652),(7387,36747,184),(7530,16266,10539),(9729,21849,3567),(9777,37198,37514),(9927,31723,11572),(10110,15644,2),(10539,16266,3292),(12002,13340,27355),(12085,37489,1204),(13630,15704,14855),(14516,34603,13419),(23335,41587,125),(34417,43652,6642)
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