leftri rightri


This is PART 37: Centers X(72001) - X(74000)

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)
Centers X(72001) - X(74000) Centers X(74001) - X(76000) Centers X(76001) - X(78000)
Centers X(78001) - X(80000) Centers X(80001) - X(82000) Centers X(82001) - X(84000)


X(72001) = X(1)X(25914)∩X(2)X(6)

Barycentrics    a*b^2 + b^3 - 4*a*b*c + b^2*c + a*c^2 + b*c^2 + c^3 : :
X(72001) = 9 X[2] - X[63009], 3 X[4383] - X[63009], 3 X[10327] + X[30614], 3 X[17597] - X[30614]

X(72001) lies on these lines: {1, 25914}, {2, 6}, {5, 5482}, {10, 3742}, {11, 25957}, {43, 4966}, {57, 17279}, {63, 4422}, {88, 33168}, {142, 44417}, {210, 60423}, {226, 3834}, {244, 3703}, {306, 16610}, {312, 1086}, {321, 7263}, {329, 7232}, {345, 17267}, {354, 49524}, {443, 49734}, {474, 65543}, {518, 62673}, {519, 4906}, {536, 24177}, {545, 56082}, {553, 17351}, {594, 19804}, {612, 71322}, {614, 5846}, {750, 29677}, {982, 3932}, {1001, 44419}, {1054, 33158}, {1125, 4682}, {1155, 59580}, {1215, 25557}, {1266, 22034}, {1329, 41682}, {1468, 25992}, {1503, 16434}, {1834, 33833}, {1997, 26132}, {1999, 17366}, {2321, 24175}, {2885, 21031}, {2886, 3836}, {2887, 3816}, {2999, 4851}, {3035, 3771}, {3058, 32948}, {3210, 3943}, {3305, 17332}, {3306, 32777}, {3315, 33091}, {3416, 5272}, {3452, 21255}, {3454, 17527}, {3649, 25591}, {3662, 4415}, {3663, 35652}, {3666, 17243}, {3687, 16602}, {3695, 24046}, {3704, 24174}, {3705, 3756}, {3714, 24178}, {3717, 21342}, {3740, 49511}, {3741, 3826}, {3752, 3912}, {3755, 4891}, {3772, 17282}, {3782, 4358}, {3812, 5835}, {3820, 49993}, {3823, 4847}, {3829, 21241}, {3831, 25466}, {3844, 3848}, {3869, 59704}, {3925, 25961}, {3948, 18739}, {3967, 24231}, {3969, 24183}, {3996, 26073}, {3999, 63147}, {4011, 17768}, {4023, 33081}, {4026, 26102}, {4035, 45204}, {4082, 28582}, {4104, 58451}, {4138, 5087}, {4220, 21167}, {4252, 13742}, {4359, 4665}, {4361, 34255}, {4363, 9776}, {4364, 44307}, {4387, 28530}, {4388, 25531}, {4413, 33171}, {4423, 26034}, {4434, 29672}, {4643, 7308}, {4656, 17235}, {4657, 17022}, {4660, 49736}, {4684, 4849}, {4854, 33125}, {4860, 33163}, {4904, 8056}, {4914, 50949}, {5192, 49745}, {5205, 33124}, {5249, 30818}, {5256, 17390}, {5284, 33086}, {5287, 17045}, {5294, 37520}, {5432, 29632}, {5437, 17284}, {5480, 37521}, {5745, 18214}, {5905, 7238}, {6057, 17155}, {6154, 71452}, {6247, 6891}, {6690, 29642}, {6692, 16608}, {6944, 15873}, {7191, 51147}, {7290, 25509}, {7292, 33078}, {7789, 21477}, {7795, 21526}, {7800, 21514}, {8167, 50295}, {8287, 46828}, {8728, 50605}, {9024, 63513}, {9041, 30615}, {9053, 10327}, {9335, 33089}, {9342, 33175}, {9345, 29663}, {9347, 29666}, {9710, 50608}, {10178, 21629}, {10479, 17529}, {11108, 49728}, {11227, 12618}, {11246, 32930}, {11679, 17278}, {12436, 50054}, {13478, 19512}, {13747, 25645}, {15048, 68938}, {16367, 59625}, {16431, 32459}, {16569, 33087}, {16593, 30822}, {16594, 27131}, {16703, 26235}, {17051, 29655}, {17054, 54433}, {17061, 29649}, {17063, 29674}, {17122, 29637}, {17123, 33085}, {17124, 24943}, {17125, 33080}, {17135, 24988}, {17205, 69439}, {17233, 17490}, {17246, 41839}, {17263, 38000}, {17266, 33116}, {17272, 51780}, {17276, 30568}, {17296, 23511}, {17334, 26840}, {17340, 32939}, {17356, 40940}, {17365, 27064}, {17370, 29841}, {17395, 34064}, {17449, 69298}, {17534, 26064}, {17540, 29473}, {17595, 17776}, {17602, 33123}, {17697, 64159}, {17717, 31242}, {17728, 29857}, {17749, 41014}, {18144, 40012}, {18149, 30631}, {18165, 50609}, {18201, 33164}, {18229, 20195}, {19649, 44882}, {19827, 29613}, {20205, 34852}, {20237, 71002}, {20306, 25681}, {20545, 53566}, {20917, 21025}, {20942, 48629}, {21240, 29571}, {21454, 54389}, {21479, 64035}, {21495, 59545}, {21500, 54075}, {21539, 69206}, {24003, 33064}, {24169, 66071}, {24176, 50042}, {24542, 71479}, {24589, 48636}, {24593, 56520}, {24789, 40480}, {25430, 41312}, {25502, 32784}, {25938, 25968}, {26118, 67865}, {26582, 31028}, {26590, 30967}, {26686, 30174}, {26688, 32859}, {26842, 41242}, {26932, 30827}, {26942, 31231}, {27002, 32851}, {27003, 33157}, {27184, 30829}, {29598, 69095}, {29679, 64149}, {29820, 33079}, {29851, 32918}, {29988, 37596}, {30748, 51150}, {30947, 32773}, {30950, 32781}, {31137, 32865}, {31151, 33106}, {31252, 33138}, {31289, 71489}, {31657, 59637}, {31993, 34824}, {32921, 59477}, {32941, 49732}, {32943, 34612}, {33084, 62711}, {33117, 51463}, {33132, 70219}, {33151, 46938}, {33170, 65112}, {36845, 71327}, {39994, 40013}, {41310, 56078}, {41313, 62818}, {42033, 62300}, {42034, 48627}, {42055, 69297}, {48845, 64167}, {49505, 59684}, {49676, 59511}, {49999, 64172}, {53534, 63139}, {56773, 59695}, {56782, 64158}, {60459, 62814}, {62240, 71638}

X(72001) = midpoint of X(i) and X(j) for these {i,j}: {10327, 17597}, {30615, 62850}
X(72001) = complement of X(4383)
X(72001) = complement of the isogonal conjugate of X(39956)
X(72001) = complement of the isotomic conjugate of X(40012)
X(72001) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 59577}, {8690, 4369}, {34860, 141}, {39956, 10}, {40012, 2887}, {42304, 2886}, {56123, 3454}, {56155, 142}, {56192, 1211}, {60789, 21255}, {60806, 8}, {60807, 46827}, {65059, 3741}
X(72001) = crosspoint of X(2) and X(40012)
X(72001) = crosssum of X(6) and X(16946)
X(72001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 37679}, {2, 141, 5743}, {2, 333, 17337}, {2, 940, 3589}, {2, 2895, 37687}, {2, 3936, 37663}, {2, 4417, 51415}, {2, 4869, 63089}, {2, 17232, 4417}, {2, 17234, 17056}, {2, 18134, 37662}, {2, 18139, 5718}, {2, 18141, 6}, {2, 25934, 53415}, {2, 32782, 5241}, {2, 32863, 37680}, {2, 33172, 1211}, {2, 37655, 37650}, {2, 37660, 62689}, {2, 37674, 6703}, {2, 37683, 17352}, {2, 63013, 47355}, {2, 69092, 141}, {57, 17279, 44416}, {244, 29687, 3703}, {321, 40688, 7263}, {982, 3932, 4884}, {1211, 33172, 141}, {1211, 69092, 33172}, {2887, 4871, 3816}, {3662, 18743, 4415}, {3763, 37682, 2}, {3782, 69251, 48631}, {3836, 3840, 2886}, {4358, 69251, 3782}, {16602, 17231, 3687}, {17063, 29674, 69091}, {17125, 33080, 41002}, {17267, 70256, 345}, {17282, 30567, 3772}, {17595, 17776, 59583}, {25957, 30957, 11}, {25961, 30942, 3925}, {26102, 33174, 4026}, {44307, 54311, 4364}


X(72002) = X(1)X(2)∩X(6)X(69300)

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

X(72002) lies on these lines: {1, 2}, {6, 69300}, {31, 1211}, {37, 33156}, {55, 69294}, {75, 32775}, {81, 33084}, {100, 32784}, {141, 750}, {171, 32782}, {210, 26061}, {345, 3989}, {468, 1973}, {524, 62846}, {594, 17602}, {748, 5743}, {756, 32777}, {894, 33065}, {896, 4643}, {902, 50295}, {940, 33081}, {968, 6536}, {984, 32779}, {1010, 30984}, {1011, 23843}, {1150, 3775}, {1155, 17237}, {1376, 32781}, {1621, 31247}, {1740, 27270}, {1842, 4207}, {2177, 4026}, {2218, 4204}, {2240, 4386}, {2308, 5739}, {2895, 62841}, {3120, 50314}, {3550, 33083}, {3589, 4023}, {3681, 32780}, {3686, 61647}, {3696, 33128}, {3712, 4364}, {3745, 32852}, {3763, 4413}, {3764, 68954}, {3772, 21020}, {3846, 24552}, {3923, 26580}, {3925, 31237}, {3936, 50302}, {3949, 17303}, {3966, 17469}, {3980, 17184}, {3994, 17281}, {3999, 51003}, {4009, 17359}, {4104, 5294}, {4193, 30980}, {4357, 4414}, {4359, 26128}, {4363, 32856}, {4389, 32845}, {4417, 32772}, {4418, 27184}, {4425, 32929}, {4438, 4981}, {4657, 46904}, {4697, 32859}, {4706, 17382}, {4748, 24683}, {4893, 47701}, {4933, 41312}, {4966, 9345}, {5078, 16405}, {5224, 32917}, {5233, 32944}, {5241, 17125}, {5263, 25760}, {5278, 6679}, {5741, 25496}, {5814, 62847}, {5955, 24443}, {6187, 8299}, {6703, 62821}, {7226, 33167}, {7234, 24921}, {8756, 68915}, {9347, 32846}, {10448, 65543}, {13588, 70619}, {16305, 68845}, {16468, 37656}, {16878, 24912}, {17122, 33172}, {17124, 69092}, {17126, 33082}, {17238, 71477}, {17280, 64178}, {17289, 32931}, {17357, 61686}, {17716, 33075}, {17740, 46901}, {19786, 32860}, {19804, 33123}, {19808, 32771}, {19822, 33144}, {19832, 70971}, {21727, 25684}, {21805, 38047}, {22230, 61366}, {24325, 33122}, {24342, 31019}, {24620, 26150}, {24697, 62838}, {25440, 35984}, {25527, 69253}, {25917, 52359}, {25958, 33109}, {25960, 32942}, {26064, 54354}, {26223, 69299}, {26446, 30272}, {26627, 49676}, {27081, 71478}, {27842, 71751}, {28605, 33152}, {28606, 33160}, {30831, 33111}, {30966, 70443}, {31034, 33682}, {31037, 32946}, {31993, 33127}, {32773, 32945}, {32776, 32932}, {32843, 70419}, {32861, 62807}, {32863, 37604}, {32949, 70484}, {33064, 59628}, {33086, 56010}, {33087, 37633}, {33114, 49457}, {33154, 64010}, {33155, 46918}, {33159, 63961}, {33170, 49448}, {37635, 43997}, {49456, 50105}, {49483, 71798}, {49515, 71795}, {50296, 70834}, {53034, 69643}, {54324, 59207}, {57040, 68935}

X(72002) = complement of X(29829)
X(72002) = X(29133)-complementary conjugate of X(513)
X(72002) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8, 29631}, {2, 42, 29647}, {2, 43, 29663}, {2, 3240, 29633}, {2, 3741, 29662}, {2, 3771, 29661}, {2, 4651, 25453}, {2, 10453, 29845}, {2, 17135, 29635}, {2, 24943, 29677}, {2, 29830, 1125}, {2, 29846, 29678}, {2, 31330, 24892}, {2, 32783, 24943}, {2, 33137, 29863}, {2, 33139, 29856}, {2, 33171, 3720}, {2, 33173, 26102}, {2, 33175, 1}, {2, 59296, 29850}, {75, 32775, 33143}, {171, 32782, 33080}, {984, 32779, 33161}, {1698, 29858, 2}, {3679, 29856, 33139}, {3920, 32778, 32854}, {4028, 69544, 67208}, {4418, 27184, 33098}, {5263, 25760, 33104}, {5263, 30832, 25760}, {6679, 70972, 5278}, {19808, 33126, 32771}, {19856, 29640, 2}, {21085, 29645, 3187}, {29865, 59306, 2}, {31037, 70482, 32946}, {33155, 46918, 49474}


X(72003) = X(1)X(2)∩X(141)X(17123)

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

X(72003) lies on these lines: {1, 2}, {141, 17123}, {238, 33085}, {244, 33157}, {312, 33147}, {333, 31289}, {354, 33159}, {748, 33082}, {982, 17279}, {1001, 33174}, {1054, 59692}, {1279, 33079}, {2887, 17283}, {3315, 33162}, {3589, 4038}, {3662, 4011}, {3685, 24169}, {3742, 17357}, {3752, 33158}, {3763, 8167}, {3834, 33097}, {3836, 32942}, {3846, 25531}, {3925, 31252}, {3932, 17598}, {3943, 59477}, {4358, 33123}, {4383, 33087}, {4387, 33149}, {4423, 32784}, {4425, 17291}, {4432, 33068}, {4703, 17227}, {5284, 32781}, {8707, 28574}, {8731, 44304}, {15485, 26034}, {16059, 37577}, {16610, 33160}, {17063, 32777}, {17125, 32782}, {17231, 32861}, {17232, 32946}, {17234, 25496}, {17243, 17600}, {17267, 33092}, {17280, 24165}, {17282, 17889}, {17290, 33154}, {17352, 32853}, {17353, 32913}, {17356, 33132}, {17449, 33166}, {17526, 37608}, {17591, 17776}, {17597, 33165}, {18134, 70942}, {18139, 32944}, {18141, 62841}, {18201, 44416}, {18743, 26128}, {24003, 33126}, {24542, 32918}, {24552, 25961}, {24988, 32945}, {25957, 33106}, {26061, 64149}, {26073, 71450}, {26098, 53665}, {26688, 33065}, {27064, 49676}, {28256, 38832}, {30818, 33130}, {31151, 63979}, {32857, 32930}, {32949, 70483}, {33081, 37680}, {33084, 37679}, {33124, 59511}, {37687, 69300}, {56460, 67265}, {62814, 69298}

X(72003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3720, 29633}, {2, 3840, 33140}, {2, 29637, 32783}, {2, 29642, 29640}, {2, 29677, 29637}, {2, 29814, 29663}, {2, 29824, 29850}, {2, 29870, 29678}, {2, 30942, 33138}, {2, 30947, 29635}, {2, 33171, 16569}, {2, 33173, 899}, {238, 69092, 33085}, {244, 33157, 33167}, {614, 29674, 32866}, {748, 33172, 33082}, {982, 17279, 33164}, {3662, 4011, 33099}, {3742, 17357, 32780}, {3836, 32942, 33109}, {4358, 33123, 33152}, {5272, 17284, 32778}, {7191, 29687, 32847}, {17232, 70485, 32946}, {17284, 25509, 5272}, {29858, 31242, 2}, {32930, 69251, 32857}


X(72004) = X(1)X(2)∩X(35)X(4199)

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

X(72004) lies on these lines: {1, 2}, {35, 4199}, {37, 33160}, {69, 37604}, {75, 33152}, {81, 69300}, {100, 31247}, {141, 17122}, {171, 1211}, {210, 32780}, {226, 24342}, {238, 5743}, {333, 70972}, {750, 32782}, {756, 32779}, {894, 59628}, {940, 33084}, {984, 33167}, {986, 5955}, {1011, 1324}, {1054, 54311}, {1213, 6690}, {1215, 19808}, {1376, 32784}, {1654, 71489}, {1757, 4104}, {2244, 17256}, {2308, 37656}, {2887, 30832}, {3052, 50296}, {3550, 50295}, {3696, 33135}, {3739, 33130}, {3740, 33159}, {3745, 32861}, {3769, 50308}, {3775, 14829}, {3791, 4886}, {3842, 33116}, {3846, 5263}, {3944, 50314}, {3966, 17716}, {3967, 50052}, {3980, 27184}, {3989, 33168}, {4026, 60714}, {4191, 34868}, {4192, 29315}, {4205, 37573}, {4213, 39579}, {4357, 17596}, {4359, 32775}, {4363, 33101}, {4365, 46918}, {4413, 33174}, {4417, 50302}, {4418, 26580}, {4425, 32932}, {4640, 24697}, {4643, 4650}, {4649, 6703}, {4682, 32846}, {4697, 33066}, {4710, 30710}, {4893, 69316}, {4981, 33119}, {5010, 37175}, {5224, 32916}, {5233, 25496}, {5241, 17123}, {5251, 8731}, {5712, 43997}, {5739, 62841}, {5741, 32772}, {6679, 17277}, {7359, 71491}, {8706, 28505}, {9347, 32852}, {10164, 64700}, {13725, 37574}, {14555, 16468}, {16058, 38903}, {17124, 33172}, {17280, 59517}, {17289, 25120}, {17332, 59574}, {17357, 58451}, {17359, 59506}, {17719, 31993}, {19344, 39578}, {19804, 26128}, {21020, 33133}, {24325, 33126}, {24552, 25960}, {24589, 33123}, {25440, 37467}, {25760, 33109}, {26034, 56010}, {26061, 63961}, {26627, 33069}, {28653, 70370}, {30966, 70448}, {31037, 32949}, {32843, 70482}, {32864, 70970}, {32917, 41809}, {32946, 70484}, {33081, 37633}, {33087, 37674}, {33121, 49457}, {33158, 44307}, {33682, 62998}, {37365, 63423}, {37759, 62226}, {37799, 57652}, {47821, 66518}, {48547, 59914}, {48643, 68999}, {49469, 70517}, {50093, 59544}, {50312, 55095}, {51294, 56078}, {59690, 70559}

X(72004) = complement of X(29837)
X(72004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8, 29635}, {2, 10, 33138}, {2, 43, 29633}, {2, 3240, 29647}, {2, 4651, 29631}, {2, 17135, 29845}, {2, 29839, 1125}, {2, 29846, 29640}, {2, 31330, 33140}, {2, 32783, 29637}, {2, 33139, 29863}, {2, 33171, 26102}, {2, 33173, 30950}, {2, 33175, 3720}, {2, 59296, 25453}, {10, 1125, 16824}, {10, 59726, 7081}, {100, 31247, 69294}, {171, 1211, 33082}, {612, 32778, 32847}, {750, 32782, 33085}, {756, 32779, 33164}, {3775, 58443, 14829}, {3846, 5263, 33106}, {3920, 69252, 32866}, {3980, 27184, 32857}, {4359, 32775, 33147}, {4418, 26580, 33099}, {29841, 70973, 49488}, {59628, 69299, 894}


X(72005) = X(1)X(2)∩X(141)X(17125)

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

X(72005) lies on these lines: {1, 2}, {141, 17125}, {244, 17279}, {344, 46901}, {748, 33080}, {1150, 31289}, {2308, 18141}, {3120, 17282}, {3315, 33165}, {3589, 9345}, {3742, 26061}, {3816, 31237}, {3834, 24725}, {3836, 33104}, {3999, 71795}, {4003, 41310}, {4009, 71798}, {4011, 33098}, {4358, 33143}, {4379, 48102}, {4422, 36263}, {4423, 32781}, {4906, 71796}, {5284, 33174}, {8167, 69294}, {9335, 33167}, {10448, 25914}, {15485, 33086}, {16610, 33156}, {17063, 33157}, {17123, 33172}, {17232, 32843}, {17234, 32944}, {17267, 32848}, {17283, 25531}, {17298, 61707}, {17341, 33115}, {17352, 32919}, {17356, 33128}, {17450, 38047}, {17597, 69298}, {17721, 21026}, {18139, 70942}, {18743, 33123}, {24003, 33122}, {24295, 26627}, {24988, 32941}, {25961, 32942}, {26073, 71451}, {26688, 33064}, {28269, 61365}, {30829, 32775}, {30944, 44304}, {31252, 33108}, {32949, 70485}, {33081, 37679}, {33084, 37687}, {33087, 37680}, {33152, 46938}, {33159, 64149}

X(72005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3720, 29663}, {2, 3840, 24892}, {2, 26102, 29647}, {2, 26103, 29845}, {2, 29642, 29678}, {2, 29677, 24943}, {2, 29851, 29661}, {2, 30947, 29631}, {2, 30957, 29662}, {2, 33173, 16569}, {2, 33175, 62711}, {244, 17279, 33161}, {614, 29687, 32854}, {748, 69092, 33080}, {4011, 69251, 33098}, {17283, 25531, 25760}


X(72006) = X(1)X(2)∩X(31)X(5743)

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

X(72006) lies on these lines: {1, 2}, {31, 5743}, {141, 17124}, {748, 5241}, {750, 1211}, {756, 33161}, {940, 69300}, {1011, 2933}, {1150, 58443}, {1213, 2268}, {1376, 69294}, {2217, 30944}, {2292, 5955}, {2308, 14555}, {2895, 37604}, {3739, 33127}, {3740, 26061}, {3826, 31237}, {3842, 33113}, {3846, 33104}, {3980, 26580}, {3989, 17740}, {3994, 50048}, {4009, 50052}, {4023, 6703}, {4104, 32912}, {4359, 33143}, {4413, 7085}, {4682, 32852}, {4706, 50063}, {4893, 69313}, {5224, 32918}, {5233, 32772}, {5263, 25960}, {5741, 50302}, {6536, 17594}, {6537, 69231}, {9330, 33164}, {9342, 33174}, {9347, 32861}, {11358, 40109}, {17064, 21027}, {17122, 32782}, {17303, 21033}, {17720, 21020}, {17737, 59772}, {19804, 32775}, {19808, 32931}, {24295, 26688}, {24342, 31053}, {24589, 26128}, {24693, 48646}, {25957, 30832}, {26064, 37603}, {26223, 59628}, {26627, 33064}, {27081, 71479}, {31247, 32784}, {32780, 63961}, {32843, 70484}, {32853, 70970}, {32916, 41809}, {33081, 37674}, {33083, 56010}, {33084, 37633}, {33156, 44307}, {33682, 63010}, {37656, 62841}, {50314, 69173}, {63100, 71489}

X(72006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8, 29845}, {2, 10, 24892}, {2, 43, 29647}, {2, 899, 29663}, {2, 4651, 29635}, {2, 26038, 29850}, {2, 29830, 25501}, {2, 29846, 29661}, {2, 31330, 29662}, {2, 32783, 29677}, {2, 33171, 30950}, {2, 33173, 25502}, {2, 33175, 26102}, {2, 59296, 29631}, {78, 1698, 27714}, {612, 69252, 32854}, {750, 1211, 33080}, {3980, 26580, 33098}, {4023, 6703, 61358}, {29677, 32783, 24943}, {58443, 70972, 1150}


X(72007) = X(1)X(33086)∩X(2)X(2308)

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

X(72007) lies on these lines: {1, 33086}, {2, 2308}, {8, 17449}, {10, 26627}, {11, 31134}, {31, 29677}, {43, 32863}, {57, 15523}, {63, 29687}, {69, 899}, {81, 29663}, {100, 33087}, {141, 750}, {149, 31137}, {171, 24943}, {244, 3416}, {312, 33067}, {320, 32931}, {333, 25961}, {343, 25938}, {354, 33074}, {443, 59307}, {599, 4413}, {896, 17279}, {940, 29647}, {982, 32854}, {1054, 33077}, {1150, 3836}, {1155, 17231}, {1211, 17124}, {1376, 33081}, {1999, 33125}, {2177, 4966}, {2239, 30945}, {2550, 31136}, {2887, 29662}, {2895, 16569}, {3011, 21255}, {3187, 24169}, {3218, 29674}, {3306, 69252}, {3315, 49506}, {3550, 33173}, {3589, 62846}, {3631, 4023}, {3662, 17763}, {3663, 49990}, {3720, 18141}, {3752, 32852}, {3769, 33123}, {3771, 71479}, {3840, 6327}, {3844, 37520}, {3873, 33079}, {3875, 49995}, {3879, 67211}, {3912, 4414}, {3932, 36263}, {3967, 71797}, {3994, 17276}, {4000, 50756}, {4001, 62673}, {4009, 17345}, {4026, 9345}, {4030, 62869}, {4062, 17296}, {4358, 4655}, {4362, 69251}, {4365, 34255}, {4388, 26139}, {4392, 32847}, {4416, 60423}, {4429, 32919}, {4434, 33122}, {4645, 30942}, {4650, 33157}, {4660, 29824}, {4671, 32857}, {4683, 18743}, {4684, 67207}, {4706, 17372}, {4850, 32846}, {4851, 46904}, {4871, 50304}, {5205, 17288}, {5269, 29686}, {5311, 54311}, {5372, 33138}, {6536, 17022}, {6646, 64178}, {6685, 63056}, {6686, 63010}, {7081, 33069}, {7232, 32856}, {9352, 33160}, {10453, 32948}, {11679, 69253}, {14459, 17373}, {14829, 24892}, {14996, 29633}, {16496, 49996}, {17063, 33075}, {17122, 32782}, {17126, 29637}, {17184, 29649}, {17227, 32775}, {17232, 29632}, {17233, 32845}, {17234, 32917}, {17291, 29636}, {17298, 29828}, {17344, 61686}, {17591, 33093}, {17595, 32848}, {17596, 32858}, {17602, 48632}, {18134, 29678}, {18139, 29661}, {18201, 33089}, {21027, 38052}, {21342, 71796}, {23958, 33167}, {24589, 50308}, {24593, 48647}, {24627, 29643}, {24725, 30818}, {25453, 37639}, {25527, 29683}, {25959, 33140}, {26037, 37653}, {26102, 33083}, {26150, 29834}, {26227, 49676}, {26840, 32925}, {27003, 32778}, {28599, 29844}, {29631, 37684}, {29679, 32913}, {29684, 62845}, {29825, 37635}, {29827, 33112}, {29850, 37683}, {29851, 71476}, {29854, 38000}, {29863, 63078}, {29867, 37642}, {30567, 69173}, {30950, 50295}, {31151, 33108}, {31237, 37646}, {32784, 37633}, {32859, 59511}, {32915, 33068}, {33076, 64149}, {33091, 62865}, {33134, 70219}, {33159, 62795}, {33164, 67335}, {33165, 62235}, {33175, 56010}, {37656, 62711}, {37674, 69294}, {44419, 62849}, {48835, 49999}, {49448, 60459}, {49455, 50000}, {49505, 49991}, {49524, 54352}, {56782, 67976}, {69297, 71793}

X(72007) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 33085, 33080}, {31, 69092, 29677}, {81, 33174, 29663}, {171, 33172, 24943}, {312, 33067, 33098}, {599, 4413, 69300}, {940, 32781, 29647}, {982, 33078, 32854}, {1155, 17231, 33156}, {3218, 29674, 33161}, {3662, 17763, 33143}, {4645, 30942, 33104}, {5205, 17288, 33065}, {14829, 25957, 24892}, {17232, 71477, 29632}, {18134, 32918, 29678}, {18139, 32916, 29661}, {18141, 26034, 3720}


X(72008) = X(1)X(2895)∩X(2)X(2308)

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

X(72009) lies on these lines: {1, 2895}, {2, 2308}, {4, 59307}, {6, 29647}, {8, 4365}, {9, 15523}, {10, 6327}, {31, 1211}, {37, 32852}, {38, 3764}, {42, 5739}, {43, 33083}, {44, 26061}, {45, 69295}, {55, 69300}, {63, 69252}, {69, 3720}, {75, 4683}, {141, 748}, {210, 33074}, {238, 24943}, {239, 32776}, {319, 32915}, {321, 4703}, {333, 24892}, {343, 25885}, {354, 17344}, {497, 31136}, {516, 70516}, {524, 62821}, {599, 4423}, {614, 17272}, {750, 5743}, {752, 70972}, {756, 3416}, {846, 33077}, {899, 14555}, {956, 28377}, {966, 59306}, {968, 4062}, {984, 32854}, {993, 49723}, {1001, 33081}, {1125, 63056}, {1150, 3846}, {1330, 31339}, {1376, 40109}, {1468, 49716}, {1621, 31143}, {1654, 4388}, {1757, 29667}, {1836, 3958}, {1899, 3691}, {2268, 71286}, {2292, 5814}, {2886, 49724}, {2887, 5278}, {3120, 5271}, {3187, 4425}, {3219, 32778}, {3305, 29687}, {3578, 32853}, {3661, 32930}, {3679, 5080}, {3681, 33076}, {3683, 33156}, {3686, 3914}, {3687, 4414}, {3696, 33094}, {3703, 17332}, {3706, 4690}, {3715, 69298}, {3751, 29685}, {3757, 33065}, {3771, 31037}, {3775, 24552}, {3876, 25308}, {3883, 3938}, {3923, 56810}, {3925, 17330}, {3936, 29661}, {3989, 17257}, {3993, 20017}, {3994, 69089}, {4023, 44419}, {4026, 61358}, {4042, 33136}, {4104, 63134}, {4357, 17017}, {4359, 4655}, {4361, 33145}, {4362, 26580}, {4383, 32781}, {4384, 69253}, {4387, 4445}, {4389, 32924}, {4416, 32912}, {4417, 29678}, {4450, 70970}, {4645, 26037}, {4651, 4660}, {4657, 71184}, {4854, 17362}, {4865, 4981}, {4886, 24723}, {4914, 49515}, {4974, 32774}, {5014, 49457}, {5220, 33162}, {5224, 32772}, {5233, 32918}, {5235, 33111}, {5241, 17124}, {5251, 48839}, {5263, 41816}, {5284, 33087}, {5311, 5847}, {5361, 33140}, {5737, 33105}, {5741, 32916}, {6535, 56082}, {6646, 17155}, {6685, 63010}, {6703, 62846}, {7226, 32866}, {7262, 32779}, {7290, 29686}, {8013, 50314}, {8616, 33175}, {10436, 64164}, {10448, 49728}, {10453, 17343}, {10477, 20961}, {11269, 14552}, {11679, 69173}, {11680, 30981}, {12514, 20653}, {12588, 28387}, {14829, 25960}, {15485, 33173}, {16475, 68945}, {16569, 33086}, {16704, 29635}, {16823, 33069}, {16825, 17184}, {17123, 33172}, {17125, 69092}, {17127, 32783}, {17135, 43990}, {17238, 70481}, {17253, 17599}, {17256, 33073}, {17260, 29854}, {17270, 20553}, {17271, 32942}, {17277, 25957}, {17306, 29684}, {17328, 32844}, {17331, 29641}, {17346, 32773}, {17347, 32940}, {17349, 29850}, {17676, 59303}, {19684, 50298}, {19742, 25453}, {19804, 33067}, {19822, 24695}, {21085, 32929}, {23682, 26085}, {24325, 32859}, {24597, 29863}, {24697, 28606}, {24725, 31993}, {25958, 33138}, {26098, 30970}, {26102, 32863}, {26227, 69299}, {27065, 29674}, {27081, 70482}, {27184, 32914}, {27714, 54421}, {28605, 33099}, {29631, 37652}, {29633, 63074}, {29642, 31017}, {29663, 32784}, {29816, 51192}, {29845, 37683}, {29846, 71476}, {29849, 38000}, {30942, 37653}, {31034, 43223}, {31089, 52133}, {32771, 33066}, {32855, 62796}, {32948, 59296}, {33079, 63961}, {33090, 49448}, {33092, 33761}, {33095, 42334}, {33100, 49474}, {33112, 59312}, {33113, 59624}, {33117, 60731}, {33160, 62838}, {33163, 54280}, {33174, 37680}, {36263, 69091}, {37319, 71288}, {41809, 50302}, {49483, 71797}, {50290, 67208}, {51196, 69544}, {63131, 70522}, {71236, 71246}

X(72008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 33082, 33080}, {6, 69294, 29647}, {75, 4683, 33098}, {141, 748, 29677}, {141, 41002, 748}, {238, 32782, 24943}, {333, 25760, 24892}, {984, 33075, 32854}, {1150, 3846, 29662}, {1621, 31143, 33084}, {1654, 4388, 31330}, {1836, 17275, 21020}, {3219, 32778, 33161}, {3966, 4643, 38}, {4388, 31330, 33104}, {4417, 32917, 29678}, {4703, 50308, 321}, {4886, 24723, 32860}, {4914, 49515, 71796}, {5739, 50295, 42}, {6327, 63100, 10}, {14555, 26034, 899}, {17257, 33088, 3989}, {17346, 32773, 32864}, {24697, 32861, 28606}, {27184, 32914, 33143}, {27184, 70969, 32914}, {31037, 71478, 3771}, {32784, 32911, 29663}, {33083, 37656, 43}, {33084, 50296, 1621}


X(72009) = X(1)X(18141)∩X(2)X(2308)

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

X(72009) lies on these lines: {1, 18141}, {2, 2308}, {57, 29674}, {69, 16569}, {141, 17122}, {171, 29637}, {244, 32866}, {306, 1054}, {312, 32857}, {320, 59511}, {354, 33079}, {750, 32783}, {899, 32863}, {940, 29633}, {982, 32847}, {1056, 3679}, {1150, 25961}, {1155, 33158}, {1330, 46827}, {1376, 33087}, {1757, 62673}, {1961, 54311}, {1999, 24169}, {2886, 31151}, {3218, 29687}, {3306, 32778}, {3416, 17063}, {3434, 31137}, {3662, 29649}, {3703, 18201}, {3720, 33086}, {3742, 33076}, {3752, 32846}, {3771, 17232}, {3834, 33130}, {3836, 14829}, {3840, 4645}, {3912, 17596}, {3914, 70219}, {3944, 30567}, {3971, 26840}, {3974, 49532}, {4001, 60423}, {4082, 24821}, {4135, 4440}, {4358, 33067}, {4388, 4871}, {4413, 33084}, {4434, 33124}, {4650, 17279}, {4655, 18743}, {4680, 53619}, {4685, 26073}, {4703, 30829}, {4860, 33169}, {4966, 60714}, {5205, 33064}, {5269, 29660}, {5739, 62711}, {6327, 30957}, {6646, 59517}, {6679, 17283}, {6685, 17300}, {6686, 62998}, {7081, 49676}, {7232, 33101}, {8167, 50296}, {9342, 69300}, {9352, 33156}, {10327, 62865}, {14996, 29663}, {15485, 63140}, {15523, 27003}, {16484, 44419}, {16610, 32861}, {16990, 17298}, {17124, 32782}, {17126, 29677}, {17231, 33160}, {17234, 32916}, {17263, 59624}, {17288, 69299}, {17291, 29645}, {17292, 59628}, {17344, 58451}, {17345, 59506}, {17375, 59298}, {17449, 33091}, {17595, 33092}, {17763, 33147}, {18139, 29640}, {19879, 37607}, {21255, 66632}, {23958, 33161}, {24003, 33066}, {24260, 31028}, {24593, 33119}, {24627, 29653}, {24988, 32864}, {25453, 37684}, {25502, 50295}, {25957, 33140}, {25959, 29662}, {26034, 26102}, {26150, 29842}, {27002, 71085}, {29632, 71479}, {29642, 71477}, {29668, 50289}, {29820, 63134}, {29824, 32948}, {29839, 59679}, {29850, 37639}, {29856, 63078}, {29862, 59491}, {30818, 33097}, {30942, 33109}, {30950, 33083}, {32780, 37520}, {32781, 37633}, {32784, 37674}, {32855, 70256}, {33074, 64149}, {33153, 62659}, {33171, 56010}, {34255, 49474}, {62235, 69298}

X(72009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 33085, 33082}, {57, 29674, 33167}, {171, 69092, 29637}, {244, 33078, 32866}, {750, 33172, 32783}, {940, 33174, 29633}, {3218, 29687, 33164}, {3662, 29649, 33152}, {3836, 14829, 33138}, {3840, 4645, 33106}, {4358, 33067, 33099}, {17763, 69251, 33147}, {18139, 32918, 29640}


X(72010) = X(2)X(4101)∩X(2)X(2308)

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

X(72010) lies on these lines: {1, 4101}, {2, 2308}, {4, 1695}, {8, 3971}, {9, 32778}, {10, 4388}, {11, 49724}, {36, 49723}, {37, 32861}, {42, 37656}, {43, 14555}, {44, 32780}, {45, 33092}, {55, 50296}, {69, 26102}, {75, 4703}, {141, 17123}, {171, 5743}, {210, 33076}, {238, 1211}, {239, 4425}, {312, 50308}, {333, 3846}, {391, 33137}, {524, 4038}, {599, 8167}, {740, 4886}, {748, 29637}, {756, 32847}, {846, 3687}, {899, 33083}, {966, 26098}, {982, 4643}, {984, 3966}, {993, 48839}, {1001, 33084}, {1125, 17778}, {1150, 25960}, {1193, 26064}, {1621, 69300}, {1654, 3741}, {1699, 5816}, {1961, 5847}, {2551, 59313}, {2886, 17330}, {2887, 17277}, {2895, 3720}, {3219, 33167}, {3305, 29674}, {3434, 3583}, {3578, 32919}, {3661, 4011}, {3666, 24697}, {3683, 33160}, {3685, 21085}, {3686, 24210}, {3696, 33095}, {3705, 17331}, {3706, 42334}, {3707, 29861}, {3715, 33165}, {3739, 33097}, {3740, 33079}, {3742, 17344}, {3757, 69299}, {3775, 32942}, {3840, 37653}, {3842, 33073}, {3876, 25306}, {3883, 3961}, {3944, 5271}, {3975, 70503}, {3989, 32842}, {4023, 60714}, {4042, 33141}, {4046, 4693}, {4357, 29821}, {4359, 4683}, {4361, 33154}, {4362, 70969}, {4364, 17600}, {4383, 32784}, {4384, 17889}, {4416, 32913}, {4417, 29640}, {4423, 33087}, {4514, 49457}, {4647, 70502}, {4651, 32947}, {4655, 19804}, {4660, 59296}, {4672, 19808}, {4716, 4854}, {4970, 9791}, {4974, 19786}, {4981, 32844}, {5046, 59307}, {5057, 21020}, {5220, 33169}, {5224, 25496}, {5233, 32916}, {5235, 33105}, {5241, 17122}, {5263, 70972}, {5272, 17272}, {5278, 25760}, {5284, 31143}, {5361, 29662}, {5692, 26893}, {5737, 17717}, {5741, 32917}, {6327, 26037}, {6536, 17011}, {6537, 70975}, {6646, 24165}, {6679, 30832}, {6685, 63002}, {7779, 17252}, {8731, 71288}, {12699, 31327}, {14459, 27804}, {14997, 29663}, {15254, 33158}, {15485, 33171}, {15523, 27065}, {16569, 26034}, {16704, 29845}, {16817, 56949}, {16823, 33064}, {16825, 27184}, {17125, 33172}, {17238, 70485}, {17248, 29644}, {17256, 33071}, {17260, 29653}, {17275, 24703}, {17300, 25501}, {17332, 69091}, {17346, 32853}, {17348, 33132}, {17349, 25453}, {17772, 34064}, {19516, 29287}, {19732, 33111}, {19742, 29631}, {19856, 32772}, {20072, 71518}, {23659, 35623}, {24325, 33066}, {24342, 41011}, {24589, 33067}, {26105, 31137}, {26117, 59303}, {26580, 32914}, {29632, 31037}, {29633, 32911}, {29635, 37652}, {29647, 63074}, {29673, 60731}, {29687, 35595}, {29820, 49511}, {29824, 43990}, {29825, 63089}, {29837, 62989}, {29846, 71478}, {29851, 31017}, {30950, 32863}, {30970, 33107}, {31330, 33106}, {31993, 33096}, {32781, 37680}, {32846, 44307}, {32848, 33761}, {32851, 59624}, {32930, 56810}, {32945, 70970}, {33074, 63961}, {33112, 59306}, {33174, 37679}, {37607, 49716}, {37608, 54429}, {38000, 71085}, {43223, 62998}, {44419, 56009}, {49710, 59628}, {56010, 63140}, {69544, 69632}

X(72010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 33082, 33085}, {9, 32778, 33164}, {10, 4388, 33109}, {75, 4703, 33099}, {238, 1211, 32783}, {333, 3846, 33140}, {748, 32782, 29637}, {756, 33075, 32847}, {966, 26098, 59312}, {984, 3966, 32866}, {1211, 41002, 238}, {3219, 69252, 33167}, {3883, 4104, 3961}, {4359, 4683, 32857}, {5278, 25760, 33138}, {5284, 31143, 33081}, {14555, 50295, 43}, {16825, 27184, 33147}, {26034, 63003, 16569}, {26580, 32914, 33152}, {32772, 41809, 19856}, {32911, 69294, 29633}, {32942, 41816, 3775}


X(72011) = X(2)X(2308)∩X(42)X(18141)

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

X(72011) lies on these lines: {2, 2308}, {42, 18141}, {57, 29687}, {88, 32855}, {141, 17124}, {171, 29677}, {244, 32854}, {750, 24943}, {940, 29663}, {1054, 32858}, {2895, 62711}, {3120, 30567}, {3306, 15523}, {3742, 33074}, {3816, 31134}, {3834, 33127}, {3836, 24892}, {3840, 33104}, {3999, 71796}, {4009, 71797}, {4138, 62621}, {4358, 33098}, {4413, 33081}, {4438, 24593}, {4645, 30957}, {4675, 31264}, {4683, 30829}, {4860, 33162}, {4871, 6327}, {5205, 33069}, {5437, 69252}, {6686, 31034}, {9335, 32866}, {9342, 33084}, {9352, 33158}, {10327, 17449}, {11680, 31151}, {14829, 25961}, {16569, 32863}, {16610, 32852}, {17063, 33078}, {17122, 33172}, {17232, 29846}, {17234, 29661}, {17291, 29847}, {17595, 69295}, {17770, 26688}, {18139, 29678}, {18201, 32862}, {18743, 33067}, {23958, 33164}, {24003, 32859}, {24177, 49990}, {24627, 29854}, {24988, 32853}, {25502, 33083}, {25957, 29662}, {26034, 30950}, {26061, 37520}, {26102, 33086}, {26840, 64178}, {27002, 29849}, {27003, 29674}, {29642, 71479}, {29647, 33174}, {29649, 33143}, {29830, 59679}, {29850, 37684}, {29851, 71477}, {29867, 63078}, {29869, 53665}, {30947, 32947}, {31137, 33110}, {31237, 37634}, {31242, 33107}, {32781, 37674}, {32848, 70256}, {32912, 62673}, {33079, 64149}, {33099, 46938}, {33131, 70219}, {33144, 62659}, {33169, 65112}, {33173, 56010}, {37462, 59307}, {49994, 71794}, {49996, 62850}, {60459, 62865}

X(72011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 29687, 33161}, {750, 69092, 24943}, {17234, 32918, 29661}, {29649, 69251, 33143}, {33174, 37633, 29647}


X(72012) = X(1)X(37656)∩X(42)X(14555)

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

X(72012) lies on these lines: {1, 37656}, {2, 2308}, {8, 64178}, {9, 33161}, {10, 33104}, {11, 17330}, {31, 5743}, {36, 48839}, {42, 14555}, {45, 32848}, {69, 30950}, {100, 50296}, {141, 17125}, {149, 3679}, {244, 4643}, {333, 25960}, {391, 11269}, {524, 9345}, {748, 1211}, {750, 5241}, {756, 3966}, {899, 50295}, {966, 30970}, {978, 26064}, {997, 64710}, {1001, 69300}, {1125, 31034}, {1654, 26139}, {1698, 33112}, {2177, 4023}, {2478, 59307}, {2895, 26102}, {3120, 4384}, {3305, 15523}, {3583, 48852}, {3624, 37635}, {3626, 21283}, {3715, 33162}, {3720, 5739}, {3739, 24725}, {3740, 33074}, {3741, 63100}, {3816, 49724}, {3826, 31134}, {3842, 33070}, {3846, 5278}, {3886, 70522}, {3938, 4104}, {4011, 56810}, {4356, 49986}, {4358, 50308}, {4359, 4703}, {4383, 29663}, {4388, 26037}, {4417, 29661}, {4423, 33081}, {4655, 24589}, {4679, 17275}, {4683, 19804}, {4850, 24697}, {4886, 32915}, {5224, 32944}, {5233, 32917}, {5235, 17717}, {5256, 6536}, {5271, 69173}, {5284, 33084}, {5741, 29678}, {6535, 30568}, {7308, 29687}, {9330, 32847}, {9350, 44419}, {10436, 61707}, {14969, 15534}, {14997, 29633}, {15254, 33156}, {15481, 71795}, {15485, 33175}, {16569, 33083}, {16823, 33065}, {16825, 26580}, {17123, 29677}, {17257, 46901}, {17260, 29643}, {17271, 25531}, {17277, 25760}, {17331, 71801}, {17332, 36263}, {17335, 33115}, {17343, 30947}, {17346, 32919}, {17348, 33128}, {17349, 29631}, {17763, 70969}, {17770, 26627}, {19732, 33105}, {19742, 29635}, {20962, 35628}, {21020, 24703}, {24552, 70972}, {25496, 41809}, {25501, 63056}, {25502, 32863}, {26038, 32948}, {26098, 59306}, {27065, 32778}, {27081, 70483}, {27714, 54386}, {29639, 63978}, {29642, 31037}, {29647, 32911}, {29674, 35595}, {29845, 37652}, {30944, 71288}, {30957, 37653}, {31143, 33087}, {32781, 37679}, {32784, 37680}, {32852, 44307}, {32855, 33761}, {32941, 70970}, {32947, 59296}, {33076, 63961}, {33086, 62711}, {33107, 59312}, {33120, 60731}, {33174, 37687}, {38390, 58379}, {40998, 70516}, {43223, 63010}, {50290, 67211}, {51571, 70535}

X(72012) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 69252, 33161}, {333, 25960, 29662}, {748, 1211, 24943}, {756, 3966, 32854}, {3846, 5278, 24892}, {4359, 4703, 33098}, {4383, 69294, 29663}, {5743, 41002, 31}, {16825, 26580, 33143}, {17123, 32782, 29677}, {50295, 63003, 899}


X(72013) = X(1)X(3814)∩X(2)X(11)

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

X(72013) lies on these lines: {1, 3814}, {2, 11}, {3, 61521}, {4, 5253}, {5, 944}, {7, 37358}, {8, 496}, {10, 3885}, {12, 3622}, {20, 7681}, {21, 499}, {35, 17566}, {36, 10199}, {37, 29680}, {42, 24217}, {56, 5046}, {57, 5057}, {78, 25522}, {81, 37373}, {86, 14008}, {104, 6929}, {119, 7967}, {142, 7678}, {145, 1329}, {165, 31224}, {226, 64149}, {238, 29662}, {244, 3944}, {312, 33089}, {329, 5729}, {354, 5087}, {355, 6975}, {377, 10591}, {388, 5187}, {392, 70776}, {404, 1479}, {405, 26127}, {442, 5550}, {474, 9669}, {495, 17533}, {513, 26910}, {515, 6945}, {516, 9352}, {517, 6963}, {518, 27131}, {535, 37587}, {551, 7951}, {614, 33133}, {693, 15283}, {748, 33140}, {750, 33106}, {756, 29676}, {858, 17111}, {899, 33141}, {908, 3873}, {936, 5178}, {938, 26129}, {940, 33107}, {946, 6943}, {958, 37162}, {962, 6922}, {971, 17618}, {982, 1647}, {986, 28096}, {993, 3582}, {999, 5080}, {1054, 33094}, {1058, 5552}, {1086, 9335}, {1125, 2476}, {1149, 37716}, {1191, 54355}, {1210, 3869}, {1279, 29665}, {1385, 6941}, {1478, 37375}, {1484, 5790}, {1532, 5731}, {1538, 10167}, {1698, 24387}, {1699, 3306}, {1737, 3877}, {1836, 27003}, {1985, 19684}, {1997, 10327}, {2320, 6980}, {2475, 10896}, {2478, 2975}, {2551, 10529}, {2887, 30957}, {3006, 18743}, {3057, 25005}, {3060, 50362}, {3085, 6931}, {3090, 10806}, {3091, 12667}, {3120, 17063}, {3218, 17728}, {3219, 4679}, {3240, 37663}, {3241, 17757}, {3251, 21260}, {3259, 67627}, {3295, 27529}, {3304, 20060}, {3305, 5231}, {3315, 33144}, {3421, 11240}, {3436, 6919}, {3452, 3681}, {3486, 26476}, {3487, 37359}, {3523, 15908}, {3576, 6932}, {3583, 17579}, {3586, 35262}, {3589, 29864}, {3617, 3813}, {3621, 21031}, {3623, 12607}, {3624, 4197}, {3636, 37719}, {3662, 71110}, {3705, 4358}, {3720, 17717}, {3741, 25960}, {3742, 17605}, {3752, 33134}, {3753, 7743}, {3756, 3782}, {3772, 7292}, {3817, 5249}, {3822, 25055}, {3838, 27186}, {3840, 25760}, {3841, 34595}, {3846, 30942}, {3868, 21616}, {3870, 30827}, {3871, 26364}, {3872, 37704}, {3876, 10916}, {3884, 18395}, {3889, 21077}, {3891, 5211}, {3898, 6702}, {3913, 31246}, {3914, 5121}, {3920, 17721}, {3932, 46938}, {3975, 62482}, {4011, 24709}, {4038, 30981}, {4188, 6284}, {4189, 5433}, {4190, 5225}, {4202, 25492}, {4294, 6921}, {4302, 13587}, {4313, 25962}, {4342, 51433}, {4383, 33142}, {4387, 33168}, {4389, 53564}, {4392, 4415}, {4417, 29824}, {4425, 25378}, {4442, 17490}, {4511, 5722}, {4514, 37758}, {4640, 61649}, {4661, 51463}, {4666, 5219}, {4671, 69091}, {4678, 9711}, {4772, 21927}, {4847, 38210}, {4850, 24210}, {4855, 66682}, {4857, 25440}, {4860, 17483}, {4861, 11373}, {4871, 25957}, {4872, 26229}, {4885, 11193}, {4999, 16865}, {5010, 6681}, {5014, 5205}, {5047, 26363}, {5056, 10585}, {5084, 5260}, {5086, 9581}, {5123, 5919}, {5133, 23304}, {5141, 7173}, {5180, 36279}, {5204, 15680}, {5226, 52254}, {5233, 17135}, {5265, 57285}, {5272, 33129}, {5276, 9599}, {5277, 9665}, {5289, 61717}, {5303, 6872}, {5311, 17722}, {5316, 24386}, {5328, 36845}, {5330, 10573}, {5333, 14009}, {5361, 41002}, {5422, 68770}, {5435, 44447}, {5439, 6845}, {5440, 18527}, {5443, 30143}, {5533, 12647}, {5603, 6882}, {5658, 8226}, {5704, 68599}, {5708, 14450}, {5718, 29814}, {5741, 10453}, {5744, 33994}, {5748, 10580}, {5818, 10943}, {5883, 18393}, {5886, 6830}, {5901, 6971}, {5902, 11813}, {6063, 40619}, {6075, 61729}, {6172, 41555}, {6173, 30311}, {6261, 6828}, {6376, 71488}, {6713, 6950}, {6735, 63993}, {6829, 11230}, {6831, 68034}, {6840, 22753}, {6850, 10598}, {6880, 59421}, {6891, 10531}, {6893, 10785}, {6900, 45630}, {6902, 11249}, {6906, 26492}, {6907, 54445}, {6909, 26333}, {6911, 18499}, {6914, 18861}, {6915, 48482}, {6923, 59391}, {6938, 38693}, {6940, 10525}, {6944, 12116}, {6946, 37820}, {6948, 10724}, {6949, 10267}, {6959, 11491}, {6965, 22758}, {6970, 37000}, {6972, 11496}, {6973, 12115}, {6979, 11500}, {6981, 10786}, {6990, 61268}, {7191, 17720}, {7491, 61534}, {7504, 10198}, {7679, 38316}, {7705, 10039}, {7746, 68893}, {7790, 27195}, {7956, 9812}, {7988, 10582}, {8033, 30992}, {8086, 8126}, {8125, 8379}, {8165, 56879}, {8727, 9776}, {9580, 31190}, {9597, 63537}, {9624, 67856}, {9668, 16371}, {9670, 20066}, {9710, 46932}, {9778, 37364}, {9780, 17527}, {9957, 17619}, {9961, 63989}, {10072, 54391}, {10177, 61008}, {10526, 45977}, {10587, 10588}, {10893, 37437}, {10980, 31164}, {11113, 15325}, {11124, 15280}, {11269, 32911}, {11393, 35973}, {11682, 67931}, {11814, 29673}, {12053, 14923}, {12114, 13729}, {12572, 62827}, {12915, 17615}, {12943, 40726}, {12953, 37256}, {13161, 28018}, {13405, 62862}, {13411, 62870}, {13747, 15171}, {14011, 64415}, {15016, 64762}, {15338, 37307}, {16062, 26094}, {16067, 19785}, {16484, 29678}, {16569, 33136}, {16610, 33131}, {16842, 31493}, {16859, 24953}, {16862, 26060}, {16920, 26686}, {17018, 37662}, {17019, 17723}, {17024, 17602}, {17064, 26724}, {17074, 34029}, {17122, 33104}, {17123, 24892}, {17124, 33109}, {17125, 33138}, {17126, 37634}, {17127, 37646}, {17174, 18165}, {17244, 20544}, {17279, 29872}, {17352, 23344}, {17449, 33101}, {17536, 19854}, {17550, 26959}, {17575, 19877}, {17595, 33100}, {17597, 33153}, {17606, 58679}, {17616, 58623}, {17681, 28734}, {17718, 29817}, {17725, 29818}, {17768, 23958}, {17777, 32933}, {17778, 30960}, {17917, 37371}, {17923, 37372}, {18135, 69254}, {18139, 30947}, {18201, 33098}, {18228, 64153}, {18230, 64443}, {18391, 62826}, {18444, 48697}, {18515, 61566}, {19634, 40215}, {19860, 50443}, {19878, 41859}, {20070, 50031}, {20107, 65142}, {20196, 24392}, {20486, 29572}, {20545, 41839}, {20942, 69301}, {21214, 21935}, {21241, 25961}, {21242, 26037}, {21252, 26913}, {22172, 24230}, {23155, 67494}, {23351, 46402}, {23542, 25513}, {23708, 54318}, {24003, 33117}, {24045, 68950}, {24239, 28606}, {24351, 30019}, {24477, 31018}, {24954, 68616}, {25079, 36568}, {25496, 29845}, {25525, 52255}, {25533, 40214}, {25681, 34772}, {25722, 66213}, {25958, 69092}, {26019, 26626}, {26098, 37633}, {26102, 33105}, {26475, 54361}, {26532, 63587}, {26637, 64409}, {26688, 33118}, {26801, 33046}, {26842, 61716}, {27383, 50206}, {27385, 63999}, {29631, 70942}, {29635, 32944}, {29638, 40172}, {29649, 32844}, {29655, 32931}, {29664, 44307}, {29667, 30818}, {29668, 32775}, {29820, 33127}, {29822, 44411}, {29827, 69294}, {29843, 46897}, {29844, 32927}, {30144, 37702}, {30147, 37735}, {30566, 32937}, {30567, 33078}, {30588, 54884}, {30699, 30778}, {30829, 69250}, {30830, 68951}, {30946, 69083}, {30950, 33111}, {30961, 71696}, {31008, 69076}, {31137, 33081}, {31145, 44847}, {31160, 37602}, {31231, 35258}, {31397, 62835}, {31418, 37462}, {32852, 70219}, {32915, 71085}, {33102, 70256}, {33112, 37674}, {33120, 59511}, {33137, 37680}, {33139, 37679}, {33864, 62697}, {34629, 35000}, {35645, 56878}, {37354, 70419}, {37355, 59297}, {37365, 70484}, {37370, 70481}, {37692, 64675}, {37726, 59388}, {38058, 64109}, {39595, 62807}, {40688, 62221}, {40998, 59491}, {42356, 62778}, {42819, 61648}, {44623, 63072}, {47399, 68378}, {48627, 48645}, {49454, 53619}, {50102, 50533}, {50444, 64673}, {50824, 61580}, {51783, 63145}, {51785, 63130}, {54342, 58453}, {55867, 66515}, {57518, 70837}, {58564, 61013}, {60919, 61026}, {60944, 64738}, {62297, 63147}, {62806, 66632}, {63964, 64953}, {64002, 64124}, {64735, 66045}, {67214, 67474}, {68946, 71609}

X(72013) = reflection of X(26910) in the X(1)X(3) X(72013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3825, 4193}, {1, 4193, 11681}, {2, 11, 11680}, {2, 149, 1376}, {2, 497, 100}, {2, 2550, 9342}, {2, 5274, 3434}, {2, 10584, 31272}, {2, 11238, 49719}, {2, 11680, 33108}, {2, 20075, 59572}, {2, 26105, 5284}, {2, 33110, 4413}, {2, 61155, 5432}, {11, 3816, 2}, {11, 3925, 3829}, {12, 3847, 5154}, {100, 497, 34611}, {100, 5284, 54348}, {149, 1376, 49719}, {244, 3944, 33146}, {312, 69134, 33089}, {354, 5087, 31053}, {474, 9669, 52367}, {496, 4187, 8}, {497, 59572, 20075}, {908, 11019, 3873}, {982, 69173, 33151}, {999, 5080, 34605}, {999, 17556, 5080}, {1125, 7741, 2476}, {1210, 41012, 3869}, {1329, 37722, 145}, {1376, 11238, 149}, {1479, 10200, 404}, {1621, 31272, 2}, {1647, 69173, 982}, {1699, 3306, 20292}, {1699, 31249, 3306}, {2478, 3086, 2975}, {3434, 5274, 10707}, {3436, 14986, 62837}, {3452, 26015, 3681}, {3576, 67857, 6932}, {3622, 5154, 12}, {3624, 25639, 4197}, {3705, 4358, 32862}, {3742, 17605, 31019}, {3817, 5249, 10129}, {3840, 25760, 33172}, {3846, 30942, 32782}, {4413, 11235, 33110}, {5084, 10527, 5260}, {5084, 47743, 10527}, {5141, 46934, 25466}, {5187, 10586, 388}, {5316, 24386, 25006}, {5432, 6667, 2}, {5432, 49736, 61155}, {6284, 6691, 4188}, {6667, 49736, 5432}, {6872, 7288, 5303}, {6919, 14986, 3436}, {7173, 25466, 5141}, {7956, 37374, 9812}, {7988, 10582, 31266}, {8167, 31245, 2}, {8227, 63963, 6828}, {9581, 19861, 5086}, {9957, 17619, 70802}, {10589, 26105, 2}, {10896, 25524, 2475}, {12053, 24982, 14923}, {17527, 24390, 9780}, {17575, 31419, 19877}, {17728, 24703, 3218}, {20075, 59572, 100}, {20196, 24392, 67097}, {24386, 25006, 64361}, {24709, 33119, 4011}, {38028, 60759, 6980}, {40998, 59491, 62838}


X(72014) = X(1)X(26724)∩X(2)X(11)

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

X(72014) lies on these lines: {1, 26724}, {2, 11}, {3, 26060}, {5, 6361}, {8, 8728}, {9, 20292}, {10, 3681}, {12, 46933}, {37, 33131}, {40, 6991}, {45, 33100}, {57, 30312}, {63, 38052}, {75, 32862}, {142, 3873}, {145, 9710}, {165, 10883}, {210, 31019}, {226, 7679}, {329, 442}, {377, 5260}, {388, 50237}, {404, 19854}, {443, 2975}, {474, 41345}, {484, 1698}, {495, 53620}, {498, 31254}, {499, 17535}, {516, 41858}, {518, 27186}, {612, 33129}, {740, 29854}, {748, 33109}, {750, 33138}, {756, 17889}, {899, 33111}, {940, 33139}, {958, 20067}, {984, 33146}, {999, 57005}, {1086, 7226}, {1211, 25959}, {1329, 18231}, {1479, 17536}, {1738, 28606}, {1836, 27065}, {1961, 33128}, {2308, 50301}, {2887, 26037}, {3006, 19804}, {3125, 69845}, {3219, 5880}, {3240, 17056}, {3295, 50207}, {3436, 4208}, {3452, 10129}, {3475, 62236}, {3525, 26470}, {3579, 6990}, {3616, 17529}, {3617, 25466}, {3634, 4193}, {3662, 4981}, {3679, 33081}, {3696, 32858}, {3697, 3824}, {3705, 24589}, {3715, 17484}, {3720, 32865}, {3739, 29667}, {3740, 31053}, {3741, 25961}, {3752, 29664}, {3755, 62840}, {3772, 5297}, {3790, 4980}, {3813, 46934}, {3822, 19875}, {3823, 29679}, {3825, 19872}, {3828, 7951}, {3836, 31330}, {3838, 27131}, {3842, 32776}, {3870, 38200}, {3876, 12609}, {3890, 24564}, {3920, 24789}, {3932, 28605}, {3936, 59296}, {3968, 12736}, {3980, 33115}, {3989, 33149}, {3996, 29830}, {4002, 17658}, {4042, 32863}, {4078, 42044}, {4188, 24953}, {4202, 19853}, {4294, 31259}, {4302, 16858}, {4359, 29641}, {4361, 33093}, {4363, 33166}, {4383, 33112}, {4384, 33075}, {4392, 40688}, {4415, 9330}, {4418, 24693}, {4425, 25352}, {4430, 25557}, {4442, 41839}, {4645, 5278}, {4651, 18134}, {4666, 20195}, {4678, 15888}, {4847, 38204}, {4859, 62833}, {4863, 29817}, {4872, 28653}, {4999, 17572}, {5014, 16823}, {5056, 15908}, {5080, 17528}, {5086, 64673}, {5133, 23305}, {5141, 46931}, {5154, 46930}, {5173, 61008}, {5178, 54392}, {5217, 15674}, {5220, 17483}, {5224, 20347}, {5235, 26034}, {5251, 17579}, {5253, 19843}, {5268, 33133}, {5271, 33078}, {5300, 16817}, {5303, 6904}, {5311, 33132}, {5435, 64737}, {5550, 24390}, {5584, 6894}, {5657, 6881}, {5687, 50726}, {5737, 33086}, {5741, 26038}, {5743, 25958}, {5745, 9352}, {5775, 17757}, {5790, 9803}, {5818, 37438}, {5853, 62862}, {5905, 38057}, {5927, 6937}, {6284, 16859}, {6327, 17277}, {6684, 6828}, {6703, 29868}, {6829, 26446}, {6830, 11231}, {6883, 18499}, {6884, 10310}, {6900, 35239}, {6932, 10175}, {6943, 31423}, {6945, 54447}, {6976, 10724}, {6980, 64193}, {6993, 64111}, {7191, 17278}, {7321, 71793}, {7486, 7681}, {7678, 9580}, {7741, 51073}, {8226, 9778}, {8580, 31266}, {8727, 64108}, {9347, 40940}, {9655, 50713}, {9668, 17542}, {9669, 16854}, {9708, 44217}, {9776, 64153}, {10303, 63980}, {10527, 17582}, {11019, 64361}, {11108, 52367}, {11220, 64113}, {11517, 63269}, {12558, 63469}, {14005, 19784}, {14009, 64425}, {15171, 17590}, {16062, 19874}, {16465, 61028}, {16569, 33105}, {16610, 29680}, {16819, 33840}, {16825, 33072}, {16830, 32774}, {16853, 26127}, {16862, 31493}, {16991, 28604}, {17020, 17723}, {17057, 51569}, {17063, 29690}, {17122, 24892}, {17123, 33104}, {17124, 33140}, {17125, 33106}, {17135, 17234}, {17140, 65198}, {17163, 17233}, {17181, 25585}, {17245, 29814}, {17337, 63979}, {17346, 20290}, {17356, 29666}, {17531, 26363}, {17605, 58451}, {17625, 60988}, {17776, 64010}, {18395, 67946}, {19732, 33083}, {19878, 37720}, {20057, 64200}, {20070, 68601}, {20556, 33838}, {20718, 26911}, {21020, 29674}, {21026, 32778}, {21027, 29687}, {21241, 25960}, {21242, 30957}, {21674, 24440}, {21926, 27268}, {21949, 33134}, {24199, 63147}, {24248, 33761}, {24325, 33117}, {24342, 26061}, {24387, 34595}, {24477, 65112}, {24703, 35595}, {25351, 33125}, {25525, 67097}, {25639, 64850}, {25970, 26540}, {26015, 61031}, {26098, 37680}, {26102, 33136}, {26593, 27475}, {26627, 33121}, {26723, 62807}, {26792, 61716}, {26893, 71714}, {27164, 70599}, {27754, 59547}, {28461, 35249}, {28611, 30172}, {28629, 34195}, {29642, 32945}, {29653, 32860}, {29661, 60714}, {29677, 31252}, {29678, 56009}, {29685, 40328}, {29850, 50302}, {29851, 32941}, {29853, 49473}, {30311, 60986}, {30315, 67046}, {30613, 59754}, {30950, 33141}, {30970, 33174}, {31151, 33080}, {32781, 56508}, {32784, 59306}, {32859, 60731}, {32929, 69755}, {33069, 49457}, {33107, 37679}, {33123, 36480}, {33137, 37633}, {33142, 37674}, {33157, 50314}, {36845, 60996}, {37572, 58449}, {38053, 62863}, {38093, 44841}, {40022, 70837}, {40216, 59255}, {42029, 69301}, {44447, 59412}, {46916, 58463}, {48628, 48648}, {48643, 64178}, {49474, 69295}, {49769, 62226}, {52255, 62838}, {55867, 64112}, {58433, 64162}, {62870, 63146}, {63287, 64343}, {64171, 70776}

X(72014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 149, 4423}, {2, 2550, 1621}, {2, 3434, 5284}, {2, 3925, 33108}, {2, 33108, 11680}, {2, 33110, 1001}, {2, 61156, 5432}, {10, 5249, 3681}, {10, 25957, 32782}, {10, 41859, 4197}, {10, 61029, 5249}, {75, 69250, 32862}, {142, 25006, 3873}, {377, 19855, 5260}, {442, 9780, 11681}, {756, 17889, 33151}, {984, 69253, 33146}, {1001, 33110, 34611}, {1329, 34501, 46932}, {1621, 2550, 49719}, {1698, 3841, 2476}, {3823, 31993, 29679}, {3826, 3925, 2}, {3836, 31330, 33172}, {3838, 61686, 27131}, {4359, 29641, 33089}, {16569, 33105, 37651}, {17529, 31419, 3616}, {19843, 37462, 5253}, {21949, 44307, 33134}, {26723, 64174, 62807}, {38200, 41867, 3870}


X(72015) = X(1)X(2)∩X(76)X(693)

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

X(72015) lies on these lines: {1, 2}, {76, 693}, {321, 3675}, {668, 30993}, {1083, 1150}, {1086, 41683}, {2087, 69512}, {2486, 18150}, {3573, 14829}, {3662, 19945}, {4033, 53564}, {4358, 71755}, {7185, 69660}, {16479, 70483}, {17245, 69519}, {17280, 71801}, {20917, 56893}, {21070, 70114}, {23814, 71557}, {24237, 61183}, {30583, 71050}, {32929, 67417}, {32942, 71819}, {36848, 71759}, {68768, 71479}

X(72015) = isotomic conjugate of the isogonal conjugate of X(24494)
X(72015) = barycentric product X(76)*X(24494)
X(72015) = barycentric quotient X(24494)/X(6)
X(72015) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3912, 71488, 68951}, {3912, 71753, 3661}


X(72016) = X(1)X(4234)∩X(2)X(3052)

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

X(72016) lies on these lines: {1, 4234}, {2, 3052}, {6, 3996}, {8, 48832}, {31, 333}, {43, 50300}, {55, 4203}, {75, 62834}, {81, 68969}, {86, 1621}, {141, 20101}, {171, 3840}, {190, 3920}, {212, 70426}, {312, 5269}, {345, 4344}, {390, 63013}, {516, 19786}, {595, 1010}, {612, 4676}, {643, 14534}, {752, 32783}, {894, 3744}, {902, 32772}, {1001, 70484}, {1043, 57280}, {1125, 33068}, {1150, 30652}, {1220, 5255}, {1376, 70481}, {1386, 32932}, {1836, 29634}, {1918, 70406}, {1961, 4432}, {1999, 49484}, {2308, 32945}, {2345, 70493}, {2886, 41806}, {3058, 29837}, {3112, 69752}, {3210, 38315}, {3474, 3616}, {3550, 25496}, {3617, 19723}, {3618, 17784}, {3666, 65166}, {3683, 16830}, {3685, 3745}, {3699, 27064}, {3750, 33682}, {3758, 3870}, {3759, 63131}, {3782, 29838}, {3838, 25529}, {3883, 19808}, {3886, 62842}, {3923, 17716}, {3943, 20069}, {3961, 4672}, {4038, 71414}, {4195, 5710}, {4307, 18134}, {4360, 32929}, {4386, 70722}, {4388, 30832}, {4389, 44447}, {4413, 70485}, {4418, 17469}, {4514, 63969}, {4650, 29652}, {4651, 68966}, {4673, 62809}, {4684, 62230}, {4685, 16477}, {5248, 37303}, {5264, 13740}, {5278, 30653}, {5294, 32850}, {5484, 64159}, {6679, 33109}, {7262, 36480}, {7290, 19804}, {8616, 25507}, {10327, 17354}, {10436, 62875}, {10453, 48805}, {11115, 40153}, {11319, 19731}, {11688, 16687}, {13735, 30116}, {13741, 49993}, {14829, 17126}, {16821, 64166}, {17018, 46922}, {17122, 25531}, {17127, 17277}, {17135, 41629}, {17147, 62855}, {17150, 17160}, {17271, 42058}, {17285, 33078}, {17289, 63134}, {17297, 33173}, {17305, 29648}, {17307, 33083}, {17601, 29650}, {17766, 32780}, {19684, 61155}, {20056, 63038}, {20064, 32782}, {20292, 26230}, {21747, 32864}, {24280, 62229}, {24295, 33079}, {24715, 29654}, {24725, 29848}, {24841, 32940}, {26065, 68589}, {26723, 69755}, {26840, 71322}, {27184, 64016}, {29636, 33094}, {29642, 50301}, {29645, 33095}, {29656, 33097}, {29686, 33067}, {29767, 39673}, {29815, 32933}, {29816, 32936}, {29819, 32845}, {29829, 34611}, {29831, 33146}, {29834, 33145}, {29842, 33154}, {29874, 48646}, {32777, 50289}, {32913, 49473}, {32914, 68999}, {32941, 62841}, {33073, 59692}, {33112, 41878}, {33116, 35263}, {33124, 50307}, {33126, 41011}, {33164, 50288}, {33309, 56191}, {33774, 69825}, {38047, 63139}, {42033, 49476}, {49470, 62845}, {49675, 71518}, {49705, 59628}, {56010, 70942}, {61358, 71451}, {62821, 71452}, {70158, 70975}

X(72016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 5263, 333}, {171, 49482, 32942}, {1621, 70482, 86}, {3685, 3745, 34064}, {3923, 17716, 32926}, {4418, 17469, 32922}, {17126, 24552, 14829}, {17150, 64010, 17160}, {29648, 32950, 17305}, {32929, 62807, 4360}, {32940, 67210, 24841}


X(72017) = X(10)X(31)∩X(81)X(145)

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

X(72017) lies on these lines: {1, 16393}, {2, 3052}, {3, 962}, {6, 19998}, {8, 16394}, {10, 31}, {42, 19738}, {55, 11322}, {81, 145}, {86, 61155}, {100, 16405}, {105, 24183}, {171, 24552}, {321, 5269}, {333, 30652}, {519, 62846}, {528, 29829}, {595, 16454}, {750, 4871}, {896, 36480}, {899, 50300}, {902, 50302}, {956, 70110}, {995, 19336}, {1086, 29831}, {1150, 5263}, {1191, 19284}, {1211, 20064}, {1279, 26627}, {1386, 4706}, {1707, 4981}, {2177, 33682}, {3187, 49468}, {3210, 62855}, {3306, 61087}, {3550, 29825}, {3622, 16397}, {3624, 8616}, {3632, 32945}, {3635, 62821}, {3636, 62849}, {3649, 36508}, {3685, 9347}, {3745, 32929}, {3758, 3935}, {3891, 4418}, {3896, 62845}, {3920, 32933}, {3923, 3994}, {3936, 4307}, {3938, 4697}, {3943, 63099}, {3980, 17469}, {3996, 20048}, {4038, 71452}, {4344, 17740}, {4359, 62834}, {4363, 20045}, {4389, 5078}, {4413, 70483}, {4649, 71451}, {4651, 63060}, {4667, 50744}, {4668, 32864}, {4676, 5297}, {4678, 5793}, {4946, 61358}, {4954, 63108}, {5276, 54389}, {5764, 63168}, {5782, 61330}, {5880, 26230}, {7290, 24589}, {7292, 24594}, {9342, 70485}, {9345, 71414}, {10578, 16398}, {11346, 56191}, {14996, 68969}, {16396, 59297}, {16399, 26626}, {16400, 64951}, {16401, 38314}, {16403, 44447}, {16830, 62838}, {17023, 63145}, {17025, 24344}, {17154, 67538}, {17277, 30653}, {17281, 50000}, {17354, 60459}, {17495, 38315}, {17595, 29823}, {19701, 21000}, {20075, 63013}, {20101, 32782}, {20292, 29634}, {21010, 69903}, {24596, 71045}, {24715, 29636}, {26282, 37764}, {26580, 64016}, {29632, 50301}, {29645, 33094}, {29648, 33068}, {29815, 32939}, {29816, 32934}, {29824, 48805}, {29834, 33149}, {29837, 34611}, {29838, 33146}, {29842, 33145}, {29847, 33095}, {29848, 33097}, {30588, 56144}, {30834, 33112}, {31229, 33108}, {31855, 48867}, {32779, 50289}, {32912, 49449}, {32932, 62807}, {32941, 50001}, {32943, 37604}, {32944, 56010}, {33122, 50307}, {33139, 49720}, {33161, 50288}, {35263, 64174}, {36534, 62235}, {37610, 62740}, {41241, 67097}, {48811, 49999}, {49476, 50105}, {49983, 50283}, {49986, 51005}, {49987, 50294}, {49991, 50115}, {49996, 50313}, {62842, 63131}

X(72017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 70482, 19684}, {4418, 17716, 3891}, {5263, 17126, 1150}


X(72018) = X(2)X(3052)∩X(238)X(5278)

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

X(72018) lies on these lines: {1, 11346}, {2, 3052}, {6, 68971}, {31, 3840}, {55, 70483}, {100, 70485}, {190, 17024}, {238, 5278}, {321, 7290}, {595, 5192}, {748, 49482}, {752, 29677}, {896, 29668}, {902, 70942}, {1001, 19684}, {1150, 17127}, {1191, 11319}, {1279, 26223}, {1621, 16058}, {3616, 6147}, {3720, 50300}, {3744, 59596}, {3758, 29817}, {3870, 41241}, {3891, 32930}, {3995, 38315}, {3996, 14997}, {4011, 17469}, {4358, 62834}, {4387, 17150}, {4415, 29831}, {4423, 70482}, {4432, 17017}, {4651, 48805}, {4676, 7191}, {4683, 29660}, {4703, 29686}, {5014, 17353}, {5264, 49993}, {5284, 70419}, {5315, 49492}, {5550, 16351}, {5710, 56983}, {8616, 32944}, {11680, 31229}, {14829, 30653}, {15485, 32772}, {16393, 49997}, {16468, 32943}, {17120, 62866}, {17135, 63060}, {17350, 62814}, {17352, 33110}, {17354, 33090}, {17697, 62804}, {17721, 56520}, {19336, 71609}, {19993, 54389}, {20012, 32911}, {20064, 69092}, {24542, 26098}, {24703, 26230}, {24723, 29666}, {24725, 29672}, {27064, 62806}, {29638, 33096}, {29650, 70520}, {29679, 49709}, {29818, 32935}, {29829, 49736}, {29836, 33101}, {29839, 31179}, {29852, 33095}, {29853, 33097}, {30834, 33107}, {33074, 49705}, {41002, 48810}, {41839, 62855}, {49681, 69301}, {61358, 71414}, {62869, 71521}, {63074, 68969}, {64016, 69251}

X(72018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {238, 24552, 5278}, {4676, 7191, 32933}, {17127, 32942, 1150}


X(72019) = X(2)X(3052)∩X(55)X(86)

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

X(72019) lies on these lines: {1, 42053}, {2, 3052}, {6, 59295}, {8, 41629}, {31, 17277}, {42, 41142}, {55, 86}, {75, 5269}, {81, 3996}, {100, 70482}, {171, 3741}, {190, 612}, {200, 3758}, {333, 17126}, {528, 29837}, {595, 56766}, {750, 30957}, {894, 40883}, {940, 68969}, {1010, 5264}, {1043, 5711}, {1086, 29838}, {1191, 56768}, {1211, 20101}, {1376, 59298}, {1621, 4210}, {2295, 21792}, {3474, 4389}, {3550, 50302}, {3616, 4428}, {3622, 8572}, {3685, 4682}, {3699, 26223}, {3745, 4360}, {3759, 62842}, {3769, 50314}, {3771, 50301}, {3871, 18185}, {3920, 32939}, {3961, 4697}, {3980, 17716}, {4061, 62231}, {4234, 30116}, {4307, 4417}, {4362, 68999}, {4413, 70481}, {4418, 32926}, {4421, 59297}, {4512, 4687}, {4640, 16830}, {4649, 71450}, {4650, 36480}, {4673, 37554}, {4676, 5268}, {4849, 17120}, {5224, 63140}, {5253, 18613}, {5278, 30652}, {5710, 20037}, {5793, 51674}, {5880, 29634}, {6327, 30832}, {7172, 14614}, {7322, 17336}, {9342, 70483}, {9345, 71452}, {9347, 32929}, {9778, 17321}, {11688, 20990}, {13735, 56191}, {15668, 21000}, {16569, 50300}, {17018, 42028}, {17122, 49482}, {17124, 25531}, {17297, 33171}, {17305, 33068}, {17307, 26034}, {17352, 26040}, {17377, 70517}, {17394, 37553}, {17490, 38315}, {17495, 62855}, {17601, 29644}, {17784, 63013}, {19284, 62804}, {19770, 59299}, {19804, 62834}, {19808, 63134}, {24715, 29645}, {25496, 56010}, {26627, 62806}, {27525, 60077}, {28606, 65166}, {29816, 32845}, {29829, 49719}, {29842, 33149}, {29847, 33094}, {30142, 63996}, {32911, 70416}, {32941, 37604}, {33076, 59628}, {33096, 59726}, {33106, 58443}, {33108, 41806}, {33116, 64174}, {33126, 50307}, {33137, 49720}, {33167, 50288}, {33682, 60714}, {36531, 59624}, {40940, 69755}, {41261, 50054}, {44446, 49748}, {49450, 62812}, {50291, 59544}, {59296, 68966}, {62821, 71451}, {63145, 69544}, {67964, 70973}

X(72019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 70484, 86}, {171, 5263, 14829}, {3745, 32932, 4360}, {3769, 50314, 55095}, {3980, 17716, 32922}, {9347, 32929, 34064}


X(72020) = X(2)X(3052)∩X(83)X(32008)

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

X(72020) lies on these lines: {1, 33309}, {2, 3052}, {11, 41806}, {31, 30957}, {55, 59298}, {83, 32008}, {86, 5284}, {109, 40420}, {171, 25531}, {190, 7191}, {238, 333}, {312, 7290}, {595, 13741}, {614, 4676}, {748, 5263}, {995, 13735}, {1001, 70481}, {1125, 33097}, {1191, 17697}, {1193, 52352}, {1222, 20039}, {1279, 27064}, {1386, 34064}, {1621, 15621}, {3242, 70742}, {3246, 3757}, {3434, 17352}, {3616, 11194}, {3622, 19722}, {3699, 3744}, {3715, 36534}, {3720, 42028}, {3752, 65166}, {3758, 4666}, {3957, 41241}, {3996, 4383}, {4011, 32926}, {4234, 49997}, {4252, 26093}, {4423, 70419}, {4432, 29821}, {4514, 17353}, {4672, 29820}, {4679, 29634}, {4703, 29660}, {4797, 26273}, {4883, 17120}, {4997, 66632}, {5211, 44416}, {5269, 30829}, {6057, 50015}, {6327, 17283}, {7262, 29668}, {8167, 70484}, {8616, 70942}, {13588, 54333}, {14829, 17127}, {15485, 25496}, {16477, 42057}, {17061, 17777}, {17123, 49482}, {17135, 68966}, {17277, 24552}, {17285, 33075}, {17305, 29666}, {17336, 62833}, {17350, 17597}, {17599, 71524}, {17605, 25529}, {17884, 18151}, {18743, 62834}, {19786, 40998}, {20011, 32911}, {20292, 27191}, {24542, 33107}, {24709, 29683}, {24725, 29853}, {24841, 29818}, {25507, 32772}, {26102, 50300}, {26139, 37634}, {28356, 71629}, {28360, 71444}, {29672, 33096}, {29814, 46922}, {29823, 33761}, {29824, 41629}, {31035, 62855}, {31289, 33109}, {32922, 32930}, {33079, 49705}, {38315, 41839}, {41002, 41816}, {41823, 49462}, {48805, 59296}, {49675, 71515}, {56983, 62804}, {62230, 64017}, {63996, 69268}, {64010, 68958}, {69024, 70722}, {69263, 70693}

X(72020) = crosssum of X(42) and X(23649)
X(72020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {238, 32942, 333}, {614, 4676, 32939}, {24542, 33107, 41878}, {29818, 32938, 24841}


X(72021) = X(2)X(3052)∩X(8)X(19276)

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

X(72021) lies on these lines: {1, 19336}, {2, 3052}, {8, 19276}, {81, 20012}, {100, 11358}, {171, 1150}, {612, 32933}, {614, 24594}, {750, 3840}, {1376, 70482}, {1621, 4191}, {2975, 19530}, {3240, 19738}, {3616, 16371}, {3617, 4921}, {3744, 26627}, {3891, 3980}, {3925, 31229}, {3996, 14996}, {4038, 71451}, {4307, 5741}, {4359, 5269}, {4421, 29822}, {4682, 32929}, {4685, 62846}, {5192, 49993}, {5264, 16454}, {5278, 17126}, {5432, 31281}, {5710, 19284}, {5743, 20064}, {8580, 41241}, {9342, 70481}, {9347, 32932}, {16393, 30116}, {17124, 49482}, {17277, 30652}, {17490, 62855}, {24589, 62834}, {24715, 29847}, {24725, 59726}, {26223, 59596}, {29661, 50299}, {29823, 70256}, {29829, 34612}, {29831, 40688}, {29837, 49719}, {29846, 50301}, {32772, 56010}, {32945, 37604}, {33074, 59628}, {33104, 58443}, {33113, 64174}, {33142, 49720}, {41002, 42058}, {41809, 63140}, {50000, 50048}, {56768, 62804}, {59296, 63060}, {62821, 71450}

X(72021) = {X(100),X(70484)}-harmonic conjugate of X(19684)


X(72022) = X(2)X(3052)∩X(10)X(748)

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

X(72022) lies on these lines: {1, 41241}, {2, 3052}, {10, 748}, {11, 31229}, {31, 4871}, {45, 29823}, {145, 1191}, {149, 17352}, {238, 1150}, {329, 405}, {614, 32933}, {995, 11346}, {1001, 29822}, {1125, 24725}, {1621, 16373}, {3246, 26227}, {3315, 17350}, {3624, 16342}, {3632, 32943}, {3635, 61358}, {3744, 26688}, {3891, 3994}, {3996, 63096}, {4358, 7290}, {4383, 19998}, {4422, 29832}, {4676, 7292}, {4679, 26230}, {4706, 32929}, {4759, 36263}, {4906, 71793}, {4946, 71414}, {5087, 67425}, {5278, 32942}, {5333, 17588}, {5695, 68958}, {7191, 49447}, {8167, 70482}, {8692, 71478}, {10453, 63060}, {11322, 54333}, {14997, 20048}, {15485, 29825}, {16393, 71609}, {16483, 62401}, {16948, 26093}, {17125, 49482}, {17126, 25531}, {19738, 29814}, {24542, 30834}, {24593, 36277}, {24709, 29658}, {25378, 29859}, {26228, 30566}, {26282, 30990}, {29830, 31179}, {29853, 33096}, {30588, 62901}, {30950, 50300}, {31035, 38315}, {31289, 33104}, {32774, 40998}, {32930, 49493}, {33854, 54389}, {40480, 65698}, {49987, 50105}, {62814, 70742}, {62869, 71515}

{X(5284),X(70481)}-harmonic conjugate of X(19684)


X(72023) = X(2)X(3052)∩X(8)X(19290)

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

X(72023) lies on these lines: {2, 3052}, {8, 19290}, {43, 19738}, {81, 59295}, {171, 5278}, {551, 17782}, {750, 3741}, {940, 20011}, {1376, 19684}, {1621, 16059}, {3616, 16417}, {4413, 70482}, {5241, 20064}, {5269, 24589}, {5297, 32933}, {7191, 24594}, {9342, 70419}, {9345, 71450}, {9350, 33682}, {9352, 16830}, {9780, 19277}, {16393, 56191}, {17122, 24552}, {19336, 30116}, {20037, 56768}, {24620, 62855}, {24693, 29683}, {29678, 50299}, {29829, 49732}, {36534, 65112}, {46933, 64424}, {59298, 70484}


X(72024) = X(2)X(3052)∩X(238)X(30957)

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

X(72024) lies on these lines: {2, 3052}, {238, 30957}, {748, 3741}, {1279, 26688}, {1616, 20039}, {1621, 59298}, {3315, 70742}, {3474, 24183}, {3616, 16857}, {3720, 19738}, {4383, 20011}, {4387, 68958}, {4423, 19684}, {4666, 41241}, {5284, 70485}, {7292, 32933}, {11346, 49997}, {16345, 70481}, {17123, 24552}, {17127, 25531}, {29824, 63060}, {37680, 59295}, {63096, 68969}
{X(4423),X(70483)}-harmonic conjugate of X(19684)


X(72025) = X(1)X(3710)∩X(2)X(902)

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

X(72025) lies on these lines: {1, 3710}, {2, 902}, {31, 29637}, {63, 29660}, {149, 29867}, {226, 29860}, {238, 1211}, {497, 29856}, {551, 56078}, {595, 28242}, {846, 1125}, {894, 29672}, {968, 29646}, {1279, 32780}, {1386, 33158}, {1621, 29633}, {1698, 62875}, {2308, 20086}, {3052, 33174}, {3120, 29871}, {3219, 29686}, {3589, 3750}, {3618, 42042}, {3624, 4512}, {3685, 29654}, {3744, 33159}, {3757, 24295}, {3771, 70481}, {3915, 19879}, {3923, 33147}, {3944, 29855}, {3961, 17353}, {3971, 29838}, {3995, 29834}, {4011, 29634}, {4414, 29666}, {4428, 47355}, {4432, 19786}, {4672, 33124}, {4676, 26128}, {4685, 63051}, {5259, 37225}, {6679, 32942}, {7191, 33167}, {7290, 32778}, {13742, 59311}, {16468, 33171}, {17024, 33161}, {17126, 29677}, {17127, 24943}, {17165, 29836}, {17279, 17716}, {17354, 32920}, {17357, 33079}, {17368, 29651}, {17398, 60711}, {17469, 32847}, {17593, 59580}, {17596, 35263}, {17598, 44416}, {17715, 38047}, {18134, 50300}, {18201, 59574}, {19836, 54354}, {21214, 37176}, {21747, 32863}, {24210, 29859}, {24542, 32772}, {24552, 33138}, {25055, 26728}, {25496, 29640}, {25531, 58443}, {26061, 62806}, {26065, 62865}, {26083, 29669}, {26098, 29858}, {26223, 29638}, {26230, 32930}, {27064, 29656}, {28595, 49709}, {29642, 70419}, {29663, 61155}, {29674, 62834}, {29676, 56519}, {29818, 33170}, {29819, 32849}, {29821, 59692}, {29831, 32925}, {29842, 41839}, {29846, 70483}, {29851, 70482}, {29852, 32929}, {29865, 33107}, {29869, 33112}, {29874, 69173}, {30653, 33080}, {31137, 37642}, {32777, 32866}, {32781, 70834}, {32857, 33123}, {32865, 48805}, {33092, 38315}, {33118, 49473}, {33132, 49484}, {33166, 67210}, {37652, 50311}, {42033, 49472}, {55901, 70790}, {62841, 63057}, {62855, 69295}, {63020, 69297}

X(72025) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 49482, 33109}, {31, 29637, 33085}, {4676, 26128, 33099}, {6679, 32942, 33140}, {17127, 24943, 33082}, {17469, 33157, 32847}, {26230, 32930, 33152}


X(72026) = X(1)X(345)∩X(2)X(902)

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

X(72026) lies on these lines: {1, 345}, {2, 902}, {31, 32782}, {55, 29633}, {57, 29660}, {149, 29863}, {165, 631}, {171, 29637}, {192, 29842}, {238, 5743}, {726, 29838}, {846, 35263}, {894, 29656}, {1125, 17596}, {1386, 33160}, {2108, 43223}, {2308, 33175}, {2895, 21747}, {3052, 32784}, {3120, 29874}, {3218, 29686}, {3434, 29856}, {3589, 60714}, {3616, 17591}, {3618, 42043}, {3685, 29645}, {3712, 17600}, {3744, 32780}, {3745, 33158}, {3749, 29659}, {3771, 70419}, {3914, 29859}, {3920, 33164}, {3923, 29634}, {3961, 5294}, {4028, 69632}, {4414, 29648}, {4417, 50300}, {4418, 26230}, {4421, 47355}, {4672, 33126}, {4697, 33124}, {5248, 37030}, {5249, 29860}, {5255, 17698}, {5259, 13731}, {5263, 6679}, {5269, 29674}, {6703, 16484}, {7081, 24295}, {11354, 37716}, {16468, 63037}, {16823, 59628}, {17126, 24943}, {17140, 29836}, {17147, 29834}, {17155, 29831}, {17353, 59684}, {17368, 29670}, {17469, 32779}, {17526, 59311}, {17594, 29646}, {17716, 32777}, {17889, 29855}, {19836, 37603}, {19875, 48798}, {21242, 41806}, {23703, 56451}, {24552, 33140}, {26065, 49448}, {26128, 32857}, {26223, 29848}, {26627, 29853}, {29632, 70482}, {29636, 32929}, {29640, 32772}, {29642, 70484}, {29647, 61155}, {29654, 32932}, {29815, 33161}, {29816, 32849}, {29819, 33168}, {29829, 71452}, {29837, 71414}, {29839, 33682}, {29865, 33112}, {29867, 33110}, {29871, 69253}, {30652, 33080}, {31137, 63078}, {32775, 33099}, {32778, 62834}, {32848, 62855}, {32855, 38315}, {33121, 49473}, {33135, 49484}, {33141, 48805}, {33156, 62807}, {33170, 67210}, {33171, 62841}, {33174, 37540}, {37646, 48810}, {37666, 50316}, {37683, 50311}, {41629, 50315}, {59574, 71322}, {69294, 70834}

X(72026) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 49482, 33106}, {31, 32783, 33082}, {3923, 29634, 33152}, {4418, 26230, 33147}, {5255, 17698, 19879}, {5263, 6679, 33138}, {17126, 24943, 33085}, {17469, 32779, 32866}, {17716, 32777, 32847}


X(72027) = X(1)X(33168)∩X(2)X(902)

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

X(72027) lies on these lines: {1, 33168}, {2, 902}, {31, 1211}, {55, 29647}, {57, 29686}, {100, 29663}, {171, 24943}, {345, 29816}, {750, 29677}, {894, 29848}, {1054, 29666}, {2308, 63009}, {2550, 29867}, {3052, 69294}, {3210, 29834}, {3434, 29863}, {3685, 29847}, {3745, 33156}, {3749, 29685}, {3771, 70482}, {3920, 33161}, {3980, 26230}, {4062, 62845}, {4418, 29634}, {4512, 6536}, {4697, 33122}, {5263, 24892}, {5269, 15523}, {5311, 59692}, {5739, 21747}, {5741, 50300}, {6703, 62849}, {9347, 33158}, {10436, 29689}, {10459, 37176}, {17126, 32783}, {17147, 29842}, {17155, 29838}, {17384, 63211}, {17594, 68945}, {17596, 29648}, {17716, 32779}, {17740, 29819}, {17889, 29874}, {20086, 33175}, {24165, 29831}, {24342, 29681}, {24552, 29662}, {26627, 29672}, {27003, 29660}, {27186, 29860}, {29632, 70484}, {29636, 32932}, {29645, 32929}, {29661, 50302}, {29678, 32772}, {29815, 33167}, {29837, 71452}, {29846, 70419}, {29855, 69253}, {29856, 33110}, {29859, 33131}, {30614, 67210}, {30652, 33082}, {31136, 37642}, {31247, 50296}, {32775, 33098}, {32781, 37540}, {32855, 62855}, {33160, 62807}, {33171, 63057}, {33173, 37604}, {36263, 59574}, {36480, 56520}, {37634, 48810}, {37639, 50311}, {48803, 54310}, {62834, 69252}

X(72027) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4418, 29634, 33143}, {17126, 32783, 33080}, {17716, 32779, 32854}


X(72028) = X(1)X(33166)∩X(2)X(902)

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

X(72028) lies on these lines: {1, 33166}, {2, 902}, {9, 29686}, {31, 29677}, {238, 24943}, {344, 29816}, {405, 28377}, {497, 29867}, {748, 5743}, {846, 29666}, {894, 29853}, {968, 29684}, {1001, 29647}, {1201, 17526}, {1279, 26061}, {1621, 29663}, {3219, 29660}, {3589, 62849}, {3616, 3989}, {3624, 4338}, {3685, 29852}, {3720, 63013}, {3771, 70483}, {3938, 17353}, {3944, 29871}, {3971, 29831}, {4011, 26230}, {4432, 32774}, {4676, 33098}, {6536, 66515}, {6679, 29662}, {7191, 33161}, {7290, 15523}, {10459, 13742}, {16468, 33173}, {17024, 33164}, {17127, 29637}, {17279, 17469}, {17352, 32945}, {17354, 32923}, {17357, 33074}, {17449, 26065}, {17776, 29819}, {18139, 50300}, {19742, 50311}, {24542, 25496}, {24892, 32942}, {26098, 29869}, {26223, 29672}, {27064, 29638}, {28352, 37176}, {29632, 70481}, {29668, 56520}, {29678, 32944}, {29687, 62834}, {29818, 33163}, {29834, 41839}, {29836, 32937}, {29838, 64178}, {29842, 31035}, {29846, 70485}, {29851, 70419}, {29855, 69173}, {29858, 33107}, {29860, 31053}, {30653, 33085}, {32854, 33157}, {32930, 33143}, {33159, 62806}, {33171, 63037}, {33174, 70834}, {38049, 67208}, {38315, 69295}, {50315, 63060}

X(72028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4676, 33123, 33098}, {17127, 29637, 33080}, {24542, 25496, 29661}


X(72029) = X(1)X(17740)∩X(2)X(902)

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

X(72029) lies on these lines: {1, 17740}, {2, 902}, {35, 37255}, {43, 3618}, {100, 29633}, {141, 171}, {142, 29860}, {165, 12610}, {193, 62841}, {238, 5241}, {612, 33164}, {750, 29637}, {752, 30832}, {1054, 1125}, {1376, 47355}, {1738, 29859}, {1961, 59692}, {2550, 29856}, {3011, 24342}, {3210, 29842}, {3306, 29660}, {3589, 56009}, {3624, 6921}, {3679, 24597}, {3745, 33160}, {3750, 6703}, {3757, 59628}, {3769, 48630}, {3771, 70484}, {3920, 33167}, {3961, 49529}, {3980, 29634}, {4023, 16477}, {4362, 48628}, {4363, 17725}, {4418, 33152}, {4434, 17289}, {4657, 17601}, {4682, 33158}, {4697, 33126}, {5205, 24295}, {5218, 29825}, {5233, 50300}, {5259, 28238}, {5263, 21242}, {5269, 32778}, {5315, 28289}, {5955, 16478}, {7081, 63019}, {7222, 33144}, {9347, 33156}, {10436, 29675}, {16394, 37716}, {17126, 33082}, {17495, 29834}, {17716, 32866}, {17779, 38049}, {18201, 71322}, {19856, 32917}, {21747, 37656}, {24165, 29838}, {24217, 48805}, {25055, 62695}, {26128, 48629}, {26627, 29638}, {26758, 32843}, {27003, 29686}, {27064, 59726}, {29640, 50302}, {29645, 32932}, {29658, 50314}, {29816, 33168}, {29829, 71451}, {29846, 70482}, {29847, 32929}, {29862, 64174}, {29863, 33110}, {29874, 69253}, {30811, 50301}, {31229, 33138}, {32775, 32857}, {32779, 32847}, {32784, 37540}, {32913, 49505}, {32942, 58443}, {33084, 40341}, {33169, 49690}, {33171, 37604}, {36531, 54357}, {37176, 59311}, {37684, 50311}, {42042, 63013}, {46918, 50756}, {48854, 59779}, {49489, 70971}, {59297, 67025}

X(72029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {171, 32783, 33085}, {3980, 29634, 33147}


X(72030) = X(1)X(344)∩X(2)X(902)

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

X(72030) lies on these lines: {1, 344}, {2, 902}, {9, 29660}, {10, 49704}, {141, 238}, {142, 3624}, {193, 16468}, {519, 17268}, {551, 25101}, {595, 28256}, {614, 33167}, {748, 32783}, {752, 17283}, {894, 1125}, {908, 29860}, {1001, 29633}, {1054, 35263}, {1279, 33159}, {1698, 60846}, {1757, 49505}, {3161, 51035}, {3246, 17357}, {3589, 16484}, {3616, 31302}, {3679, 16487}, {3731, 25055}, {3763, 8692}, {3771, 70485}, {3923, 48627}, {3952, 29836}, {4011, 33152}, {4026, 51127}, {4402, 49474}, {4423, 37581}, {4432, 16706}, {4473, 49520}, {4649, 6329}, {4655, 48637}, {4676, 32857}, {4693, 17366}, {4709, 29590}, {4759, 6646}, {4902, 50116}, {4966, 16477}, {5222, 49469}, {5241, 17123}, {5263, 31289}, {5294, 29820}, {5550, 26806}, {6666, 36531}, {7191, 33164}, {7229, 16020}, {7290, 29674}, {8245, 10165}, {15492, 51003}, {16801, 17277}, {16823, 24295}, {16825, 48628}, {17045, 60690}, {17121, 49764}, {17127, 29677}, {17234, 50300}, {17264, 49472}, {17265, 50301}, {17279, 32847}, {17280, 50023}, {17288, 49710}, {17307, 50297}, {17336, 50285}, {17337, 48810}, {17338, 36480}, {17339, 49455}, {17349, 50311}, {17352, 32941}, {17356, 24715}, {17368, 24331}, {17526, 21214}, {19856, 20179}, {21242, 32942}, {24542, 29640}, {24597, 31137}, {24821, 59579}, {25893, 59767}, {25992, 37588}, {26223, 29853}, {26685, 49448}, {26688, 29848}, {27064, 29672}, {27065, 29686}, {29632, 70483}, {29642, 70481}, {29818, 33166}, {29831, 64178}, {29834, 31035}, {29838, 59517}, {29869, 33107}, {29871, 69173}, {31229, 33140}, {32866, 33157}, {32930, 33147}, {33087, 40341}, {33099, 33123}, {33165, 49690}, {34595, 66676}, {36232, 71705}, {37681, 50316}, {48640, 50308}, {49532, 54389}, {49740, 51126}, {50295, 63121}, {50303, 53665}, {50315, 68966}, {61647, 70219}

X(72030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {238, 29637, 33082}, {3246, 17357, 33076}, {3763, 8692, 50296}, {17127, 29677, 33085}, {24542, 32944, 29640}


X(72031) = X(2)X(902)∩X(31)X(5743)

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

X(72031) lies on these lines: {2, 902}, {31, 5743}, {42, 63013}, {100, 29647}, {171, 32782}, {612, 33161}, {750, 24943}, {1054, 29648}, {1376, 29663}, {2177, 6703}, {2308, 63037}, {2550, 29863}, {3306, 29686}, {3589, 9350}, {3980, 33143}, {4643, 9340}, {4682, 33156}, {4995, 17398}, {5263, 29662}, {5269, 69252}, {5294, 59684}, {5955, 62847}, {6536, 35258}, {9347, 33160}, {14555, 21747}, {17122, 29677}, {17325, 63212}, {17490, 29834}, {17495, 29842}, {17740, 29816}, {24342, 29665}, {24552, 58443}, {26223, 59726}, {26227, 59628}, {26627, 29656}, {27714, 37552}, {29678, 50302}, {29683, 50314}, {29829, 71450}, {29837, 71451}, {29846, 70484}, {29847, 32932}, {30831, 50301}, {31136, 63078}, {33175, 37604}, {37540, 69294}, {37716, 51669}


X(72032) = X(2)X(902)∩X(238)X(29677)

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

X(72032) lies on these lines: {2, 902}, {238, 29677}, {344, 29819}, {614, 33161}, {748, 1211}, {1001, 29663}, {1125, 26223}, {1201, 13742}, {1647, 56519}, {2308, 63057}, {3246, 33074}, {3305, 29686}, {3624, 3648}, {4011, 33143}, {4423, 7085}, {4906, 71795}, {5284, 29647}, {7290, 29687}, {16468, 20086}, {17279, 32854}, {17341, 33072}, {17352, 32943}, {17356, 33094}, {17526, 28352}, {18141, 21747}, {24542, 29678}, {24552, 31289}, {26105, 29863}, {26688, 29656}, {27064, 29853}, {27065, 29660}, {27131, 29860}, {27538, 29836}, {29632, 70485}, {29642, 70483}, {29661, 32944}, {29662, 41806}, {29818, 30614}, {29831, 59517}, {29851, 70481}

X(72032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {238, 29677, 33080}, {24542, 70942, 29678}


X(72033) = X(2)X(902)∩X(31)X(5241)

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

X(72033) lies on these lines: {2, 902}, {31, 5241}, {141, 750}, {165, 6536}, {899, 3618}, {1376, 29647}, {2345, 62659}, {4023, 32455}, {4371, 50756}, {4413, 47355}, {5297, 33161}, {5437, 29686}, {6174, 17398}, {9458, 17368}, {17122, 24943}, {17124, 29677}, {17763, 48628}, {19530, 28377}, {21242, 29662}, {21747, 63003}, {24620, 29834}, {26040, 29867}, {26758, 32946}, {29633, 61156}, {30834, 50299}, {32775, 48629}, {33143, 48627}, {40341, 69300}


X(72034) = X(2)X(902)∩X(141)X(748)

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

X(72034) lies on these lines: {2, 902}, {141, 748}, {3618, 3720}, {3624, 31019}, {4365, 4402}, {4423, 12329}, {4683, 48637}, {5241, 17125}, {5284, 29663}, {6329, 62821}, {7292, 33161}, {7308, 29686}, {13742, 28352}, {17123, 24943}, {17341, 32844}, {17449, 26685}, {21027, 31183}, {21242, 31289}, {26105, 29867}, {26688, 29672}, {29660, 35595}, {29661, 70942}, {29662, 31229}, {29851, 70485}, {31136, 37650}, {32930, 48627}, {33098, 48629}, {49690, 69298}


X(72035) = X(1)X(5905)∩X(8)X(71515)

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

X(72035) lies on these lines: {1, 5905}, {8, 71515}, {31, 11680}, {43, 17784}, {72, 68847}, {149, 2308}, {171, 3816}, {238, 3925}, {390, 42042}, {497, 50303}, {516, 29821}, {595, 3822}, {752, 32942}, {902, 33107}, {982, 64016}, {1215, 49709}, {1279, 33097}, {1386, 33095}, {1699, 29658}, {1707, 29676}, {1836, 33147}, {1961, 40998}, {3052, 17717}, {3058, 4649}, {3434, 16468}, {3632, 63009}, {3744, 33096}, {3757, 49705}, {3840, 20101}, {3923, 32866}, {3944, 62834}, {3957, 61707}, {3961, 21060}, {4011, 50289}, {4038, 49736}, {4138, 29860}, {4307, 26102}, {4388, 32783}, {4423, 50301}, {4432, 33073}, {4450, 32944}, {4512, 29657}, {4514, 4672}, {4640, 17722}, {4650, 17721}, {4660, 70481}, {4676, 4865}, {4942, 49679}, {5057, 17469}, {5255, 17757}, {5263, 70972}, {5429, 30384}, {5836, 66645}, {5903, 63513}, {6327, 29637}, {7191, 32857}, {7290, 17889}, {8616, 26098}, {9580, 16475}, {12699, 16478}, {17024, 33098}, {17127, 33104}, {17483, 29818}, {17484, 67210}, {17591, 44447}, {17598, 17768}, {17716, 24703}, {17766, 27064}, {17778, 71414}, {19993, 49532}, {20064, 30942}, {20075, 42043}, {20086, 50001}, {21282, 29850}, {21747, 33142}, {24552, 33082}, {24695, 62865}, {24725, 62806}, {24892, 30653}, {26840, 28508}, {28368, 66658}, {28494, 33068}, {28566, 33079}, {29633, 32947}, {29662, 30652}, {29675, 62875}, {29817, 64164}, {29819, 33100}, {29820, 50307}, {29827, 63140}, {31034, 71452}, {32773, 50300}, {32844, 33167}, {32847, 32930}, {32861, 49484}, {32948, 70483}, {33066, 49473}, {33084, 48805}, {33105, 70834}, {33154, 38315}, {34611, 61358}, {38832, 69056}, {48827, 68602}, {61661, 66065}, {63002, 71450}, {63010, 71451}

X(72035) = reflection of X(33085) in X(32942)
X(72035) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 33106, 33140}, {238, 63979, 33109}, {497, 50303, 62841}, {4388, 49482, 32783}, {4676, 4865, 33164}, {5057, 17469, 33152}, {8616, 26098, 29640}, {17127, 33104, 33138}


X(72036) = X(1)X(7)∩X(8)X(28512)

Barycentrics    3*a^3 + a*b^2 - b^3 + a*b*c + b^2*c + a*c^2 + b*c^2 - c^3 : :
X(72036) = 5 X[1] - 4 X[4021], 2 X[3775] - 3 X[5263], 10 X[3775] - 9 X[17271], 4 X[3775] - 3 X[33082], 5 X[5263] - 3 X[17271], 6 X[17271] - 5 X[33082]

X(72036) lies on these lines: {1, 7}, {8, 28512}, {11, 171}, {31, 33108}, {42, 20095}, {145, 28522}, {190, 50288}, {193, 3632}, {238, 3826}, {319, 28498}, {320, 49473}, {495, 5255}, {497, 37604}, {528, 4649}, {595, 28375}, {752, 3775}, {894, 17766}, {902, 29640}, {942, 68847}, {984, 64016}, {1001, 50301}, {1155, 17722}, {1386, 24715}, {1738, 4989}, {1757, 24393}, {1836, 17716}, {2269, 11010}, {2308, 33110}, {2550, 16468}, {2783, 7972}, {3052, 33111}, {3056, 5903}, {3057, 66645}, {3058, 4038}, {3244, 20090}, {3434, 62841}, {3474, 17591}, {3550, 5218}, {3626, 62989}, {3741, 20101}, {3744, 33097}, {3745, 33095}, {3755, 69632}, {3790, 3923}, {3883, 24342}, {3920, 33099}, {3935, 61707}, {3944, 5269}, {3957, 64164}, {3961, 41011}, {4279, 69056}, {4360, 17764}, {4363, 49506}, {4418, 32866}, {4429, 50300}, {4440, 49464}, {4450, 32772}, {4514, 4697}, {4644, 49498}, {4645, 29637}, {4660, 29633}, {4672, 32850}, {4865, 33167}, {4974, 69755}, {5264, 7951}, {5710, 12943}, {5711, 9668}, {6327, 32783}, {6646, 28508}, {6767, 48825}, {11246, 17598}, {11529, 48827}, {16823, 49705}, {17126, 33104}, {17300, 71414}, {17364, 49458}, {17365, 49675}, {17469, 20292}, {17483, 67210}, {17593, 17726}, {17601, 17723}, {17602, 65698}, {17717, 37540}, {17725, 61716}, {17784, 42043}, {17889, 62834}, {19856, 50295}, {20064, 31330}, {20072, 49510}, {20075, 42042}, {21282, 29631}, {21747, 33139}, {24280, 49445}, {24325, 49709}, {24464, 50616}, {24552, 33085}, {24695, 49448}, {24723, 28494}, {24821, 49527}, {24892, 30652}, {26842, 29818}, {28313, 34747}, {28369, 29012}, {28562, 33682}, {28566, 33076}, {29010, 37740}, {29040, 45287}, {29327, 66650}, {29335, 57282}, {29365, 66639}, {29657, 35258}, {29815, 33098}, {29816, 33100}, {29819, 33102}, {29862, 35263}, {31034, 71451}, {32846, 49484}, {32947, 70482}, {33072, 33164}, {33087, 48805}, {33094, 62807}, {33145, 62855}, {33149, 38315}, {34611, 62821}, {35023, 37662}, {37588, 49745}, {41319, 70495}, {41845, 50114}, {48856, 63975}, {49459, 67964}, {49469, 50284}, {49474, 51192}, {49477, 62392}, {49479, 49704}, {49491, 49695}, {49493, 49681}, {49710, 60731}, {49719, 61358}, {49772, 64017}, {50015, 50117}, {50016, 51196}, {50291, 51090}, {61169, 71612}, {62998, 71450}, {63056, 71452}

X(72036) = reflection of X(i) in X(j) for these {i,j}: {3632, 4431}, {33082, 5263}
X(72036) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 33109, 33138}, {171, 63979, 33106}, {902, 33112, 29640}, {1836, 17716, 33152}, {2550, 50303, 16468}, {3923, 50289, 32847}, {4344, 24248, 1}, {4645, 49482, 29637}, {4660, 70419, 29633}, {17126, 33104, 33140}, {17469, 20292, 33147}, {24695, 68589, 49448}, {50291, 51090, 51294}, {50307, 63969, 1}


X(72037) = X(1)X(20066)∩X(7)X(67210)

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

X(72037) lies on these lines: {1, 20066}, {7, 67210}, {10, 20064}, {31, 3925}, {42, 4307}, {149, 37604}, {165, 29688}, {171, 11680}, {200, 61707}, {516, 5311}, {528, 62821}, {750, 3816}, {752, 70972}, {756, 64016}, {902, 29661}, {1621, 50301}, {2308, 2550}, {3058, 9345}, {3120, 5269}, {3474, 46901}, {3550, 29678}, {3632, 20086}, {3664, 67209}, {3745, 33094}, {3822, 5264}, {3870, 64164}, {3890, 66645}, {3920, 33098}, {3923, 69301}, {3938, 50307}, {3989, 44447}, {4038, 34611}, {4344, 29819}, {4349, 67208}, {4418, 32854}, {4450, 50302}, {4645, 24943}, {4649, 49719}, {4660, 29647}, {4697, 5014}, {5263, 33080}, {5880, 17469}, {9347, 33095}, {9352, 17722}, {17126, 24892}, {17300, 71452}, {17716, 20292}, {17778, 71451}, {20095, 42042}, {20101, 31330}, {21060, 41011}, {21282, 29635}, {24248, 29816}, {24715, 62807}, {25439, 49744}, {29663, 32948}, {29677, 49482}, {29682, 35258}, {29815, 32857}, {30652, 33138}, {30970, 63140}, {31034, 71450}, {32864, 49720}, {32933, 50288}, {32947, 70484}, {33072, 33161}, {33105, 37540}, {33107, 56010}, {33110, 62841}, {33149, 62855}, {34612, 61358}, {50001, 63057}, {51433, 67969}, {62834, 69253}, {67964, 71631}

X(72037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {171, 33104, 29662}, {3550, 33112, 29678}, {4418, 50289, 32854}, {4660, 70482, 29647}, {17126, 33109, 24892}, {17716, 20292, 33143}, {32948, 70419, 29663}


X(72038) = X(11)X(31)∩X(42)X(390)

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

X(72038) lies on these lines: {1, 17484}, {11, 31}, {42, 390}, {43, 20095}, {149, 16468}, {193, 50001}, {238, 33104}, {244, 64016}, {329, 67210}, {495, 3915}, {497, 2308}, {595, 7951}, {614, 4312}, {748, 3826}, {896, 17721}, {902, 5218}, {995, 4316}, {1191, 12943}, {1193, 4302}, {1201, 4293}, {1279, 24725}, {1572, 4530}, {3058, 61358}, {3120, 7290}, {3775, 24552}, {3790, 32854}, {3840, 20064}, {3876, 68847}, {3914, 4989}, {3994, 49681}, {4307, 30950}, {4388, 24943}, {4432, 33070}, {4450, 70942}, {4512, 29688}, {4660, 70483}, {4666, 64164}, {4676, 32844}, {4756, 49534}, {5057, 33143}, {5311, 40998}, {5542, 41011}, {5698, 46901}, {5905, 29818}, {6327, 29677}, {7191, 33098}, {8616, 29678}, {9340, 17728}, {9668, 16466}, {11269, 21747}, {11551, 28082}, {15485, 33112}, {17024, 33099}, {17127, 24892}, {17449, 24695}, {17469, 24703}, {17717, 70834}, {17722, 62838}, {17723, 70520}, {20101, 30957}, {26098, 29661}, {26227, 49705}, {29663, 32947}, {30331, 61652}, {30653, 33140}, {31034, 71414}, {32577, 64159}, {32931, 49709}, {32942, 33080}, {32948, 70485}, {33096, 62806}, {35023, 37663}, {41242, 49506}, {43179, 67209}, {48805, 69300}, {49736, 62821}, {50743, 59579}, {62834, 69173}, {62998, 71452}, {63002, 71451}

X(72038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4676, 32844, 33161}, {8616, 33107, 29678}, {17127, 33106, 24892}, {32947, 70481, 29663}


X(72039) = X(1)X(4190)∩X(8)X(71518)

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

X(72039) lies on these lines: {1, 4190}, {8, 71518}, {10, 20101}, {43, 4307}, {55, 50301}, {165, 29657}, {171, 2886}, {516, 1961}, {528, 4038}, {612, 33099}, {750, 33106}, {846, 64174}, {2550, 62841}, {3434, 37604}, {3550, 29640}, {3664, 3979}, {3745, 24715}, {3791, 69755}, {3920, 32857}, {3935, 64164}, {3961, 50307}, {3980, 32866}, {4418, 32847}, {4457, 62231}, {4645, 32783}, {4649, 34612}, {4660, 70484}, {4675, 17715}, {4682, 33095}, {4697, 32850}, {4886, 28498}, {5263, 33085}, {5269, 17889}, {5439, 68847}, {5880, 17716}, {6154, 37631}, {9345, 34611}, {9347, 33094}, {10459, 20067}, {17122, 63979}, {17126, 33138}, {17764, 34064}, {17778, 71450}, {17784, 42042}, {19856, 33083}, {20020, 49532}, {20064, 26037}, {20069, 28522}, {20292, 33152}, {21282, 29845}, {24342, 63134}, {25439, 48868}, {26040, 50303}, {26098, 56010}, {26806, 71517}, {26842, 67210}, {29633, 32948}, {29816, 33102}, {29820, 63969}, {32853, 49720}, {32939, 50288}, {33072, 33167}, {33111, 37540}, {48696, 49744}, {49719, 62821}, {50408, 59313}, {58679, 66645}, {59312, 63140}, {62865, 68589}, {63056, 71451}

X(72039) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {171, 33109, 33140}, {3980, 50289, 32866}, {5880, 17716, 33147}, {32948, 70482, 29633}


X(72040) = X(1)X(329)∩X(238)X(2886)

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

X(72040) lies on these lines: {1, 329}, {36, 28364}, {43, 20075}, {238, 2886}, {390, 42043}, {497, 16468}, {595, 3814}, {614, 32857}, {748, 33109}, {1201, 20067}, {1279, 33096}, {3246, 33130}, {3550, 59572}, {3632, 63037}, {3683, 17722}, {3698, 66645}, {3820, 5255}, {3944, 7290}, {4011, 32847}, {4090, 49704}, {4135, 50015}, {4307, 25502}, {4388, 29637}, {4432, 33071}, {4649, 49736}, {4660, 70485}, {4676, 33167}, {4679, 17716}, {4871, 20101}, {5044, 68847}, {5057, 33147}, {5698, 17591}, {5903, 63511}, {7081, 49705}, {7191, 33099}, {7262, 17721}, {8167, 50301}, {15485, 26098}, {17063, 64016}, {17123, 63979}, {17127, 33140}, {17350, 29844}, {17484, 29818}, {17784, 36634}, {20064, 30957}, {24703, 33152}, {25728, 63017}, {26105, 37604}, {26791, 70841}, {26792, 67210}, {29633, 70481}, {29640, 33107}, {29662, 30653}, {29817, 61707}, {29820, 41011}, {32844, 33164}, {32866, 32930}, {32942, 33082}, {32947, 70483}, {49500, 53619}, {49709, 59511}, {62998, 71414}, {63010, 71452}

X(72040) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {238, 33106, 33138}, {26105, 50303, 37604}


X(72041) = X(1)X(9782)∩X(11)X(750)

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

X(72041) lies on these lines: {1, 9782}, {11, 750}, {31, 3826}, {100, 50301}, {165, 29682}, {171, 24892}, {200, 64164}, {390, 3720}, {528, 9345}, {612, 4312}, {899, 4307}, {976, 11551}, {3474, 3989}, {3550, 29661}, {3626, 31303}, {3664, 67207}, {3722, 4675}, {3775, 33080}, {3790, 4418}, {3938, 5542}, {3980, 32854}, {4038, 49719}, {4293, 10459}, {4302, 59305}, {4316, 30116}, {4349, 67211}, {4414, 64174}, {4682, 33094}, {5218, 29678}, {5269, 69253}, {5718, 35023}, {5880, 33143}, {6154, 17392}, {9347, 24715}, {9776, 29818}, {17124, 63979}, {17300, 71451}, {17449, 68589}, {17766, 26627}, {20101, 26037}, {24393, 32912}, {24988, 50300}, {27577, 59316}, {29647, 32948}, {29662, 33109}, {29663, 70482}, {32919, 49720}, {33110, 37604}, {33112, 56010}, {34612, 62821}, {48696, 48868}, {49732, 61358}, {59306, 63140}, {61707, 67097}, {63056, 71450}

X(72041) = {X(32948),X(70484)}-harmonic conjugate of X(29647)


X(72042) = X(1)X(26792)∩X(31)X(3816)

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

X(72042) lies on these lines: {1, 26792}, {31, 3816}, {238, 11680}, {329, 29818}, {614, 4862}, {748, 3925}, {899, 17784}, {1647, 1707}, {3246, 33127}, {3720, 3945}, {3769, 24709}, {3915, 17757}, {3924, 51423}, {3938, 21060}, {4011, 32854}, {4021, 17017}, {4388, 29677}, {4666, 61707}, {4679, 17469}, {4871, 20064}, {4896, 41011}, {4906, 71797}, {7290, 69173}, {10582, 64164}, {15485, 29661}, {17125, 63979}, {17127, 29662}, {17271, 32942}, {17766, 26688}, {20095, 36634}, {21929, 54382}, {24552, 70972}, {24703, 33143}, {29647, 70481}, {29663, 70483}, {29682, 66515}, {29689, 60846}, {31018, 67210}, {32947, 70485}, {49736, 61358}, {50001, 63009}, {63002, 71452}, {63010, 71414}

X(72042) = {X(15485),X(33107)}-harmonic conjugate of X(29661)


X(72043) = X(2)X(902)∩X(10)X(26627)

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

X(72043) lies on these lines: {2, 902}, {10, 26627}, {31, 17337}, {42, 4648}, {43, 37635}, {612, 4859}, {750, 3826}, {756, 17276}, {899, 63008}, {1201, 17582}, {1376, 29661}, {1654, 26037}, {1698, 26064}, {2177, 17245}, {2308, 37681}, {2550, 30950}, {3011, 38204}, {3120, 38052}, {3925, 17124}, {3946, 5311}, {4358, 24693}, {4418, 17339}, {4675, 21805}, {5241, 31134}, {5268, 69253}, {5297, 33143}, {5437, 29690}, {7679, 9364}, {9330, 32857}, {9342, 33111}, {9350, 17056}, {10459, 37462}, {11269, 40333}, {17122, 24892}, {17283, 24943}, {17286, 29687}, {17296, 70522}, {17315, 32860}, {17324, 33125}, {17327, 32781}, {17329, 33067}, {17375, 59296}, {17381, 29663}, {19804, 32854}, {21747, 37650}, {24725, 61686}, {24988, 50302}, {25502, 33110}, {25957, 30832}, {26038, 32949}, {29640, 61156}, {29678, 63344}, {33112, 62711}, {37680, 50301}, {49732, 62849}, {61358, 63401}

X(72043) = {X(3925),X(17124)}-harmonic conjugate of X(29662)


X(72044) = X(2)X(902)∩X(9)X(1647)

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

X(72044) lies on these lines: {2, 902}, {9, 1647}, {11, 1253}, {42, 26105}, {75, 24709}, {149, 62711}, {244, 4679}, {748, 3816}, {978, 26127}, {1201, 5084}, {1479, 28257}, {1654, 26139}, {2177, 51415}, {2478, 28352}, {3058, 9350}, {3120, 4859}, {3161, 4141}, {3646, 21674}, {3720, 63008}, {3756, 36263}, {3771, 27141}, {3846, 29677}, {3877, 26727}, {3915, 17527}, {4414, 5121}, {4423, 29661}, {4648, 20978}, {4871, 50304}, {5211, 64178}, {5272, 69173}, {5284, 29678}, {7292, 33143}, {7308, 29690}, {8167, 33105}, {9335, 33099}, {9345, 63401}, {11269, 37681}, {11814, 26227}, {16484, 37651}, {16602, 33094}, {16706, 25378}, {17051, 54352}, {17063, 33098}, {17123, 24892}, {17261, 50533}, {17283, 25531}, {17286, 69252}, {17339, 33161}, {17375, 26069}, {17381, 32944}, {17449, 31018}, {17717, 63344}, {18743, 32854}, {21214, 37162}, {24217, 37680}, {24943, 25960}, {25072, 29639}, {25502, 33107}, {26102, 37635}, {26103, 32949}, {26688, 29655}, {27131, 29820}, {27742, 38025}, {29638, 30867}, {29647, 70942}, {29676, 35595}, {29689, 30852}, {29845, 70485}, {30331, 62660}, {30578, 49532}, {30829, 32844}, {30957, 33080}, {31136, 63003}, {31137, 37656}, {31242, 33083}, {32866, 46938}, {33141, 37687}, {37663, 62849}, {59506, 71796}

X(72044) = {X(748),X(3816)}-harmonic conjugate of X(29662)


X(72045) = X(1)X(2)∩X(31)X(17337)

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

X(72045) lies on these lines: {1, 2}, {31, 17337}, {748, 3826}, {756, 17278}, {902, 26040}, {2308, 37650}, {3120, 7308}, {3305, 69253}, {3925, 17125}, {4418, 17338}, {5241, 31237}, {8167, 33136}, {9330, 33147}, {17123, 33104}, {17245, 61358}, {17259, 32781}, {17260, 33125}, {17263, 32860}, {17265, 33081}, {17277, 25961}, {17335, 33067}, {17889, 35595}, {19804, 33161}, {25878, 61357}, {26724, 33143}, {27065, 33098}, {31252, 32782}, {33111, 37687}, {33127, 61686}, {38204, 41011}, {44412, 47513}

X(72045) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10, 29677}, {2, 899, 29661}, {2, 16569, 29678}, {2, 26037, 24943}, {2, 26038, 29632}, {2, 33139, 25502}, {2, 59296, 29851}, {17277, 25961, 33080}


X(72046) = X(1)X(2)∩X(11)X(17124)

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

X(72046) lies on these lines: {1, 2}, {11, 17124}, {88, 33154}, {748, 37634}, {750, 3816}, {756, 17728}, {902, 26105}, {968, 31190}, {1468, 17527}, {2650, 24954}, {3035, 62849}, {3120, 5437}, {3306, 69173}, {4038, 37651}, {4703, 24593}, {6174, 17782}, {6691, 10448}, {9335, 33152}, {9342, 33141}, {9345, 37662}, {11814, 26223}, {16602, 33128}, {17051, 62869}, {17063, 33143}, {17122, 33104}, {17125, 37646}, {18743, 33161}, {20196, 62819}, {25378, 33068}, {25934, 61356}, {25960, 33080}, {26127, 37603}, {27002, 32776}, {27003, 33098}, {30829, 33119}, {30867, 33069}, {31272, 33111}, {32771, 37758}, {33101, 65112}, {33167, 46938}, {37162, 37608}, {37663, 62821}, {51415, 61358}, {59506, 71795}

X(72046) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4871, 29677}, {2, 26102, 29678}, {2, 26103, 29632}, {2, 29829, 6686}, {2, 29845, 29663}, {2, 30947, 29846}, {2, 30950, 29661}, {2, 30957, 24943}, {2, 33142, 62711}, {612, 31249, 1647}


X(72047) = X(1)X(872)∩X(7)X(181)

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

X(72047) lies on the Feuerbach circumhyperbola and these lines: {1, 872}, {4, 29309}, {7, 181}, {8, 7064}, {9, 3996}, {21, 60731}, {79, 69755}, {104, 8708}, {210, 314}, {256, 4685}, {312, 56087}, {341, 45032}, {391, 40779}, {646, 4111}, {941, 20012}, {2298, 57397}, {2321, 60675}, {3685, 32635}, {3686, 4876}, {3751, 56766}, {3886, 4866}, {6601, 14555}, {23836, 50520}, {40408, 41610}, {40439, 56048}, {43073, 63977}

X(72047) = isotomic conjugate of X(4059)
X(72047) = X(i)-cross conjugate of X(j) for these (i,j): {3709, 646}, {4113, 8}, {4560, 3699}
X(72047) = X(i)-isoconjugate of X(j) for these (i,j): {31, 4059}, {34, 22060}, {56, 3720}, {57, 20963}, {58, 39793}, {65, 70143}, {109, 6372}, {222, 40975}, {604, 3739}, {651, 68881}, {1014, 2667}, {1106, 3706}, {1395, 70154}, {1397, 20888}, {1400, 18166}, {1402, 17175}, {1407, 3691}, {1408, 21020}, {1412, 16589}, {1414, 50497}, {1415, 47672}, {1434, 21753}, {3669, 70144}, {4436, 43924}, {4754, 66996}, {4891, 16945}, {7341, 21699}, {16947, 53478}, {57181, 70145}
X(72047) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 3720}, {2, 4059}, {8, 4891}, {10, 39793}, {11, 6372}, {1146, 47672}, {2968, 48264}, {3161, 3739}, {5452, 20963}, {6552, 3706}, {6741, 48393}, {11517, 22060}, {24771, 3691}, {38991, 68881}, {40582, 18166}, {40599, 16589}, {40602, 70143}, {40605, 17175}, {40608, 50497}, {59577, 21020}, {62584, 70154}, {62585, 20888}
X(72047) = cevapoint of X(8) and X(210)
X(72047) = barycentric product X(i)*X(j) for these {i,j}: {8, 32009}, {312, 40433}, {646, 50520}, {2321, 40439}, {3596, 57397}, {3701, 40408}, {4391, 8708}, {6057, 59147}
X(72047) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 4059}, {8, 3739}, {9, 3720}, {21, 18166}, {33, 40975}, {37, 39793}, {55, 20963}, {200, 3691}, {210, 16589}, {219, 22060}, {284, 70143}, {312, 20888}, {314, 16748}, {333, 17175}, {345, 70154}, {346, 3706}, {522, 47672}, {644, 4436}, {646, 53363}, {650, 6372}, {663, 68881}, {1334, 2667}, {2321, 21020}, {3161, 4891}, {3239, 48264}, {3699, 70145}, {3700, 48393}, {3701, 53478}, {3706, 70156}, {3709, 50497}, {3712, 70155}, {3939, 70144}, {3996, 29773}, {4069, 61163}, {4515, 4111}, {6057, 52579}, {7064, 21820}, {7081, 4754}, {8708, 651}, {32009, 7}, {40408, 1014}, {40433, 57}, {40439, 1434}, {50520, 3669}, {52370, 22369}, {57397, 56}, {59147, 552}, {70157, 70162}


X(72048) = X(1)X(872)∩X(2)X(13476)

Barycentrics    (b + c)*(2*a*b + a*c + b*c)*(a*b + 2*a*c + b*c) : :
X(72048) = X[64581] + 2 X[68077]

X(72048) lies on these lines: {1, 872}, {2, 13476}, {10, 4043}, {19, 14004}, {37, 3896}, {65, 19874}, {75, 756}, {321, 46772}, {594, 60676}, {596, 984}, {759, 8708}, {876, 4977}, {1089, 39708}, {1215, 4751}, {2214, 5276}, {3696, 56237}, {3728, 41683}, {3739, 3952}, {4022, 39697}, {4033, 21699}, {4557, 17260}, {4664, 17038}, {4698, 4883}, {4732, 56134}, {5224, 39712}, {5257, 60677}, {9330, 70852}, {16709, 18827}, {17335, 20964}, {17450, 39739}, {18082, 46196}, {20011, 27268}, {21805, 58396}, {22271, 69519}, {22289, 71598}, {27823, 56174}, {33295, 40438}, {39711, 49447}, {39737, 51488}, {40627, 69478}, {42285, 66674}, {59517, 70162}

X(72048) = isogonal conjugate of X(70143)
X(72048) = isotomic conjugate of X(17175)
X(72048) = X(i)-cross conjugate of X(j) for these (i,j): {514, 3952}, {4079, 4033}, {21727, 1018}, {22042, 4552}, {22044, 190}
X(72048) = X(i)-isoconjugate of X(j) for these (i,j): {1, 70143}, {6, 18166}, {28, 22060}, {31, 17175}, {32, 16748}, {58, 3720}, {60, 39793}, {81, 20963}, {110, 6372}, {163, 47672}, {593, 16589}, {662, 68881}, {757, 2667}, {763, 21820}, {849, 21020}, {1019, 70144}, {1333, 3739}, {1408, 3706}, {1412, 3691}, {1509, 21753}, {1790, 40975}, {2194, 4059}, {2203, 70154}, {2206, 20888}, {3733, 4436}, {4111, 7341}, {46289, 70153}, {50497, 52935}, {57129, 70145}
X(72048) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 17175}, {3, 70143}, {9, 18166}, {10, 3720}, {37, 3739}, {39, 70153}, {115, 47672}, {244, 6372}, {1084, 68881}, {1214, 4059}, {1500, 62646}, {4075, 21020}, {6376, 16748}, {6741, 48264}, {16587, 4754}, {40586, 20963}, {40591, 22060}, {40599, 3691}, {40603, 20888}, {40607, 2667}, {55065, 48393}, {59577, 3706}, {62564, 70154}
X(72048) = cevapoint of X(i) and X(j) for these (i,j): {10, 756}, {37, 40607}
X(72048) = trilinear pole of line {661, 4151}
X(72048) = barycentric product X(i)*X(j) for these {i,j}: {10, 32009}, {313, 57397}, {321, 40433}, {594, 40439}, {1089, 40408}, {1577, 8708}, {4033, 50520}, {6535, 59147}
X(72048) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18166}, {2, 17175}, {6, 70143}, {10, 3739}, {37, 3720}, {42, 20963}, {71, 22060}, {75, 16748}, {141, 70153}, {210, 3691}, {226, 4059}, {306, 70154}, {321, 20888}, {512, 68881}, {523, 47672}, {594, 21020}, {661, 6372}, {756, 16589}, {762, 21699}, {872, 21753}, {1018, 4436}, {1089, 53478}, {1215, 4754}, {1500, 2667}, {1824, 40975}, {2171, 39793}, {2321, 3706}, {3700, 48264}, {3950, 4891}, {3952, 70145}, {4024, 48393}, {4033, 53363}, {4062, 70155}, {4079, 50497}, {4557, 70144}, {4651, 29773}, {6535, 52579}, {8708, 662}, {18082, 18089}, {21020, 70156}, {32009, 86}, {40408, 757}, {40433, 81}, {40439, 1509}, {40521, 61163}, {40607, 62646}, {45223, 46368}, {50520, 1019}, {57397, 58}, {59147, 6628}, {69621, 70162}
{X(872),X(3842)}-harmonic conjugate of X(4687)


X(72049) = X(513)X(4380)∩X(514)X(4079)

Barycentrics    (b - c)*(2*a*b + a*c + b*c)*(a*b + 2*a*c + b*c) : :
X(72049) = 4 X[47666] - X[69522], 3 X[661] - 2 X[42327], 3 X[7199] - 4 X[42327], X[17217] - 3 X[47774]

X(72049) lies on these lines: {513, 4380}, {514, 4079}, {661, 7199}, {798, 1019}, {812, 47947}, {876, 4977}, {1022, 32009}, {1027, 40433}, {1308, 8708}, {3669, 57167}, {4562, 65161}, {4762, 47915}, {4785, 48587}, {7192, 24948}, {9295, 25054}, {10566, 47970}, {17217, 47774}, {20979, 47908}, {27193, 43067}, {29404, 47996}, {40439, 69475}, {48000, 68881}

X(72049) = midpoint of X(20979) and X(47908)
X(72049) = reflection of X(i) in X(j) for these {i,j}: {7199, 661}, {68881, 48000}
X(72049) = isogonal conjugate of X(70144)
X(72049) = isotomic conjugate of X(70145)
X(72049) = isotomic conjugate of the anticomplement of X(17205)
X(72049) = X(8708)-anticomplementary conjugate of X(17135)
X(72049) = X(i)-cross conjugate of X(j) for these (i,j): {3122, 75}, {17205, 2}, {23795, 6548}, {23821, 7}, {23822, 335}, {23823, 86}, {23827, 62626}, {47917, 514}, {48409, 693}
X(72049) = X(i)-isoconjugate of X(j) for these (i,j): {1, 70144}, {6, 4436}, {31, 70145}, {32, 53363}, {58, 61163}, {99, 21753}, {100, 20963}, {101, 3720}, {109, 3691}, {110, 16589}, {163, 21020}, {249, 50538}, {648, 22369}, {662, 2667}, {692, 3739}, {765, 68881}, {1018, 70143}, {1110, 47672}, {1252, 6372}, {1331, 40975}, {1415, 3706}, {1576, 53478}, {1783, 22060}, {2149, 48264}, {4111, 4565}, {4556, 21699}, {4557, 18166}, {4567, 50497}, {4891, 34080}, {5546, 39793}, {17175, 69826}, {20888, 32739}, {21820, 52935}, {43076, 62646}
X(72049) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 70145}, {3, 70144}, {9, 4436}, {10, 61163}, {11, 3691}, {115, 21020}, {244, 16589}, {513, 68881}, {514, 47672}, {650, 48264}, {661, 6372}, {1015, 3720}, {1084, 2667}, {1086, 3739}, {1146, 3706}, {4858, 53478}, {4988, 48393}, {5521, 40975}, {6376, 53363}, {8054, 20963}, {16592, 4754}, {17761, 62646}, {38986, 21753}, {39006, 22060}, {40615, 4059}, {40618, 70154}, {40619, 20888}, {40620, 17175}, {40621, 4891}, {40627, 50497}, {55064, 4111}, {55065, 52579}, {55066, 22369}
X(72049) = cevapoint of X(i) and X(j) for these (i,j): {514, 661}, {1577, 20909}
X(72049) = crosssum of X(20963) and X(68881)
X(72049) = trilinear pole of line {244, 17761}
X(72049) = crossdifference of every pair of points on line {2667, 20963}
X(72049) = barycentric product X(i)*X(j) for these {i,j}: {75, 50520}, {514, 32009}, {523, 40439}, {693, 40433}, {1111, 8708}, {1577, 40408}, {3261, 57397}, {4024, 59147}
X(72049) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4436}, {2, 70145}, {6, 70144}, {11, 48264}, {37, 61163}, {75, 53363}, {244, 6372}, {512, 2667}, {513, 3720}, {514, 3739}, {522, 3706}, {523, 21020}, {649, 20963}, {650, 3691}, {661, 16589}, {693, 20888}, {784, 70162}, {798, 21753}, {810, 22369}, {1015, 68881}, {1019, 18166}, {1086, 47672}, {1459, 22060}, {1577, 53478}, {2643, 50538}, {3120, 48393}, {3122, 50497}, {3667, 4891}, {3676, 4059}, {3733, 70143}, {4017, 39793}, {4024, 52579}, {4025, 70154}, {4041, 4111}, {4079, 21820}, {4369, 4754}, {4705, 21699}, {4750, 70155}, {4824, 59219}, {6591, 40975}, {7192, 17175}, {7199, 16748}, {8708, 765}, {10566, 18089}, {17494, 29773}, {32009, 190}, {40408, 662}, {40433, 100}, {40439, 99}, {47672, 70156}, {50520, 1}, {57397, 101}, {59147, 4610}, {68968, 71330}


X(72050) = X(30)X(511)∩X(86)X(1019)

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

X(72050) lies on these lines: {30, 511}, {86, 1019}, {649, 4763}, {650, 48016}, {661, 26777}, {693, 48577}, {798, 48551}, {1213, 4129}, {1635, 45315}, {1654, 47935}, {3572, 31308}, {3768, 4063}, {3776, 48013}, {3835, 4790}, {4106, 4932}, {4120, 48567}, {4367, 5625}, {4369, 4728}, {4375, 4784}, {4380, 4813}, {4382, 48107}, {4467, 23731}, {4500, 49293}, {4560, 48597}, {4733, 4807}, {4750, 48550}, {4786, 47882}, {4806, 25381}, {4810, 49292}, {4830, 48024}, {4897, 69291}, {4905, 70929}, {4928, 31147}, {4940, 31286}, {4958, 47870}, {4984, 47782}, {6615, 24417}, {7192, 48114}, {7659, 48042}, {9791, 48150}, {16892, 49297}, {17217, 48580}, {17494, 47991}, {20090, 48334}, {21196, 47988}, {21297, 31148}, {23729, 69292}, {24697, 27929}, {24924, 26798}, {25259, 48104}, {25380, 70711}, {26824, 48147}, {27483, 27854}, {31144, 69532}, {31150, 48544}, {31290, 47932}, {31336, 62558}, {39548, 67024}, {42327, 71469}, {43067, 48071}, {44449, 48101}, {45313, 45675}, {45661, 47767}, {45674, 47756}, {45679, 47784}, {45745, 47978}, {45746, 47937}, {47653, 47900}, {47663, 48076}, {47664, 47908}, {47677, 47907}, {47768, 47786}, {47778, 66524}, {47787, 48576}, {47814, 58178}, {47874, 65701}, {47886, 48543}, {47926, 47939}, {47952, 48588}, {47962, 47984}, {47971, 49298}, {47976, 69310}, {47981, 48404}, {48008, 48026}, {48043, 53580}, {48060, 48270}, {48067, 48269}, {48138, 49272}, {48145, 49273}, {48266, 49282}, {48417, 53586}, {48566, 69496}, {48624, 69309}, {50449, 69522}, {50497, 69979}, {58182, 65449}, {62324, 68999}, {68881, 69978}, {69359, 69973}

X(72050) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4776, 4763}, {649, 48049, 25666}, {649, 48079, 48049}, {1635, 47759, 45315}, {3835, 47761, 45678}, {4380, 4813, 48000}, {4382, 48107, 49291}, {4728, 4979, 47763}, {4728, 47763, 4369}, {4763, 4776, 25666}, {4763, 48049, 4776}, {4786, 48554, 47882}, {4928, 47762, 45663}, {4979, 20295, 4369}, {7192, 48114, 49289}, {17494, 48019, 47991}, {20295, 47763, 4728}, {31147, 47762, 4928}, {45313, 47760, 45675}, {47768, 47786, 47879}, {48008, 48592, 48026}, {48013, 49294, 3776}, {48016, 48041, 650}, {48060, 49284, 48270}, {48071, 49287, 43067}


X(72051) = X(1)X(4759)∩X(8)X(9)

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

X(72051) lies on these lines: {1, 4759}, {2, 44446}, {8, 9}, {10, 4473}, {21, 645}, {45, 4676}, {63, 30947}, {190, 15254}, {238, 17261}, {239, 49452}, {333, 4519}, {405, 69493}, {894, 1125}, {968, 70742}, {1001, 17336}, {1698, 3923}, {1757, 3244}, {2975, 33845}, {3219, 29824}, {3616, 50127}, {3617, 50126}, {3622, 17350}, {3623, 3751}, {3647, 70117}, {3683, 4009}, {3731, 70419}, {3786, 52352}, {3928, 26103}, {3993, 17121}, {4011, 29827}, {4422, 24723}, {4427, 35595}, {4512, 27538}, {4645, 25101}, {4655, 17266}, {4672, 16826}, {4684, 61000}, {4704, 16475}, {5057, 37330}, {5205, 62838}, {5263, 16814}, {5695, 17335}, {6651, 17292}, {9791, 17353}, {15481, 68969}, {16020, 20073}, {16468, 17319}, {16477, 29584}, {16815, 27949}, {16817, 41872}, {16885, 49470}, {17125, 62300}, {17244, 24695}, {17254, 29637}, {17263, 17768}, {17268, 33082}, {17312, 17770}, {17326, 24295}, {17338, 24248}, {17339, 50295}, {17777, 54357}, {18230, 24280}, {21371, 54290}, {24342, 51073}, {24349, 25728}, {25082, 70930}, {27065, 32932}, {27385, 27420}, {29607, 33149}, {29632, 69057}, {30331, 49707}, {30568, 71476}, {30970, 32930}, {32922, 49522}, {41002, 42033}, {46933, 50314}, {49458, 51297}, {49462, 68966}, {49482, 51294}, {56077, 56203}, {56288, 69029}, {60711, 71786}, {61686, 65166}, {62818, 70485}

X(72051) = barycentric product X(i)*X(j) for these {i,j}: {8, 29584}, {190, 48562}, {312, 16477}
X(72051) = barycentric quotient X(i)/X(j) for these {i,j}: {16477, 57}, {29584, 7}, {48562, 514}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 3685, 60731}, {9, 71524, 3685}, {45, 4676, 16830}, {190, 15254, 16823}, {1001, 17336, 62222}, {25101, 51090, 4645}, {25728, 66515, 24349}


X(72052) = X(1)X(11346)∩X(2)X(37)

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

X(72052) lies on these lines: {1, 11346}, {2, 37}, {9, 63060}, {10, 65022}, {42, 4096}, {45, 3187}, {72, 3241}, {81, 17261}, {190, 17019}, {210, 27804}, {213, 29584}, {226, 65021}, {306, 4029}, {376, 67887}, {519, 14020}, {551, 3159}, {756, 3896}, {894, 1255}, {975, 19336}, {1215, 58381}, {1500, 59212}, {1621, 60723}, {1824, 7714}, {1959, 3970}, {1961, 32936}, {1962, 3971}, {1999, 4921}, {2321, 41809}, {2325, 69544}, {2895, 17315}, {2901, 3679}, {3219, 34064}, {3227, 56037}, {3247, 19684}, {3294, 16834}, {3578, 50093}, {3616, 64562}, {3700, 36900}, {3701, 3743}, {3720, 42055}, {3723, 19717}, {3731, 5278}, {3740, 64161}, {3773, 6536}, {3842, 4365}, {3876, 50602}, {3931, 52353}, {3936, 4098}, {3943, 56810}, {3950, 3969}, {3952, 37593}, {3954, 17389}, {3967, 29822}, {3989, 46909}, {3994, 43223}, {4024, 31150}, {4026, 69301}, {4052, 30588}, {4078, 4972}, {4090, 21806}, {4102, 31144}, {4360, 27065}, {4425, 48647}, {4427, 4682}, {4432, 29816}, {4439, 29685}, {4527, 8013}, {4651, 49462}, {4696, 62831}, {4854, 69250}, {4883, 20068}, {4968, 27785}, {4981, 32915}, {5249, 22019}, {5257, 60203}, {5271, 16676}, {5287, 32933}, {5294, 59585}, {5295, 53620}, {6535, 50298}, {6539, 70264}, {6541, 48648}, {7265, 44550}, {7283, 51669}, {7757, 22036}, {8025, 17351}, {9791, 33078}, {10707, 66070}, {11239, 52345}, {15254, 17150}, {15569, 17165}, {16052, 57808}, {16418, 56538}, {16674, 19701}, {16677, 19732}, {16777, 19722}, {16814, 19742}, {16826, 32026}, {16857, 50072}, {17011, 41241}, {17021, 32939}, {17140, 49523}, {17184, 17243}, {17242, 32782}, {17244, 33146}, {17246, 69251}, {17247, 33172}, {17258, 32863}, {17299, 63100}, {17316, 32859}, {17317, 17483}, {17319, 32911}, {17336, 37685}, {17350, 62801}, {17372, 43990}, {17393, 63074}, {17592, 64178}, {17679, 50066}, {18098, 42037}, {18146, 27801}, {19332, 50044}, {20691, 71598}, {21078, 22004}, {21802, 41249}, {21807, 34611}, {21816, 29617}, {22001, 31164}, {22002, 22014}, {22024, 31161}, {23878, 58361}, {25423, 58360}, {25728, 62808}, {26037, 49452}, {27064, 62851}, {27186, 62229}, {27811, 71117}, {29580, 69528}, {29653, 48646}, {29814, 49447}, {29854, 33154}, {30568, 62816}, {31302, 62866}, {32864, 51294}, {32937, 62840}, {34607, 43214}, {36911, 62564}, {38314, 51673}, {42039, 42057}, {42042, 71612}, {42043, 71619}, {42054, 50111}, {42471, 64426}, {45315, 57133}, {45671, 57068}, {46904, 59517}, {49520, 62867}, {49724, 49737}, {49980, 62296}, {50083, 64071}, {50110, 50306}, {50113, 56541}, {50125, 50256}, {50129, 70518}, {50290, 69296}, {59315, 71601}, {60724, 69505}, {62807, 71524}, {71525, 71561}

X(72052) = X(i)-Ceva conjugate of X(j) for these (i,j): {17393, 50587}, {30598, 10}
X(72052) = X(1333)-isoconjugate of X(39711)
X(72052) = X(37)-Dao conjugate of X(39711)
X(72052) = barycentric product X(i)*X(j) for these {i,j}: {10, 17393}, {75, 50587}, {190, 48551}, {321, 63074}, {3952, 48079}, {4033, 48011}
X(72052) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 39711}, {17393, 86}, {48011, 1019}, {48079, 7192}, {48551, 514}, {50587, 1}, {63074, 81}
X(72052) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 192, 50106}, {2, 3175, 321}, {2, 3995, 3175}, {2, 42044, 4980}, {2, 50106, 4359}, {37, 3175, 2}, {37, 3995, 321}, {756, 3993, 3896}, {1962, 3971, 46897}, {3247, 56082, 19684}, {4425, 69295, 48647}, {4681, 44307, 17147}, {4704, 41839, 28606}, {6541, 69294, 48648}, {17147, 44307, 24589}, {17781, 29574, 42045}, {22034, 31025, 321}, {28606, 41839, 4358}, {31993, 62227, 321}, {41313, 50068, 2}, {42029, 51488, 2}, {42057, 50777, 42039}, {50093, 50292, 3578}


X(72053) = X(2)X(4912)∩X(9)X(312)

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

X(72053) lies on these lines: {2, 4912}, {9, 312}, {37, 70742}, {44, 41839}, {45, 27064}, {63, 30829}, {75, 27065}, {190, 3305}, {210, 71524}, {321, 17335}, {344, 33066}, {345, 62706}, {346, 4886}, {391, 42030}, {748, 49447}, {749, 63519}, {756, 4676}, {1150, 20942}, {1211, 17339}, {1743, 34064}, {1999, 16885}, {2895, 17240}, {3008, 62229}, {3161, 14555}, {3175, 17349}, {3219, 18743}, {3294, 70462}, {3550, 42056}, {3683, 27538}, {3685, 3715}, {3699, 4512}, {3758, 8025}, {3759, 3995}, {3769, 64178}, {3782, 17338}, {3790, 41002}, {3912, 32100}, {4009, 71476}, {4034, 4102}, {4096, 8616}, {4358, 5372}, {4370, 5743}, {4383, 17261}, {4387, 60731}, {4422, 27184}, {4423, 62222}, {4473, 32777}, {4514, 27549}, {4664, 32911}, {4687, 5333}, {4759, 17716}, {5233, 56078}, {5250, 44720}, {5273, 6557}, {5278, 42034}, {5284, 49499}, {5302, 19582}, {5325, 62297}, {5739, 17264}, {5905, 17263}, {6057, 70969}, {6172, 18141}, {7262, 59517}, {7308, 25728}, {8580, 65166}, {10453, 15481}, {11106, 44722}, {15254, 32937}, {15485, 42054}, {15492, 35652}, {16669, 58820}, {17184, 17341}, {17234, 17781}, {17241, 32859}, {17277, 42029}, {17286, 41816}, {17315, 63009}, {17329, 33172}, {17333, 69092}, {17342, 32782}, {17350, 44307}, {17393, 63074}, {17778, 41313}, {18134, 25101}, {18228, 32851}, {19684, 51488}, {19739, 29580}, {19786, 26685}, {19796, 37650}, {19808, 54389}, {25269, 42051}, {25430, 42028}, {25496, 51294}, {26688, 62796}, {30854, 56244}, {31018, 33116}, {32933, 35595}, {32943, 50075}, {37595, 71635}, {37758, 55868}, {41242, 64425}, {48630, 63100}, {50068, 63051}, {50296, 69297}, {52258, 59639}, {59506, 71477}, {63096, 69539}

X(72053) = X(604)-isoconjugate of X(39711)
X(72053) = X(3161)-Dao conjugate of X(39711)
X(72053) = crossdifference of every pair of points on line {51641, 58155}
X(72053) = barycentric product X(i)*X(j) for these {i,j}: {8, 17393}, {312, 63074}, {314, 50587}, {645, 48551}, {646, 48011}, {3699, 48079}
X(72053) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 39711}, {17393, 7}, {48011, 3669}, {48079, 3676}, {48551, 7178}, {50587, 65}, {63074, 57}
X(72053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 30568, 333}, {190, 3305, 19804}, {333, 30568, 312}, {3161, 14555, 42033}, {7308, 25728, 32939}, {15492, 35652, 37652}, {17277, 56082, 42029}


X(72054) = X(9)X(3791)∩X(10)X(3175)

Barycentrics    (b + c)*(-a^2 - 2*a*b - 2*a*c + b*c) : :
X(72054) = 4 X[756] - X[4457], 3 X[756] - X[4651], 5 X[756] - X[71631], 4 X[3995] + X[4457], 3 X[3995] + X[4651], 5 X[3995] + X[71631], 3 X[4457] - 4 X[4651], 5 X[4457] - 4 X[71631], 5 X[4651] - 3 X[71631]

X(72054) lies on these lines: {1, 33309}, {2, 3994}, {9, 3791}, {10, 3175}, {37, 714}, {38, 31035}, {42, 4096}, {43, 4664}, {45, 4362}, {171, 17261}, {190, 1961}, {192, 26038}, {210, 3993}, {321, 3842}, {333, 51294}, {344, 26128}, {354, 49520}, {519, 41002}, {537, 3720}, {726, 44307}, {740, 756}, {748, 49472}, {846, 4434}, {872, 58400}, {982, 22220}, {984, 10453}, {1089, 58386}, {1100, 71515}, {1125, 6534}, {1211, 6541}, {1255, 4756}, {1698, 42029}, {1757, 34064}, {1962, 3952}, {2321, 70972}, {2664, 32026}, {2887, 4078}, {3159, 49598}, {3244, 3988}, {3305, 32921}, {3578, 49995}, {3666, 6686}, {3681, 49471}, {3712, 59726}, {3715, 49488}, {3740, 4681}, {3741, 35652}, {3743, 4075}, {3840, 50777}, {3920, 4432}, {3932, 4425}, {3943, 21085}, {3950, 4104}, {3977, 58443}, {3980, 17262}, {3989, 4358}, {4009, 6685}, {4015, 4065}, {4026, 69297}, {4028, 4029}, {4038, 62222}, {4082, 50290}, {4090, 37593}, {4098, 21060}, {4135, 31993}, {4359, 28516}, {4365, 4732}, {4387, 36480}, {4415, 4892}, {4422, 29654}, {4423, 49455}, {4527, 70516}, {4533, 50590}, {4535, 56810}, {4672, 5311}, {4685, 49462}, {4704, 17592}, {4771, 70696}, {4942, 15668}, {4974, 27065}, {5268, 32934}, {5287, 32935}, {5297, 32936}, {5506, 43993}, {6535, 41809}, {6536, 69296}, {9330, 32860}, {9345, 71793}, {9791, 33079}, {13405, 70289}, {17018, 50111}, {17019, 32938}, {17021, 32940}, {17056, 21093}, {17135, 42041}, {17242, 33084}, {17243, 33064}, {17244, 33103}, {17246, 24169}, {17247, 33174}, {17258, 33085}, {17263, 33147}, {17264, 32783}, {17336, 62841}, {17450, 20068}, {17591, 30829}, {17598, 70610}, {17716, 71524}, {17763, 33761}, {18185, 23343}, {18743, 31242}, {19804, 49445}, {20942, 29827}, {21020, 62227}, {21805, 27804}, {21830, 21883}, {22034, 62226}, {24068, 27784}, {24165, 49523}, {24325, 32925}, {24631, 27481}, {25351, 33145}, {25496, 30568}, {25501, 49483}, {25502, 51035}, {26037, 42044}, {26102, 42055}, {26223, 50293}, {26580, 69295}, {28594, 71029}, {28606, 59511}, {29642, 41313}, {29688, 30566}, {29814, 49491}, {29822, 58381}, {29824, 42039}, {29854, 33151}, {30950, 42053}, {31318, 64429}, {31330, 50094}, {32915, 49457}, {32924, 35595}, {34595, 56215}, {37595, 71521}, {42034, 59312}, {42057, 49515}, {44419, 49994}, {49452, 59296}, {49988, 58629}, {50302, 56082}, {52875, 59596}, {56123, 56222}, {59585, 59692}, {69294, 69301}

X(72054) = midpoint of X(756) and X(3995)
X(72054) = barycentric product X(i)*X(j) for these {i,j}: {10, 17319}, {3952, 48049}
X(72054) = barycentric quotient X(i)/X(j) for these {i,j}: {17319, 86}, {48049, 7192}
X(72054) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 1215, 10180}, {37, 3967, 43223}, {37, 3971, 1215}, {37, 21838, 28592}, {37, 21902, 21827}, {37, 71525, 3985}, {190, 1961, 4697}, {321, 3842, 27798}, {3666, 59517, 24003}, {3740, 4681, 4970}, {3932, 4425, 28595}, {3967, 43223, 1215}, {3971, 43223, 3967}, {3989, 4358, 6682}, {4078, 4656, 2887}, {4415, 29653, 4892}, {4704, 27538, 17592}, {17763, 33761, 59624}, {26102, 49447, 42055}, {27065, 32928, 4974}, {28606, 64178, 59511}


X(72055) = X(2)X(18193)∩X(8)X(4082)

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

X(72055) lies on these lines: {2, 18193}, {8, 4082}, {9, 2319}, {43, 17261}, {75, 4942}, {171, 42056}, {190, 3740}, {200, 71524}, {210, 3685}, {238, 4096}, {239, 3971}, {312, 3715}, {333, 4009}, {346, 70973}, {612, 70742}, {756, 16830}, {984, 70942}, {1215, 17260}, {1376, 17336}, {1757, 59517}, {1961, 17120}, {1999, 64178}, {3219, 5205}, {3305, 16823}, {3683, 3699}, {3702, 32635}, {3705, 18228}, {3729, 26038}, {3731, 59297}, {3757, 3952}, {3769, 16885}, {3790, 14555}, {3876, 49492}, {3967, 17277}, {3974, 70969}, {4023, 42033}, {4078, 62998}, {4104, 17280}, {4126, 4514}, {4201, 59685}, {4359, 4756}, {4422, 33126}, {4438, 30867}, {4473, 59692}, {4512, 71529}, {4886, 6057}, {4903, 11679}, {5220, 18743}, {5268, 17350}, {5272, 31302}, {6646, 62673}, {6685, 51294}, {7174, 70485}, {7226, 26688}, {7308, 24349}, {7322, 70419}, {8167, 49499}, {8580, 25728}, {9330, 26223}, {9780, 39589}, {14829, 15481}, {16814, 59596}, {17123, 42054}, {17165, 35595}, {17254, 33174}, {17266, 33064}, {17268, 33084}, {17338, 33144}, {17777, 25006}, {21060, 25101}, {25957, 69057}, {26103, 62823}, {26264, 26867}, {26685, 29634}, {26791, 29639}, {26792, 69250}, {26840, 60423}, {27002, 36263}, {28058, 56244}, {29607, 33147}, {29641, 31018}, {32932, 63961}, {32939, 61686}, {32944, 42041}, {33100, 71102}, {37656, 69301}, {37679, 49447}, {38000, 59511}, {38057, 56084}, {49698, 49736}, {49707, 64162}, {56082, 59296}, {59216, 64083}, {59298, 62818}

X(72055) = barycentric product X(i)*X(j) for these {i,j}: {8, 17319}, {3699, 48049}
X(72055) = barycentric quotient X(i)/X(j) for these {i,j}: {17319, 7}, {48049, 3676}
X(72055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 27538, 7081}, {312, 3715, 60731}, {756, 27064, 16830}, {1961, 71515, 17120}, {3305, 32937, 16823}, {3729, 30393, 26038}, {3952, 27065, 3757}, {15481, 59506, 14829}, {18228, 27549, 3705}, {21060, 25101, 29839}


X(72056) = X(1)X(2)∩X(9)X(71636)

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

X(72056) lies on these lines: {1, 2}, {9, 71636}, {100, 29348}, {333, 71639}, {518, 43290}, {1376, 49499}, {3035, 49698}, {3158, 27538}, {3210, 67066}, {3684, 71786}, {3685, 3689}, {3711, 60731}, {3712, 4152}, {3911, 49707}, {3996, 4519}, {4962, 48008}, {5687, 69493}, {17120, 71634}, {17336, 61153}, {17596, 49508}, {24349, 46917}, {32937, 64135}, {49456, 60714}, {49695, 51415}, {62218, 71476}, {62706, 71526}

X(72056) = X(5381)-Ceva conjugate of X(644)
X(72056) = X(4526)-Dao conjugate of X(52626)
X(72056) = barycentric product X(i)*X(j) for these {i,j}: {646, 25569}, {3699, 4763}
X(72056) = barycentric quotient X(i)/X(j) for these {i,j}: {4763, 3676}, {25569, 3669}
X(72056) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {200, 71529, 7081}, {3689, 3699, 3685}, {3935, 17780, 5205}, {5524, 70841, 239}, {56385, 56386, 29577}


X(72057) = X(2)X(3999)∩X(8)X(4533)

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

X(72057) lies on these lines: {2, 3999}, {8, 4533}, {10, 48646}, {38, 6686}, {42, 4096}, {43, 51035}, {69, 53673}, {72, 52353}, {210, 321}, {756, 4090}, {899, 42054}, {1215, 59306}, {1962, 71634}, {2238, 69505}, {2292, 70741}, {2895, 53672}, {3006, 4126}, {3175, 19998}, {3219, 3699}, {3242, 26688}, {3678, 3701}, {3681, 4358}, {3697, 56318}, {3711, 32929}, {3715, 26227}, {3717, 5741}, {3720, 42056}, {3740, 17165}, {3782, 71102}, {3848, 17146}, {3873, 26103}, {3876, 4696}, {3877, 4487}, {3896, 3971}, {3920, 41241}, {3936, 21060}, {3969, 4082}, {3983, 17164}, {3992, 4134}, {3994, 4685}, {3995, 4849}, {4005, 17751}, {4009, 17135}, {4080, 21949}, {4104, 69296}, {4135, 71631}, {4359, 26038}, {4413, 71793}, {4430, 30829}, {4450, 49991}, {4517, 25298}, {4640, 17780}, {4661, 18743}, {4662, 25253}, {4723, 5692}, {4756, 32932}, {4767, 7081}, {4847, 30566}, {4884, 62620}, {4935, 9957}, {4980, 59296}, {4981, 32931}, {5014, 31018}, {5423, 5739}, {5524, 32936}, {6685, 42041}, {7322, 19684}, {14555, 53661}, {16602, 17154}, {16610, 20068}, {17140, 61686}, {17149, 62627}, {20011, 35652}, {20052, 64563}, {20683, 59212}, {21093, 48645}, {21870, 27804}, {21884, 52893}, {22016, 22271}, {24988, 59684}, {25244, 25735}, {25277, 58693}, {25728, 64135}, {25734, 46917}, {26792, 32850}, {27549, 33113}, {29824, 59506}, {29982, 64581}, {30957, 49503}, {31242, 49448}, {32933, 67097}, {33066, 60459}, {37619, 57151}, {37656, 53660}, {37679, 71794}, {41809, 53663}, {42038, 49508}, {42044, 59295}, {46909, 59511}, {48644, 70522}, {48647, 69298}, {48648, 69297}, {49693, 69173}, {53620, 69493}, {56082, 62218}, {62838, 71529}

X(72057) = X(6741)-Dao conjugate of X(52061)
X(72057) = barycentric product X(i)*X(j) for these {i,j}: {10, 17336}, {3952, 31209}, {4033, 48294}
X(72057) = barycentric quotient X(i)/X(j) for these {i,j}: {3700, 52061}, {17336, 86}, {31209, 7192}, {48294, 1019}
X(72057) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {210, 3952, 321}, {210, 3967, 4651}, {756, 4090, 46897}, {756, 71637, 43223}, {3681, 27538, 4358}, {3696, 71117, 321}, {3715, 59597, 26227}, {3740, 17165, 24589}, {3952, 4651, 3967}, {3967, 4651, 321}, {3971, 21805, 3896}, {4005, 59577, 17751}, {4090, 43223, 71637}, {32937, 63961, 4359}, {43223, 71637, 46897}, {69297, 69300, 48648}, {69298, 69299, 48647}


X(72058) = X(2)X(4864)∩X(8)X(1392)

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

X(72058) lies on these lines: {2, 4864}, {8, 1392}, {43, 49472}, {63, 43290}, {78, 44720}, {190, 64135}, {200, 312}, {210, 71476}, {333, 62218}, {341, 4420}, {345, 6555}, {960, 70743}, {1997, 20015}, {3681, 17780}, {3683, 71636}, {3689, 27538}, {3693, 71526}, {3703, 4152}, {3711, 4042}, {3769, 21805}, {3870, 30829}, {3891, 54309}, {3935, 18743}, {3940, 68245}, {3961, 70942}, {3974, 70971}, {4417, 49991}, {4767, 32929}, {4886, 7172}, {4942, 32932}, {4952, 5211}, {4997, 24392}, {5014, 70794}, {5423, 42033}, {7256, 56440}, {15519, 18228}, {17124, 51055}, {17264, 53673}, {17728, 49707}, {19804, 67097}, {25308, 61166}, {31233, 62814}, {31627, 65199}, {32851, 64083}, {32918, 50075}, {32922, 67066}, {32939, 46917}, {50105, 53660}

X(72058) = X(2968)-Dao conjugate of X(52061)
X(72058) = barycentric product X(i)*X(j) for these {i,j}: {8, 17336}, {646, 48294}, {3699, 31209}
X(72058) = barycentric quotient X(i)/X(j) for these {i,j}: {3239, 52061}, {17336, 7}, {31209, 3676}, {48294, 3669}
X(72058) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {200, 3699, 312}, {210, 71639, 71476}, {71476, 71529, 71639}


X(72059) = X(2)X(16496)∩X(8)X(3452)

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

X(72059) lies on these lines: {2, 16496}, {8, 3452}, {9, 36630}, {75, 59597}, {200, 3685}, {210, 333}, {312, 3711}, {321, 4767}, {644, 28055}, {894, 4090}, {1043, 59577}, {1376, 62222}, {1961, 71634}, {1999, 21805}, {3158, 71524}, {3219, 17780}, {3243, 26103}, {3681, 5205}, {3697, 16824}, {3701, 4720}, {3740, 16823}, {3750, 42056}, {3757, 63961}, {3790, 5423}, {3816, 49698}, {3886, 4903}, {3952, 32932}, {3971, 5524}, {3974, 70973}, {3996, 4009}, {4030, 4152}, {4096, 17261}, {4126, 32851}, {4388, 49991}, {4420, 46877}, {4421, 17336}, {4512, 71636}, {4640, 43290}, {4645, 21060}, {4673, 59598}, {4899, 20103}, {5233, 30615}, {5250, 70743}, {5263, 59596}, {5293, 70741}, {5297, 8025}, {5333, 46897}, {5692, 68245}, {6057, 70971}, {7172, 70969}, {7174, 59298}, {7322, 59297}, {8580, 24349}, {9350, 62300}, {9458, 27002}, {11019, 49707}, {15519, 52653}, {16602, 24841}, {17147, 54309}, {17260, 29670}, {17277, 58629}, {17319, 42043}, {20942, 49460}, {21870, 34064}, {27549, 64083}, {29673, 30867}, {30829, 41711}, {31018, 63139}, {32937, 67097}, {32948, 69057}, {33153, 71102}, {36634, 49455}, {37619, 52923}, {37682, 51055}, {42054, 56009}, {49501, 70256}, {50286, 63089}, {53672, 69301}, {56086, 56102}, {59506, 68969}, {61156, 71793}

X(72059) = X(25280)-Ceva conjugate of X(17261)
X(72059) = X(i)-isoconjugate of X(j) for these (i,j): {1402, 65071}, {1412, 65070}
X(72059) = X(i)-Dao conjugate of X(j) for these (i,j): {40599, 65070}, {40605, 65071}, {60714, 29820}
X(72059) = barycentric product X(i)*X(j) for these {i,j}: {8, 17261}, {9, 25280}, {312, 60714}, {333, 4096}, {646, 4879}, {3699, 25666}
X(72059) = barycentric quotient X(i)/X(j) for these {i,j}: {210, 65070}, {333, 65071}, {4096, 226}, {4879, 3669}, {4964, 30719}, {17261, 7}, {25280, 85}, {25666, 3676}, {60714, 57}
X(72059) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {200, 27538, 3685}, {210, 3699, 7081}, {210, 7081, 60731}, {3886, 59599, 4903}, {4096, 60714, 17261}


X(72060) = X(30)X(511)∩X(100)X(667)

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

X(72060) lies on these lines: {1, 19947}, {2, 3251}, {8, 6161}, {10, 45666}, {11, 4162}, {30, 511}, {100, 667}, {104, 29348}, {145, 764}, {149, 21301}, {214, 48330}, {239, 4775}, {650, 52959}, {663, 899}, {693, 70809}, {1022, 51093}, {1145, 48329}, {1317, 3669}, {1320, 48333}, {1734, 13277}, {1862, 18344}, {1960, 4763}, {2530, 62401}, {3035, 31288}, {3036, 20317}, {3241, 14421}, {3635, 23814}, {3679, 4448}, {3716, 28603}, {3912, 47761}, {4040, 62325}, {4041, 38325}, {4063, 5541}, {4462, 12531}, {4502, 50012}, {4543, 6546}, {4705, 19998}, {4728, 4895}, {4730, 47776}, {4825, 31150}, {4871, 17072}, {4905, 7972}, {4959, 48273}, {6154, 50499}, {6542, 47763}, {6544, 68829}, {6633, 57021}, {9269, 51071}, {9897, 48265}, {10609, 50336}, {10707, 31149}, {11607, 54230}, {14422, 45328}, {15343, 36236}, {15863, 59672}, {16173, 47841}, {17310, 47762}, {17756, 69481}, {20095, 31291}, {20980, 50028}, {21302, 29824}, {21630, 69359}, {23057, 69346}, {24864, 53535}, {25416, 48346}, {25666, 58158}, {30117, 48302}, {31209, 58157}, {31251, 31272}, {32028, 36237}, {32847, 48324}, {33337, 69311}, {33814, 39227}, {35962, 53376}, {40891, 47759}, {41140, 47760}, {41191, 48331}, {42322, 50501}, {45678, 53571}, {47814, 58159}, {47874, 68897}, {48049, 58164}, {48079, 58169}, {48111, 64056}, {48189, 50764}, {48285, 50335}, {48307, 60353}, {48332, 49771}, {48345, 70732}, {48352, 50016}, {48577, 71771}, {49988, 50507}, {50001, 50352}, {58334, 66199}, {62296, 70525}, {70288, 70769}

X(72060) = isogonal conjugate of X(39443)
X(72060) = crossdifference of every pair of points on line {6, 1646}
X(72060) = {X(3679),X(68824)}-harmonic conjugate of X(4448)


X(72061) = X(1)X(2)∩X(100)X(537)

Barycentrics    3*a^3 - 4*a^2*b + 2*a*b^2 - 4*a^2*c + 3*a*b*c - b^2*c + 2*a*c^2 - b*c^2 : :
X(72061) = 2 X[3935] + X[17763], X[3935] + 2 X[70841], X[17763] - 4 X[70841], 4 X[214] - X[9457], 2 X[3689] + X[32927], 2 X[4434] + X[62236], X[20095] + 2 X[21093]

X(72061) lies on these lines: {1, 2}, {31, 765}, {55, 23343}, {57, 66979}, {100, 537}, {190, 678}, {210, 16482}, {214, 9457}, {244, 43290}, {518, 34583}, {522, 3158}, {524, 16504}, {528, 70752}, {529, 67439}, {536, 3689}, {545, 57021}, {740, 4954}, {750, 51055}, {756, 71051}, {867, 12607}, {1621, 42056}, {1962, 46912}, {2177, 3570}, {3685, 4937}, {3699, 3722}, {3711, 16494}, {3913, 52242}, {4152, 4422}, {4383, 16501}, {4414, 71636}, {4418, 24345}, {4421, 23832}, {4432, 4767}, {4434, 62236}, {4781, 24821}, {4849, 16507}, {4952, 51402}, {6174, 9041}, {8616, 70736}, {8715, 13589}, {10196, 70793}, {16495, 21805}, {16500, 19723}, {17155, 64135}, {17318, 24408}, {19515, 37727}, {20095, 21093}, {21870, 50124}, {23644, 63526}, {23858, 24820}, {24427, 64161}, {24709, 53534}, {27918, 50120}, {31201, 49703}, {32775, 48821}, {32917, 51034}, {32918, 71639}, {32931, 48805}, {32937, 53340}, {34607, 69455}, {36815, 40172}, {42720, 50127}, {44663, 67416}, {46973, 67425}, {50078, 56176}, {50126, 71451}, {51035, 70909}, {56009, 70992}, {60714, 69539}

X(72061) = X(513)-isoconjugate of X(39443)
X(72061) = X(39026)-Dao conjugate of X(39443)
X(72061) = barycentric product X(6381)*X(19621)
X(72061) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 39443}, {19621, 37129}
X(72061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17780, 9458}, {2, 50079, 71753}, {3158, 67066, 32925}, {3935, 70841, 17763}, {17318, 27921, 24408}


X(72062) = X(1)X(6)∩X(32)X(1252)

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

X(72062) lies on these lines: {1, 6}, {32, 1252}, {41, 68825}, {100, 1017}, {101, 20331}, {145, 35092}, {650, 6161}, {896, 67432}, {899, 5091}, {1015, 57192}, {1026, 37540}, {3204, 68828}, {3240, 3573}, {3758, 16820}, {4585, 36275}, {5277, 68812}, {5375, 54230}, {6790, 54389}, {17281, 49998}, {24281, 53337}, {52946, 67583}, {52963, 70834}, {62846, 71082}

X(72062) = X(514)-isoconjugate of X(39443)
X(72062) = crossdifference of every pair of points on line {513, 3999}
X(72062) = barycentric product X(536)*X(19621)
X(72062) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 39443}, {19621, 3227}
X(72062) = {X(1),X(67385)}-harmonic conjugate of X(49515)


X(72063) = X(2)X(37)∩X(6)X(1016)

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

X(72063) lies on these lines: {2, 37}, {6, 1016}, {8, 16482}, {9, 23891}, {44, 24509}, {45, 874}, {145, 16507}, {519, 16495}, {545, 30866}, {594, 71050}, {646, 4422}, {668, 4370}, {889, 35123}, {1083, 70417}, {2321, 57038}, {2325, 6381}, {3161, 4391}, {3770, 17340}, {3943, 70809}, {3950, 68967}, {4033, 4473}, {4582, 17262}, {7258, 25536}, {9024, 36798}, {16672, 71820}, {17261, 69538}, {17350, 36275}, {20092, 39994}, {20331, 31002}, {23354, 24482}, {25728, 69034}, {36804, 70287}, {45666, 68101}, {49517, 71837}, {52716, 71770}, {70732, 71560}

X(72063) = X(649)-isoconjugate of X(39443)
X(72063) = X(5375)-Dao conjugate of X(39443)
X(72063) = crossdifference of every pair of points on line {667, 33917}
X(72063) = barycentric product X(19621)*X(35543)
X(72063) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 39443}, {19621, 739}


X(72064) = X(100)X(667)∩X(512)X(4763)

Barycentrics    (b - c)*(3*a^3 + 4*a^2*b - 2*a*b^2 + 4*a^2*c - 3*a*b*c + b^2*c - 2*a*c^2 + b*c^2) : :
X(72064) = X[4728] - 3 X[47837], X[4730] + 5 X[27013], X[4834] + 2 X[65449], 2 X[25666] + X[58175], X[47776] + 3 X[47836], 5 X[31209] + X[58173], 2 X[31288] + X[50499], 2 X[50501] + X[52601], X[48049] + 2 X[58177]

X(72064) lies on these lines: {100, 667}, {512, 4763}, {514, 9508}, {900, 69328}, {1635, 29188}, {3826, 6008}, {4063, 36848}, {4083, 5883}, {4705, 47763}, {4728, 47837}, {4730, 27013}, {4776, 4834}, {4777, 31010}, {6002, 28603}, {6006, 70740}, {25666, 58175}, {28209, 48003}, {29058, 45679}, {29070, 47776}, {29150, 47835}, {30595, 48171}, {31209, 58173}, {31288, 50499}, {47761, 50501}, {47767, 68836}, {47814, 58181}, {48049, 58177}, {48573, 68894}

X(72064) = midpoint of X(i) and X(j) for these {i,j}: {4063, 36848}, {4705, 47763}, {4776, 4834}, {30595, 48171}, {47761, 50501}, {47814, 58181}
X(72064) = reflection of X(i) in X(j) for these {i,j}: {4776, 65449}, {52601, 47761}


X(72065) = X(2)X(1757)∩X(31)X(765)

Barycentrics    3*a^3 + 4*a^2*b - 2*a*b^2 + 4*a^2*c - 3*a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(72065) = X[32930] - 4 X[71515]

X(72065) lies on these lines: {2, 1757}, {31, 765}, {81, 42056}, {519, 32930}, {536, 32938}, {537, 32911}, {551, 27065}, {748, 51055}, {756, 46922}, {1999, 4937}, {3241, 70742}, {3679, 6539}, {3681, 50300}, {4005, 50064}, {4418, 50127}, {4664, 61358}, {4683, 48821}, {4753, 41242}, {4756, 49489}, {5311, 63108}, {6057, 28337}, {9458, 62795}, {16669, 32927}, {16834, 32925}, {17011, 50777}, {17378, 70874}, {17781, 50091}, {27064, 31136}, {28333, 33067}, {31161, 32914}, {32772, 51034}, {32860, 49721}, {32928, 50124}, {41241, 49712}

X(72065) = {X(31161),X(68966)}-harmonic conjugate of X(32914)


X(72066) = X(6)X(1016)∩X(75)X(4675)

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

X(72066) lies on these lines: {6, 1016}, {75, 4675}, {350, 50123}, {668, 50113}, {1909, 4727}, {3241, 60861}, {3264, 29619}, {3770, 17314}, {4007, 52716}, {4033, 29588}, {4358, 17315}, {4460, 29802}, {4671, 31011}, {4889, 17787}, {5564, 24589}, {17145, 28597}, {17319, 69538}, {17388, 70809}, {17389, 17790}, {24004, 63052}, {30866, 50112}, {40875, 50125}, {49517, 71838}, {50087, 64133}


X(72067) = X(1)X(2)∩X(31)X(51055)

Barycentrics    3*a^3 - 4*a^2*b + 2*a*b^2 - 4*a^2*c - 3*a*b*c - b^2*c + 2*a*c^2 - b*c^2 : :
X(72067) = 2 X[3957] + X[32914], X[3957] + 2 X[71517], X[32914] - 4 X[71517], 2 X[3748] + X[32923]

X(72067) lies on these lines: {1, 2}, {31, 51055}, {536, 3748}, {537, 1621}, {744, 69519}, {3750, 69539}, {4418, 17715}, {4664, 62849}, {4688, 32945}, {4864, 32917}, {5284, 42056}, {10389, 17155}, {15570, 32919}, {16064, 68760}, {17469, 46922}, {24841, 70520}, {31161, 32930}, {32771, 48805}, {32844, 37703}, {32920, 62862}, {32925, 62856}, {32927, 42819}, {33112, 49696}, {33123, 48821}, {38316, 64178}, {49491, 70834}, {49746, 71798}, {50078, 51715}, {50126, 71452}, {50300, 62806}, {51035, 71794}, {60714, 70992}

X(72067) = {X(3957),X(71517)}-harmonic conjugate of X(32914)


X(72068) = X(1)X(2)∩X(55)X(42054)

Barycentrics    3*a^3 - 4*a^2*b + 2*a*b^2 - 4*a^2*c + 2*a*b*c - b^2*c + 2*a*c^2 - b*c^2 : :
X(72068) = X[6765] + 2 X[8669]

X(72068) lies on these lines: {1, 2}, {55, 42054}, {537, 4421}, {678, 32933}, {726, 3158}, {1376, 42053}, {2796, 34607}, {3689, 32920}, {3699, 17715}, {3722, 4011}, {3749, 4090}, {3971, 67066}, {4052, 54946}, {4096, 4428}, {4432, 59597}, {4434, 41711}, {8715, 49127}, {10389, 59517}, {16496, 59679}, {17063, 43290}, {17596, 71636}, {17766, 25568}, {20075, 21093}, {24165, 64135}, {28562, 28609}, {32927, 42044}, {49455, 60714}, {50127, 59676}, {62834, 71634}

X(72068) = reflection of X(i) in X(j) for these {i,j}: {34625, 49608}, {49636, 59722}
X(72068) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {200, 71520, 16825}, {3870, 70841, 29649}, {3961, 29670, 36480}


X(72069) = X(1)X(2)∩X(55)X(42055)

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

X(72069) lies on these lines: {1, 2}, {55, 42055}, {537, 4428}, {726, 10389}, {1001, 4096}, {1707, 49535}, {2796, 10385}, {3052, 49491}, {3175, 3748}, {3243, 71489}, {3475, 17766}, {3722, 3980}, {3749, 49479}, {3750, 49455}, {3923, 17715}, {3971, 62856}, {4011, 71630}, {4052, 30331}, {4421, 42053}, {4654, 28562}, {4864, 32916}, {4865, 37703}, {17469, 19738}, {17716, 42028}, {19723, 41711}, {26098, 49696}, {32923, 50106}, {32927, 62862}, {33111, 49695}, {37553, 49464}, {38316, 59517}, {41629, 49490}, {62875, 71521}

X(72069) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 29670, 29668}, {1, 71520, 29649}, {3870, 71517, 16825}, {3938, 29651, 36480}


X(72070) = X(2)X(1757)∩X(31)X(51055)

Barycentrics    3*a^3 + 4*a^2*b - 2*a*b^2 + 4*a^2*c + 3*a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(72070) = X[4418] - 4 X[71518]

X(72070) lies on these lines: {2, 1757}, {31, 51055}, {38, 46922}, {81, 537}, {354, 16482}, {519, 4418}, {536, 32940}, {551, 3219}, {894, 31136}, {3758, 54352}, {3873, 50300}, {3989, 29580}, {4644, 33120}, {4649, 69539}, {4664, 62821}, {4683, 28333}, {4688, 32864}, {4722, 68966}, {7277, 32844}, {9458, 37520}, {16834, 17155}, {17017, 63108}, {17019, 50777}, {17120, 17449}, {17154, 69632}, {17378, 71795}, {17763, 31161}, {26223, 31137}, {31178, 32914}, {32915, 49721}, {32924, 50124}, {32929, 51093}, {32930, 50127}, {32948, 62240}, {33067, 48821}, {33162, 62230}, {37633, 42056}, {42028, 42039}, {49455, 63039}, {49499, 62846}, {51035, 71793}


X(72071) = X(2)X(1757)∩X(6)X(42054)

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

X(72071) lies on these lines: {2, 1757}, {6, 42054}, {44, 29651}, {193, 69297}, {519, 4217}, {551, 41229}, {1707, 71634}, {3175, 50283}, {3751, 4011}, {3961, 71635}, {3980, 71521}, {4383, 42053}, {4663, 35652}, {4685, 50127}, {4722, 29649}, {5220, 29644}, {16669, 32920}, {17781, 50287}, {19722, 50094}, {19738, 42041}, {20464, 42042}, {23812, 38057}, {29652, 49712}, {29668, 41241}, {31161, 63060}, {32935, 42051}, {32938, 42044}, {49455, 63074}, {49685, 56082}

X(72071) = {X(3751),X(71515)}-harmonic conjugate of X(4011)


X(72072) = X(2)X(1757)∩X(6)X(42055)

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

X(72072) lies on these lines: {2, 1757}, {6, 42055}, {38, 19738}, {519, 50043}, {551, 62874}, {940, 4096}, {984, 42028}, {3175, 32935}, {3751, 3980}, {3758, 29652}, {3874, 48867}, {4011, 62819}, {4362, 41629}, {4641, 29651}, {4644, 29673}, {4697, 64070}, {4722, 16825}, {4865, 7277}, {4921, 32771}, {17120, 62865}, {19722, 29644}, {19723, 24325}, {24821, 58820}, {29649, 71630}, {29650, 62235}, {29668, 54352}, {29670, 62795}, {29820, 71635}, {32940, 49488}, {33165, 62230}, {37685, 49455}, {42045, 71795}, {42051, 50283}, {42057, 50127}, {48812, 67976}, {49520, 62808}, {49535, 62834}, {63057, 69297}

X(72072) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3751, 71518, 3980}, {62819, 71521, 4011}


X(72073) = X(2)X(1757)∩X(81)X(4096)

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

X(72073) lies on these lines: {2, 1757}, {81, 4096}, {756, 42028}, {984, 19738}, {1215, 4921}, {3175, 4663}, {3751, 32930}, {3938, 71635}, {4418, 4685}, {4722, 17763}, {5220, 19722}, {5904, 48867}, {16669, 32923}, {19723, 32771}, {20086, 69297}, {24821, 45222}, {32911, 42055}, {32914, 63060}, {32935, 50106}, {32945, 71638}, {33761, 58381}, {42041, 46922}, {42044, 50283}

X(72073) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4722, 71630, 41629}, {41629, 71630, 17763}


X(72074) = X(2)X(1757)∩X(81)X(42054)

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

X(72074) lies on these lines: {2, 1757}, {81, 42054}, {3679, 50234}, {3751, 4418}, {4644, 33117}, {4663, 32940}, {4722, 32914}, {7277, 33072}, {20068, 69632}, {20072, 29685}, {31161, 41629}, {31178, 63060}, {32911, 42053}, {32930, 42057}, {32935, 42044}, {32938, 35652}, {32943, 71638}, {42025, 50094}, {42028, 42041}, {42039, 46922}, {49455, 63095}, {50106, 50283}, {62230, 69298}


X(72075) = X(2)X(4864)∩X(75)X(200)

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

X(72075) lies on these lines: {2, 4864}, {7, 15519}, {8, 6933}, {31, 765}, {37, 71526}, {42, 17393}, {55, 17336}, {57, 43290}, {65, 70743}, {75, 200}, {100, 71793}, {145, 1997}, {190, 3158}, {210, 17335}, {312, 3935}, {319, 7172}, {341, 3811}, {344, 6555}, {518, 71529}, {612, 17394}, {1088, 65199}, {1376, 49499}, {2340, 24524}, {3685, 59597}, {3689, 32937}, {3699, 3870}, {3711, 3757}, {3759, 4849}, {3769, 70841}, {3873, 17780}, {3957, 30829}, {3961, 25496}, {3996, 42034}, {4090, 4676}, {4323, 64499}, {4421, 62222}, {4640, 71636}, {4702, 4903}, {4737, 69275}, {4899, 59584}, {4952, 29840}, {5205, 41711}, {5423, 17264}, {5524, 32920}, {6557, 12630}, {7081, 49450}, {7256, 56439}, {7322, 51488}, {9458, 62869}, {10578, 17263}, {15570, 26103}, {17122, 51055}, {17277, 62218}, {17329, 44419}, {17596, 49501}, {17597, 31233}, {17716, 71634}, {18134, 49991}, {20015, 28808}, {20937, 32926}, {20942, 66469}, {24477, 49714}, {25306, 61166}, {25568, 32850}, {30318, 40420}, {32916, 50075}, {32939, 64135}, {33116, 63168}, {34772, 44720}, {36845, 37758}, {42033, 53661}, {48696, 69493}, {49447, 60714}, {49465, 59298}, {49503, 59679}, {49536, 59593}, {56084, 64146}, {62822, 67343}, {65020, 66063}, {71451, 71630}, {71477, 71639}

X(72075) = barycentric product X(i)*X(j) for these {i,j}: {765, 26572}, {36639, 67038}
X(72075) = barycentric quotient X(i)/X(j) for these {i,j}: {26572, 1111}, {36639, 2170}
X(72075) = {X(3699),X(3870)}-harmonic conjugate of X(18743)


X(72076) = X(1)X(312)∩X(2)X(4864)

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

X(72076) lies on these lines: {1, 312}, {2, 4864}, {8, 50393}, {31, 51055}, {75, 3957}, {190, 62856}, {333, 3243}, {968, 24841}, {1233, 64133}, {1621, 49499}, {3263, 17394}, {3475, 4514}, {3699, 10582}, {3705, 37703}, {3748, 24349}, {3757, 42871}, {3758, 62806}, {3769, 62867}, {3870, 19804}, {4441, 17393}, {4661, 17335}, {4664, 71794}, {4666, 30829}, {4851, 70456}, {5423, 38314}, {7262, 49535}, {7321, 20075}, {8616, 49491}, {10389, 32939}, {10453, 15570}, {10578, 32851}, {14829, 62815}, {16823, 41711}, {17165, 62862}, {17241, 33091}, {17317, 20020}, {17715, 49479}, {17724, 29843}, {17774, 58463}, {18134, 49466}, {18743, 29817}, {20045, 62866}, {24477, 30608}, {25557, 63139}, {26227, 62863}, {29651, 49675}, {32923, 49470}, {32937, 42819}, {33124, 36479}, {34860, 37573}, {42029, 68969}, {44720, 54392}, {49447, 62849}, {49490, 71517}, {51099, 63140}, {62229, 63977}

X(72076) = {X(32923),X(67209)}-harmonic conjugate of X(49470)


X(72077) = X(1)X(4487)∩X(2)X(4864)

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

X(72077) lies on these lines: {1, 4487}, {2, 4864}, {8, 6856}, {42, 17793}, {81, 7256}, {200, 4359}, {321, 3935}, {354, 17780}, {518, 71479}, {3158, 32933}, {3623, 6552}, {3681, 71476}, {3689, 17165}, {3699, 3957}, {3722, 4090}, {3744, 41241}, {3811, 4696}, {3870, 4358}, {3873, 71529}, {3896, 32927}, {3930, 71492}, {3938, 70942}, {3961, 32772}, {4042, 26227}, {4421, 71793}, {4430, 24593}, {4849, 20045}, {4861, 4935}, {4942, 32929}, {4952, 29832}, {4981, 29670}, {5014, 25568}, {5425, 67343}, {5524, 32923}, {7081, 62236}, {9776, 15519}, {17150, 21870}, {17264, 53660}, {17469, 71634}, {18139, 49991}, {21805, 71520}, {27003, 43290}, {31161, 71450}, {33113, 63168}, {49482, 71637}, {49694, 61648}, {50748, 69298}, {51583, 59584}, {59181, 65199}, {63159, 68245}

X(72077) = reflection of X(71479) in X(71639)


X(72078) = X(1)X(996)∩X(2)X(4864)

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

X(72078) lies on these lines: {1, 996}, {2, 4864}, {8, 36867}, {145, 30588}, {321, 3957}, {518, 71478}, {896, 49535}, {902, 49491}, {1150, 3243}, {1155, 17146}, {1279, 41241}, {1441, 37736}, {1621, 62222}, {3006, 37703}, {3475, 5014}, {3722, 49479}, {3748, 17165}, {3870, 4359}, {3873, 71477}, {3896, 3979}, {3935, 24589}, {3936, 49466}, {3938, 50302}, {3952, 42819}, {4428, 71793}, {4487, 54318}, {4689, 17154}, {4879, 35353}, {4981, 29651}, {7081, 62863}, {7321, 20095}, {10389, 32933}, {10578, 33113}, {15570, 29824}, {16823, 62236}, {17051, 37762}, {17126, 51055}, {17450, 70841}, {17724, 29835}, {20045, 49478}, {20905, 63161}, {21806, 49464}, {21870, 68958}, {24542, 49529}, {24594, 46917}, {26227, 42871}, {29670, 62869}, {29822, 49465}, {29830, 49688}, {31025, 49467}, {31161, 71414}, {31178, 71451}, {32920, 67209}, {32937, 62862}, {33112, 49695}, {33122, 36479}, {41711, 70316}, {46909, 49675}, {49499, 61155}, {49700, 61707}, {50305, 70970}, {58560, 71639}, {62867, 71520}

X(72078) = {X(3979),X(32923)}-harmonic conjugate of X(3896)


X(72079) = X(1)X(1120)∩X(2)X(4864)

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

X(72079) lies on these lines: {1, 1120}, {2, 4864}, {8, 17718}, {55, 62222}, {75, 3935}, {85, 65199}, {100, 49499}, {145, 17721}, {200, 19804}, {312, 3870}, {354, 71529}, {518, 71477}, {519, 17717}, {750, 51055}, {1155, 71636}, {2177, 49447}, {3158, 32939}, {3306, 43290}, {3315, 31233}, {3681, 71478}, {3689, 24349}, {3711, 16823}, {3722, 4676}, {3748, 27538}, {3758, 42720}, {3759, 20045}, {3812, 70743}, {3938, 32944}, {3957, 18743}, {3961, 50302}, {3996, 42029}, {4023, 50310}, {4090, 17715}, {4126, 63287}, {4414, 49501}, {4434, 49498}, {4514, 25568}, {4689, 31302}, {4851, 70452}, {5205, 42871}, {5233, 49466}, {5774, 68889}, {7081, 41711}, {10584, 65020}, {15570, 30947}, {15934, 68245}, {17233, 50744}, {17234, 49991}, {17241, 60459}, {17264, 53661}, {17336, 61155}, {17386, 50000}, {17387, 62668}, {17780, 64149}, {20058, 26738}, {25439, 69493}, {26227, 49450}, {29675, 49693}, {29839, 30615}, {30608, 49714}, {31161, 71451}, {32851, 63168}, {32917, 50075}, {32927, 49470}, {33165, 50748}, {42042, 70713}, {49490, 70841}, {49491, 56010}, {71452, 71630}

X(72079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3699, 30829}, {26227, 62236, 49450}, {32927, 67207, 49470}


X(72080) = X(1)X(341)∩X(2)X(4864)

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

X(72080) lies on these lines: {1, 341}, {2, 4864}, {8, 44840}, {42, 31005}, {55, 49499}, {75, 3870}, {171, 51055}, {190, 10389}, {312, 3957}, {350, 17018}, {354, 71639}, {518, 71476}, {519, 33111}, {846, 49501}, {1621, 17336}, {3243, 14829}, {3475, 32850}, {3550, 49491}, {3622, 6555}, {3681, 17335}, {3685, 4942}, {3699, 4666}, {3742, 71529}, {3744, 3758}, {3748, 32937}, {3750, 49447}, {3755, 19830}, {3757, 4042}, {3769, 49490}, {3873, 71479}, {3920, 17394}, {3935, 19804}, {3938, 32772}, {3952, 62862}, {3979, 32920}, {4417, 49466}, {4428, 62222}, {4650, 49535}, {4676, 17715}, {4851, 20056}, {4906, 59298}, {5437, 43290}, {7081, 42871}, {7321, 17784}, {8236, 56084}, {9352, 17146}, {10327, 17241}, {10578, 33116}, {10580, 37758}, {17319, 69866}, {17361, 63134}, {17379, 40883}, {17594, 24841}, {26098, 49695}, {27538, 42819}, {29641, 37703}, {29670, 49675}, {29817, 30829}, {29838, 65969}, {29839, 49688}, {31161, 71452}, {31178, 71450}, {32923, 67207}, {32927, 67209}, {33126, 36479}, {33169, 50748}, {37736, 69765}, {42034, 68969}, {42697, 64146}, {49451, 55095}, {49465, 59297}, {51058, 71492}

X(72080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3757, 41711, 49450}, {3979, 32920, 49470}, {49490, 71520, 3769}


X(72081) = X(31)X(765)∩X(42)X(17336)

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

X(72081) lies on these lines: {31, 765}, {42, 17336}, {210, 3758}, {518, 70485}, {756, 17394}, {1757, 32916}, {1992, 5423}, {3715, 4687}, {3751, 18743}, {3759, 32937}, {3769, 4090}, {3974, 62231}, {4082, 17377}, {4104, 19827}, {4383, 49499}, {4661, 41241}, {4663, 27538}, {4676, 71515}, {4849, 17350}, {7262, 71634}, {7322, 46922}, {15481, 59297}, {17123, 51055}, {17346, 53663}, {17351, 59295}, {17393, 61358}, {25496, 50075}, {27064, 49450}, {29821, 49501}, {32911, 71794}, {37683, 59596}, {50077, 69089}


X(72082) = X(8)X(19833)∩X(31)X(51055)

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

X(72082) lies on these lines: {8, 19833}, {31, 51055}, {81, 49499}, {312, 62819}, {354, 70485}, {518, 70484}, {3751, 19804}, {3758, 3873}, {3759, 17140}, {4514, 4644}, {4664, 71793}, {4676, 62867}, {4697, 49498}, {4883, 17350}, {4981, 41847}, {5311, 49501}, {7174, 42028}, {7226, 17394}, {17120, 17597}, {17241, 33166}, {17336, 29814}, {17361, 29667}, {17378, 63147}, {17387, 32862}, {17716, 49535}, {19717, 62868}, {20068, 62801}, {24841, 62845}, {28582, 58820}, {31233, 65112}, {31302, 37595}, {32913, 32916}, {32932, 64165}, {32939, 68588}, {32940, 49470}, {46922, 62833}, {49447, 62821}, {49490, 71518}, {49491, 62841}, {62844, 69493}


X(72083) = X(6)X(69505)∩X(518)X(41241)

Barycentrics    2*a^3 + 4*a^2*b - 2*a*b^2 + 4*a^2*c - 2*a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(72083) = 3 X[41241] - 2 X[70483]

X(72083) lies on these lines: {6, 69505}, {518, 41241}, {896, 71634}, {1757, 32917}, {1992, 53661}, {3578, 53663}, {3616, 18490}, {3629, 50000}, {3681, 70419}, {3751, 4358}, {3896, 32938}, {3952, 4663}, {3994, 49685}, {4090, 4722}, {4427, 21870}, {5739, 5772}, {14997, 49499}, {15481, 29822}, {16669, 20045}, {17025, 49501}, {17351, 19998}, {17365, 71102}, {21805, 71521}, {37639, 59596}, {46909, 49712}, {49693, 61707}, {62222, 69539}, {71414, 71515}, {71489, 71637}


X(72084) = X(354)X(41241)∩X(518)X(70482)

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

X(72084) lies on these lines: {354, 41241}, {518, 70482}, {1100, 20068}, {2308, 49491}, {3751, 4359}, {3758, 4430}, {3873, 70481}, {3896, 32940}, {4358, 62819}, {4644, 5014}, {4663, 17140}, {4722, 49479}, {8025, 49515}, {17120, 62814}, {17127, 51055}, {17350, 62866}, {17450, 71515}, {17469, 49535}, {17771, 29685}, {19738, 62833}, {31302, 62801}, {32913, 32918}, {32929, 64165}, {32933, 68588}, {33091, 62230}, {37685, 49499}, {42045, 63147}, {49490, 71452}, {62867, 71521}, {71450, 71518}


X(72085) = X(312)X(3751)∩X(518)X(70481)

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

X(72085) lies on these lines: {312, 3751}, {518, 70481}, {748, 51055}, {3681, 3758}, {3699, 62812}, {3744, 71635}, {3759, 17165}, {3769, 4722}, {3996, 50127}, {4388, 47359}, {4430, 41241}, {4650, 71634}, {4663, 32937}, {4676, 71452}, {7322, 42028}, {10180, 51297}, {17017, 49501}, {17018, 17336}, {17351, 20012}, {17360, 69296}, {17361, 29679}, {17386, 69301}, {26223, 49450}, {27064, 64070}, {30829, 62819}, {32772, 50075}, {32911, 49499}, {32912, 32918}, {32938, 49470}, {33066, 59406}, {37684, 59596}, {44720, 54421}, {49447, 61358}, {49478, 70742}, {49490, 71515}, {71450, 71521}


X(72086) = X(1)X(17336)∩X(6)X(49499)

Barycentrics    2*a^3 + 4*a^2*b - 2*a*b^2 + 4*a^2*c + a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(72086) = 5 X[3758] - 2 X[36534], 3 X[3758] - 2 X[70419], 3 X[36534] - 5 X[70419]

X(72086) lies on these lines: {1, 17336}, {6, 49499}, {8, 11008}, {10, 17361}, {69, 5772}, {75, 3751}, {86, 5223}, {145, 17351}, {190, 68588}, {238, 51055}, {320, 59406}, {518, 3758}, {537, 70681}, {894, 49450}, {984, 17394}, {1100, 31302}, {1279, 71635}, {1698, 48638}, {1757, 17335}, {3242, 17120}, {3616, 15481}, {3618, 38046}, {3622, 16814}, {3685, 64165}, {3717, 17378}, {3759, 4663}, {3790, 17386}, {3873, 70483}, {3932, 17387}, {4026, 17329}, {4307, 49698}, {4356, 49748}, {4389, 5850}, {4393, 28582}, {4644, 32850}, {4645, 47359}, {4649, 17393}, {4664, 62222}, {4667, 4899}, {4672, 49498}, {4676, 49490}, {4684, 17354}, {4687, 5220}, {4751, 60731}, {4764, 49486}, {4860, 31233}, {4883, 70742}, {4966, 17342}, {5542, 17352}, {7174, 46922}, {7277, 50289}, {10327, 62230}, {16468, 49491}, {16474, 69493}, {16475, 24841}, {17227, 38047}, {17317, 27549}, {17350, 49478}, {17360, 34379}, {17364, 49524}, {17371, 49511}, {17379, 49515}, {17771, 29659}, {18743, 62819}, {20050, 49485}, {24821, 50281}, {27191, 59372}, {29617, 51124}, {32912, 32917}, {32935, 49470}, {33682, 49503}, {41847, 49712}, {49489, 49532}, {49493, 49685}, {49695, 50303}, {49697, 50301}, {49714, 68589}, {50075, 50302}, {50127, 68969}, {70461, 70610}

X(72086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {894, 64070, 49450}, {4649, 49447, 17393}, {4663, 24349, 3759}, {49490, 71521, 4676}


X(72087) = X(1)X(64436)∩X(31)X(765)

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

X(72087) lies on these lines: {1, 64436}, {2, 49697}, {31, 765}, {42, 17319}, {43, 71794}, {200, 4418}, {210, 57024}, {3681, 32916}, {3689, 32938}, {3711, 32771}, {3873, 9458}, {3920, 71634}, {3935, 4090}, {3938, 70485}, {3996, 71630}, {4849, 32927}, {5263, 71637}, {5524, 17165}, {6541, 53660}, {9342, 49491}, {9350, 49499}, {17336, 17782}, {17780, 32913}, {21060, 32947}, {21805, 32914}, {21870, 32928}, {24165, 54309}, {25568, 33117}, {26037, 55076}, {27538, 67207}, {32912, 71529}, {32915, 59597}, {32943, 59596}, {32949, 49991}, {49996, 62998}, {59511, 62236}, {66469, 71452}

X(72087) = {X(3935),X(4090)}-harmonic conjugate of X(32930)


X(72088) = X(1)X(3159)∩X(2)X(49697)

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

X(72088) lies on these lines: {1, 3159}, {2, 49697}, {31, 51055}, {1215, 62863}, {1621, 49491}, {1962, 24841}, {3219, 49535}, {3243, 31330}, {3244, 23812}, {3475, 33120}, {3742, 9458}, {3748, 32940}, {3873, 32916}, {3938, 70484}, {3957, 4418}, {3979, 17140}, {4430, 29651}, {4661, 24331}, {4864, 32772}, {4883, 32927}, {5542, 32948}, {15570, 32943}, {17146, 17596}, {17763, 62867}, {24349, 67209}, {25531, 71637}, {26034, 51099}, {29688, 58371}, {29851, 49529}, {29853, 59406}, {30942, 62815}, {30957, 44841}, {32771, 42871}, {32914, 49490}, {32920, 62866}, {32923, 49478}, {32935, 62862}, {32938, 42819}, {32949, 49466}, {33069, 36479}, {33119, 37703}, {49499, 62849}, {49704, 64164}, {49746, 71797}

X(72088) = {X(3957),X(49479)}-harmonic conjugate of X(4418)


X(72089) = X(1)X(56150)∩X(2)X(49697)

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

X(72089) lies on these lines: {1, 56150}, {2, 49697}, {6, 71786}, {8, 25385}, {10, 11520}, {200, 3980}, {210, 29651}, {3240, 49455}, {3243, 4871}, {3306, 49535}, {3681, 29670}, {3689, 32935}, {3699, 49490}, {3711, 24325}, {3749, 71515}, {3751, 70841}, {3870, 4011}, {3875, 4946}, {3923, 3935}, {3938, 70483}, {3952, 67207}, {3961, 70419}, {3979, 27538}, {4104, 29669}, {4413, 49491}, {4434, 64070}, {4849, 32920}, {4892, 71327}, {5205, 49498}, {5524, 24349}, {6541, 53661}, {6686, 62850}, {6745, 49536}, {16825, 21805}, {17593, 49501}, {17717, 49698}, {17718, 49693}, {21870, 32921}, {24003, 42871}, {24331, 63961}, {24552, 71637}, {25568, 29673}, {29676, 49707}, {29828, 49510}, {31034, 49996}, {32913, 71529}, {32927, 49488}, {32931, 49458}, {36480, 46897}, {37660, 49449}, {41711, 59511}, {49479, 67097}, {49499, 56009}

X(72089) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3870, 4090, 4011}, {32931, 62236, 49458}


X(72090) = X(1)X(979)∩X(2)X(49697)

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

X(72090) lies on these lines: {1, 979}, {2, 49697}, {10, 50393}, {55, 49491}, {63, 49535}, {171, 51055}, {518, 29651}, {1215, 42871}, {3242, 29644}, {3243, 3741}, {3475, 29673}, {3681, 24331}, {3748, 32935}, {3749, 71518}, {3750, 49499}, {3751, 71517}, {3757, 49498}, {3791, 64165}, {3840, 62815}, {3870, 3980}, {3873, 29670}, {3923, 3957}, {3938, 70482}, {3979, 24349}, {3996, 31178}, {4090, 4666}, {4362, 49490}, {4438, 37703}, {4864, 25496}, {4871, 44841}, {5272, 71634}, {6685, 62850}, {16496, 43223}, {17018, 24259}, {17140, 67207}, {17165, 67209}, {17592, 24841}, {19732, 49449}, {23812, 68589}, {24325, 41711}, {25385, 36845}, {29642, 49529}, {29649, 62867}, {29650, 62814}, {29652, 49675}, {29668, 46897}, {29669, 49511}, {29672, 59406}, {32771, 49458}, {32920, 49478}, {32923, 49488}, {32927, 62866}, {32931, 62863}, {32938, 62862}, {32946, 49466}, {33064, 36479}, {49451, 62226}, {62819, 71520}

X(72090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3870, 49479, 3980}, {46897, 62869, 29668}


X(72091) = X(1)X(26688)∩X(2)X(49697)

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

X(72091) lies on these lines: {1, 26688}, {2, 49697}, {42, 17794}, {354, 9458}, {518, 32918}, {519, 33107}, {1215, 62236}, {3243, 30957}, {3689, 32940}, {3699, 62867}, {3870, 32930}, {3935, 4418}, {3938, 70481}, {3952, 3979}, {3957, 4090}, {3961, 70482}, {3996, 31161}, {4661, 29670}, {4849, 32923}, {5524, 17140}, {7191, 71634}, {17124, 51055}, {17778, 49996}, {21870, 32924}, {24003, 62863}, {25568, 33120}, {27003, 49535}, {27538, 67209}, {29690, 49707}, {29846, 49529}, {29848, 59406}, {32931, 41711}, {32937, 67207}, {32942, 71637}, {33105, 49698}, {33166, 50748}, {42042, 70720}, {42043, 71794}, {66469, 71451}, {67066, 68588}, {68969, 71630}


X(72092) = X(1)X(3952)∩X(2)X(49697)

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

X(72092) lies on these lines: {1, 3952}, {2, 49697}, {8, 21027}, {100, 49491}, {518, 32917}, {519, 33112}, {750, 51055}, {1054, 17146}, {2177, 49499}, {3218, 49535}, {3243, 30942}, {3475, 33117}, {3699, 17450}, {3748, 32938}, {3870, 4418}, {3935, 49479}, {3938, 70419}, {3957, 32930}, {3979, 17165}, {4090, 29817}, {4430, 29670}, {4661, 29651}, {4864, 32944}, {5235, 49449}, {5772, 33171}, {7292, 71634}, {9458, 64149}, {17117, 49983}, {17300, 49996}, {17763, 49490}, {24325, 62236}, {24349, 67207}, {24841, 46904}, {26227, 49498}, {29632, 49529}, {29638, 59406}, {30957, 62815}, {31161, 68969}, {31314, 68875}, {32771, 41711}, {32843, 49466}, {32927, 49478}, {32931, 42871}, {32937, 67209}, {33065, 36479}, {33115, 37703}, {33170, 50748}, {42042, 71794}, {46897, 49675}, {49704, 61707}, {49771, 61652}, {59511, 62863}


X(72093) = X(31)X(765)∩X(42)X(17261)

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

X(72093) lies on these lines: {31, 765}, {42, 17261}, {43, 71793}, {210, 4670}, {333, 71637}, {756, 24437}, {3219, 71634}, {3681, 25496}, {3699, 4722}, {3935, 71515}, {4090, 17763}, {4134, 60684}, {4418, 21805}, {4547, 25526}, {4849, 32938}, {8013, 63885}, {9340, 43290}, {9458, 32913}, {16670, 67066}, {17779, 20068}, {20086, 49994}, {21060, 29631}, {21870, 32936}, {25960, 47359}, {26688, 49498}, {32919, 59596}, {33107, 49697}, {37687, 49491}, {50016, 71117}, {67207, 70742}


X(72094) = X(1)X(20068)∩X(42)X(62300)

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

X(72094) lies on these lines: {1, 20068}, {31, 51055}, {42, 62300}, {81, 49491}, {3758, 62869}, {3873, 25496}, {3894, 60684}, {3920, 49535}, {3957, 71518}, {4418, 49490}, {4672, 62863}, {4883, 32938}, {5542, 29850}, {11038, 29853}, {17120, 29818}, {17146, 29821}, {17155, 68588}, {17378, 71796}, {17763, 62819}, {25961, 47359}, {29817, 71521}, {32860, 64165}, {32914, 49479}, {32930, 62867}, {32935, 62866}, {32940, 49478}, {49499, 62821}


X(72095) = X(43)X(62300)∩X(63)X(716234)

Barycentrics    a^3 + 4*a^2*b - 2*a*b^2 + 4*a^2*c - 2*a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(72095) = 3 X[29668] - 4 X[70942]

X(72095) lies on these lines: {43, 62300}, {63, 71634}, {200, 71521}, {518, 29668}, {740, 4942}, {1150, 71637}, {1215, 4042}, {1743, 71520}, {1757, 29670}, {3244, 30568}, {3681, 32772}, {3711, 4697}, {3751, 4090}, {3846, 47359}, {3870, 71515}, {3923, 3996}, {3967, 49497}, {3974, 71333}, {3979, 70742}, {3980, 21805}, {4135, 49495}, {4641, 71639}, {4661, 29652}, {4734, 24821}, {4759, 10389}, {4849, 32935}, {5223, 6685}, {5272, 49535}, {6686, 62823}, {21060, 29635}, {21870, 32934}, {26098, 49697}, {27064, 49458}, {29650, 49448}, {29842, 59408}, {29844, 49536}, {32912, 71479}, {32937, 49488}, {37679, 49491}, {42043, 62222}, {50127, 71450}, {59406, 69299}, {59511, 64070}, {59517, 68588}, {67097, 71518}, {69218, 71492}

X(72095) = {X(3751),X(4090)}-harmonic conjugate of X(29649)


X(72096) = X(1)X(4704)∩X(6)X(49491)

Barycentrics    a^3 + 4*a^2*b - 2*a*b^2 + 4*a^2*c + 2*a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(72096) = 8 X[4670] - 5 X[36480], 6 X[4670] - 5 X[50302], 3 X[36480] - 4 X[50302]

X(72096) lies on these lines: {1, 4704}, {6, 49491}, {10, 3620}, {86, 49503}, {238, 51055}, {518, 4670}, {519, 4307}, {726, 68588}, {740, 64165}, {894, 49458}, {1125, 5223}, {1449, 49464}, {1757, 24331}, {3243, 49482}, {3244, 3729}, {3306, 71634}, {3622, 51294}, {3626, 25590}, {3632, 17116}, {3636, 3731}, {3664, 49536}, {3751, 16825}, {3758, 49675}, {3836, 47359}, {3870, 71518}, {3873, 29668}, {3923, 49490}, {4001, 29669}, {4011, 62867}, {4430, 29652}, {4644, 17766}, {4649, 49455}, {4666, 71515}, {4672, 42871}, {4675, 49693}, {4697, 41711}, {4759, 38316}, {4864, 50300}, {4966, 50313}, {5686, 25352}, {6685, 62823}, {6686, 10980}, {10436, 49510}, {15570, 71638}, {16496, 33682}, {17154, 67211}, {17770, 36479}, {20057, 25269}, {20068, 67208}, {24231, 50287}, {24325, 64070}, {24349, 49488}, {28582, 50281}, {29649, 62819}, {29650, 62865}, {29651, 32912}, {29670, 32913}, {32935, 49478}, {32938, 62866}, {42045, 71796}, {46897, 54352}, {49483, 49497}, {49495, 50117}, {49676, 59406}, {49689, 68999}, {49696, 50303}, {49698, 50301}, {50127, 71414}, {60723, 62825}, {62812, 71520}

X(72096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {894, 49498, 49458}, {3751, 49479, 16825}, {4649, 49499, 49455}


X(72097) = X(6)X(71790)∩X(8)X(61707)

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

X(72097) lies on these lines: {6, 71790}, {8, 61707}, {42, 62222}, {518, 32944}, {1757, 71478}, {3218, 71634}, {3681, 50302}, {3751, 17763}, {3935, 71521}, {3957, 71515}, {4663, 32927}, {4672, 62236}, {4756, 49471}, {4849, 32940}, {4899, 61652}, {7292, 49535}, {14829, 71637}, {17125, 51055}, {17154, 17779}, {17350, 67207}, {21060, 29845}, {21870, 32845}, {24821, 64161}, {25760, 47359}, {29834, 59408}, {31302, 67211}, {32843, 49529}, {32912, 71477}, {32930, 68969}, {32931, 64070}, {33065, 59406}, {33112, 49697}, {37680, 49491}, {41241, 49675}, {42043, 71793}, {46897, 49712}, {50127, 71451}, {64178, 68588}, {67209, 70742}


X(72098) = X(1)X(19743)∩X(8)X(64164)

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

X(72098) lies on these lines: {1, 19743}, {8, 64164}, {518, 32772}, {748, 51055}, {3751, 32914}, {3873, 70942}, {3935, 71518}, {3957, 71521}, {3996, 4418}, {4042, 32771}, {4663, 32923}, {4697, 62236}, {4942, 32915}, {7191, 49535}, {17120, 67210}, {17350, 67209}, {19684, 49503}, {24821, 27804}, {24841, 71184}, {25957, 47359}, {26223, 49498}, {27003, 71634}, {29817, 71515}, {31302, 67208}, {32911, 49491}, {32912, 71476}, {32913, 71479}, {32925, 68588}, {32930, 49490}, {32938, 49478}, {32949, 49529}, {33069, 59406}, {42042, 71793}, {49499, 61358}, {50127, 71452}


X(72099) = X(11)X(244)∩X(75)X(1577)

Barycentrics    (b - c)*(a^3*b - 2*a*b^3 + a^3*c - 2*a^2*b*c + a*b^2*c + b^3*c + a*b*c^2 - 2*a*c^3 + b*c^3) : :
X(72099) = 2 X[68956] + X[71091]

X(72099) lies on these lines: {11, 244}, {75, 1577}, {86, 1019}, {513, 41311}, {514, 4357}, {661, 4364}, {876, 48350}, {903, 45665}, {4369, 17305}, {4389, 4444}, {5241, 47784}, {17237, 55244}, {17320, 40459}, {21124, 21131}, {21143, 48131}, {21192, 21200}, {21211, 69359}, {27081, 46915}, {41312, 68829}, {46894, 70818}, {52745, 69535}, {67625, 68376}, {68956, 71091}

X(72099) = X(i)-isoconjugate of X(j) for these (i,j): {100, 35107}, {692, 35155}
X(72099) = X(i)-Dao conjugate of X(j) for these (i,j): {1086, 35155}, {8054, 35107}, {35089, 190}
X(72099) = crossdifference of every pair of points on line {101, 922}
X(72099) = barycentric product X(i)*X(j) for these {i,j}: {514, 35103}, {693, 68887}, {3261, 5163}, {4750, 46799}
X(72099) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 35155}, {649, 35107}, {5163, 101}, {35103, 190}, {68887, 100}
X(72099) = {X(17237),X(55244)}-harmonic conjugate of X(71771)


X(72100) = X(1)X(4760)∩X(2)X(3721)

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

X(72100) lies on these lines: {1, 4760}, {2, 3721}, {8, 24699}, {65, 536}, {192, 65695}, {524, 3868}, {537, 24404}, {599, 20911}, {712, 5902}, {1992, 21216}, {2176, 70993}, {2292, 41312}, {2295, 4664}, {3726, 24282}, {3873, 35101}, {3894, 8682}, {3959, 17141}, {4465, 69493}, {4740, 21281}, {4950, 33865}, {5969, 33890}, {16834, 54382}, {17137, 51051}, {20590, 71795}, {21808, 41313}, {21937, 69239}, {30136, 71512}, {30139, 71513}, {49533, 69028}, {67977, 68890}, {68769, 69539}, {69247, 71437}


X(72101) = X(1)X(4760)∩X(65)X(712)

Barycentrics    a^3*b - 2*a*b^3 + a^3*c + a*b^2*c + b^3*c + a*b*c^2 - 2*a*c^3 + b*c^3 : :
X(72101) = 3 X[5883] - 2 X[59515]

X(72101) lies on these lines: {1, 4760}, {65, 712}, {536, 50193}, {742, 4084}, {3721, 24254}, {3754, 71642}, {3868, 8682}, {3874, 35101}, {3905, 69234}, {4950, 33866}, {5883, 59515}, {5903, 68890}, {16822, 36283}, {17141, 69244}, {17760, 69247}, {24166, 71086}, {29691, 71790}, {30136, 71510}, {30139, 71509}, {68897, 71503}, {69249, 71436}

X(72101) = reflection of X(71642) in X(3754)


X(72102) = X(8)X(144)∩X(32)X(35103)

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

X(72102) lies on these lines: {8, 144}, {32, 35103}, {40, 17760}, {194, 1046}, {257, 3923}, {484, 71438}, {519, 20065}, {712, 69232}, {758, 71523}, {1697, 49528}, {2802, 71803}, {3125, 71778}, {3212, 17738}, {3496, 16822}, {4393, 62812}, {4674, 71775}, {5119, 71436}, {5903, 33952}, {7774, 49609}, {11010, 71437}, {15903, 16925}, {17733, 66152}, {29649, 71501}, {30124, 33870}, {32985, 49549}, {35101, 69235}, {37567, 70090}, {53332, 69242}

X(72102) = {X(3496),X(24282)}-harmonic conjugate of X(16822)


X(72103) = X(40)X(71436)∩X(46)X(17760)

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

X(72103) lies on these lines: {40, 71436}, {46, 17760}, {484, 71437}, {712, 69234}, {1046, 21216}, {1759, 16822}, {2093, 3729}, {2242, 35103}, {3125, 71780}, {3336, 71438}, {3509, 24282}, {3754, 71643}, {3874, 71523}, {4362, 66152}, {5119, 49528}, {5902, 33952}, {5903, 66147}, {17141, 69240}, {17497, 32912}, {24254, 36283}, {24628, 71073}, {29649, 71427}, {30119, 33870}, {30124, 33868}, {33866, 63817}, {36279, 70090}


X(72104) = X(1)X(24282)∩X(315)X(519)

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

X(72104) lies on these lines: {1, 24282}, {32, 35103}, {145, 33867}, {315, 519}, {517, 3905}, {758, 71522}, {2802, 71804}, {3125, 71779}, {3241, 68909}, {3735, 16822}, {3754, 71808}, {3875, 7982}, {3879, 12559}, {3924, 53332}, {4360, 66650}, {4561, 24440}, {4674, 71776}, {7763, 15903}, {9620, 17760}, {20535, 50029}, {29649, 71506}, {30136, 71427}, {30144, 57029}, {34511, 49549}, {69240, 71046}

X(72104) = {X(15903),X(49609)}-harmonic conjugate of X(7763)


X(72105) = X(1)X(24282)∩X(7)X(50010)

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

X(72205) lies on these lines: {1, 24282}, {7, 50010}, {335, 24249}, {942, 3905}, {3754, 71804}, {3875, 11529}, {3881, 71522}, {3924, 17141}, {4360, 66640}, {4561, 17063}, {5883, 71644}, {9620, 49528}, {17760, 69224}, {22836, 24166}, {24291, 24349}, {26234, 49454}, {29649, 71508}, {30139, 71500}, {30143, 69856}, {49521, 54318}, {58565, 71808}, {60683, 64133}


X(72106) = X(1)X(24282)∩X(7)X(145)

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

X(72106) lies on these lines: {1, 24282}, {7, 145}, {65, 3905}, {2241, 35103}, {3125, 71781}, {3721, 16822}, {3754, 71644}, {3874, 71522}, {4051, 32029}, {4360, 66646}, {4561, 24174}, {4658, 17103}, {5883, 71808}, {9620, 71436}, {11533, 17321}, {17141, 49487}, {17143, 33930}, {17753, 50010}, {19860, 49521}, {20911, 49454}, {22836, 57029}, {24166, 30144}, {24333, 33890}, {28082, 53332}, {29649, 71504}, {30136, 71500}, {30139, 71427}, {30147, 69856}, {37549, 59509}, {69242, 71046}


X(72107) = X(10)X(762)∩X(172)X(519)

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

X(72107) lies on these lines: {1, 71089}, {8, 3509}, {10, 762}, {65, 4071}, {172, 519}, {226, 69594}, {518, 4167}, {712, 24211}, {758, 4109}, {910, 4168}, {1215, 21965}, {1400, 2321}, {2276, 49609}, {3686, 5279}, {3727, 29655}, {3754, 71008}, {3868, 4165}, {3959, 29673}, {3985, 21049}, {4084, 4153}, {4095, 40663}, {4119, 5836}, {4659, 17950}, {4987, 7270}, {5257, 27714}, {5883, 71809}, {16549, 49781}, {17164, 21029}, {17760, 24318}, {20352, 53129}, {20461, 21024}, {21025, 69297}, {21044, 56318}, {22021, 38408}, {23942, 48642}, {24240, 69256}, {26532, 70095}, {35103, 69260}, {36500, 69240}, {49688, 70946}, {50582, 70461}, {59512, 71840}, {69038, 71436}

X(72107) = {X(65),X(4136)}-harmonic conjugate of X(4071)


X(72108) = X(1)X(7)∩X(10)X(17211)

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

X(72108) lies on these lines: {1, 7}, {10, 17211}, {11, 24240}, {36, 15903}, {65, 4920}, {226, 68478}, {244, 69035}, {519, 20553}, {527, 5291}, {712, 4071}, {758, 65116}, {946, 24172}, {986, 33949}, {1086, 68995}, {1269, 17762}, {1738, 69575}, {1959, 53590}, {3120, 69699}, {3661, 4054}, {3676, 28478}, {3754, 71812}, {3912, 71427}, {4109, 70968}, {5074, 71840}, {5883, 71810}, {5902, 24241}, {6381, 18066}, {6549, 49764}, {11813, 21208}, {14210, 49676}, {17205, 70810}, {20911, 56949}, {24318, 69247}, {30806, 32856}, {33064, 33936}, {35103, 69174}, {40690, 71843}, {53600, 57015}, {57029, 71085}

X(72108) = reflection of X(71089) in X(69174)
X(72108) = {X(65),X(4920)}-harmonic conjugate of X(24211)


X(72109) = X(100)X(667)∩X(514)X(661)

Barycentrics    (b - c)*(-2*a^3*b + 4*a^2*b^2 - 2*a*b^3 - 2*a^3*c + 3*a^2*b*c - 3*a*b^2*c + b^3*c + 4*a^2*c^2 - 3*a*b*c^2 + b^2*c^2 - 2*a*c^3 + b*c^3) : :
X(72109) = 2 X[239] - 5 X[31209], X[693] - 4 X[3912], X[4391] - 4 X[70732], X[47666] + 2 X[71771], 2 X[650] + X[6542], 2 X[14321] + X[24133], 2 X[17310] + X[31150], X[20016] - 7 X[27115], 5 X[29590] - 8 X[31287], 2 X[32847] + X[47729], X[40891] - 4 X[44567]

X(72109) lies on these lines: {100, 667}, {239, 31209}, {513, 17264}, {514, 661}, {650, 6542}, {1635, 70727}, {1643, 17389}, {3797, 28898}, {3799, 9320}, {4147, 26015}, {4562, 42722}, {4664, 69535}, {4763, 5029}, {5098, 27486}, {6008, 20533}, {6544, 71753}, {8661, 50355}, {9260, 29824}, {14321, 24133}, {17230, 62552}, {17294, 68835}, {17310, 31150}, {17354, 53535}, {20016, 27115}, {20901, 21440}, {20906, 37788}, {20940, 21613}, {29583, 62635}, {29590, 31287}, {29989, 30016}, {30583, 71050}, {30836, 30857}, {32847, 47729}, {32849, 47763}, {32851, 47761}, {40459, 47762}, {40891, 44567}, {45679, 68823}, {60577, 70288}, {64867, 71000}, {69102, 69333}

X(72109) = crossdifference of every pair of points on line {31, 1646}


X(72110) = X(2)X(37)∩X(31)X(765)

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

X(72110) lies on these lines: {2, 37}, {31, 765}, {44, 70724}, {190, 24685}, {210, 24482}, {518, 24495}, {528, 4518}, {537, 2108}, {846, 42056}, {3570, 17336}, {3681, 24494}, {3758, 68875}, {3807, 14439}, {4169, 35957}, {4370, 57030}, {4448, 4926}, {6174, 71641}, {6184, 52151}, {6546, 69532}, {10196, 14437}, {17233, 24318}, {17240, 71759}, {17242, 69009}, {17262, 27912}, {17297, 70090}, {17315, 71844}, {17346, 71757}, {17393, 71133}, {17780, 62838}, {20693, 63049}, {27538, 69715}, {27919, 51053}, {32041, 43270}, {48630, 70865}, {49447, 52908}


X(72111) = X(2)X(187)∩X(3)X(3734)

Barycentrics    2*a^4 - 3*a^2*b^2 - 3*a^2*c^2 - 2*b^2*c^2 : :
X(72111) = 3 X[2] + X[14907], 3 X[183] - X[17131], 3 X[183] + X[31859], 3 X[574] + X[17131], 3 X[574] - X[31859], 3 X[11168] - X[64093], 5 X[631] - X[9744], X[11185] + 3 X[33008], 3 X[44543] - X[62203]

See Stanley Rabinowitz, Antreas Hatzipolakis and Peter Moses, euclid 9344.

X(72111) lies on these lines: {2, 187}, {3, 3734}, {5, 7830}, {6, 15482}, {15, 69166}, {16, 69159}, {30, 58446}, {32, 6683}, {35, 69256}, {36, 69136}, {39, 385}, {76, 33004}, {83, 35007}, {98, 15483}, {99, 8589}, {115, 8356}, {140, 626}, {141, 542}, {183, 538}, {193, 63952}, {194, 31652}, {230, 4045}, {302, 14905}, {303, 14904}, {315, 31455}, {325, 7810}, {384, 15513}, {474, 36812}, {543, 11168}, {575, 40108}, {599, 7622}, {623, 44223}, {624, 52650}, {631, 3788}, {754, 3815}, {993, 27076}, {1003, 8588}, {1500, 71449}, {1506, 7750}, {1656, 7825}, {1975, 15515}, {2482, 5939}, {2548, 32978}, {2549, 32457}, {2794, 37451}, {2896, 7769}, {3053, 7808}, {3054, 6722}, {3096, 7874}, {3111, 5108}, {3329, 5008}, {3523, 7795}, {3524, 69206}, {3526, 7784}, {3530, 7789}, {3589, 41413}, {3619, 33216}, {3763, 11288}, {3767, 32990}, {3785, 7759}, {3793, 9300}, {3819, 35060}, {3917, 14962}, {4048, 55674}, {5007, 7786}, {5013, 7751}, {5023, 69172}, {5024, 7798}, {5041, 6179}, {5052, 60702}, {5054, 7778}, {5077, 7617}, {5103, 38230}, {5116, 14994}, {5149, 34473}, {5171, 67859}, {5188, 37334}, {5206, 7770}, {5210, 11286}, {5237, 69138}, {5238, 69146}, {5309, 17008}, {5355, 22329}, {5432, 69174}, {5433, 69260}, {5461, 15597}, {5661, 40879}, {6292, 7807}, {6308, 51827}, {6644, 14767}, {6655, 39565}, {6656, 7749}, {6680, 8362}, {6781, 8370}, {7496, 10130}, {7618, 32817}, {7619, 22110}, {7689, 59556}, {7739, 37667}, {7746, 7791}, {7747, 32992}, {7748, 32832}, {7752, 7873}, {7754, 53096}, {7756, 59635}, {7762, 9698}, {7763, 7854}, {7764, 7767}, {7768, 69197}, {7774, 63939}, {7775, 31489}, {7777, 7811}, {7781, 15815}, {7782, 31276}, {7790, 17004}, {7792, 66417}, {7794, 69418}, {7799, 63044}, {7801, 16990}, {7802, 16921}, {7803, 33258}, {7809, 17005}, {7813, 37671}, {7814, 7929}, {7818, 69413}, {7820, 35297}, {7822, 16925}, {7827, 63047}, {7828, 33021}, {7832, 33259}, {7833, 47617}, {7834, 16043}, {7835, 16986}, {7838, 31406}, {7840, 55801}, {7844, 11287}, {7846, 39784}, {7850, 63021}, {7852, 7857}, {7855, 31457}, {7866, 44535}, {7867, 33233}, {7869, 15720}, {7872, 13881}, {7879, 7888}, {7883, 7925}, {7887, 7935}, {7890, 63929}, {7896, 69158}, {7899, 7928}, {7910, 32966}, {7911, 32967}, {7912, 7936}, {7914, 32954}, {7924, 14061}, {7926, 9939}, {7931, 31168}, {7938, 7940}, {7944, 33245}, {7947, 32027}, {8150, 34870}, {8289, 41134}, {8354, 53419}, {8358, 43291}, {8360, 44381}, {8368, 34573}, {8556, 15301}, {8722, 13860}, {8891, 15246}, {9301, 44422}, {9734, 64653}, {9828, 53736}, {10104, 13334}, {10168, 44380}, {10182, 59706}, {11007, 40544}, {11008, 63949}, {11163, 63942}, {11184, 66455}, {11185, 33008}, {11187, 30747}, {12040, 22165}, {12055, 41622}, {12100, 32459}, {13196, 55695}, {13349, 22687}, {13350, 22689}, {13357, 39603}, {13468, 15048}, {14023, 31400}, {14041, 39601}, {14096, 21444}, {14148, 15598}, {14650, 34227}, {14711, 15602}, {14810, 24256}, {14869, 49112}, {15031, 33256}, {15491, 18907}, {15589, 34511}, {15702, 37690}, {15712, 59545}, {16509, 36523}, {16589, 17684}, {18424, 33017}, {18546, 44526}, {18840, 60323}, {18860, 22712}, {19694, 31268}, {24206, 37459}, {26244, 48860}, {30542, 44558}, {31450, 63934}, {31467, 63932}, {32479, 35955}, {32815, 34504}, {32838, 33023}, {32867, 32982}, {32883, 32980}, {32960, 69209}, {32983, 43618}, {32986, 43620}, {33003, 69430}, {33224, 63121}, {33226, 69385}, {33234, 69141}, {33260, 70210}, {33272, 69407}, {33771, 71593}, {36521, 59780}, {37242, 67872}, {37450, 38737}, {37686, 70524}, {41750, 63018}, {43238, 69181}, {43239, 69187}, {43619, 63957}, {44543, 62203}, {47044, 47047}, {50571, 51186}, {50774, 63633}, {52262, 71185}, {52718, 63533}, {52793, 69097}, {53033, 61820}, {53142, 69453}, {55732, 61814}, {59197, 65767}, {59530, 64027}, {63548, 63924}, {67215, 67551}, {68079, 71187}

X(72111) = midpoint of X(i) and X(j) for these {i,j}: {183, 574}, {5475, 14907}, {8722, 13860}, {17131, 31859}
X(72111) = complement of X(5475)
X(72111) = complement of the isogonal conjugate of X(67310)
X(72111) = X(67310)-complementary conjugate of X(10)
X(72111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 187, 7804}, {2, 316, 7603}, {2, 7761, 625}, {2, 7771, 187}, {2, 7831, 7853}, {2, 7934, 31275}, {2, 14907, 5475}, {2, 31173, 66511}, {2, 55164, 31173}, {2, 64018, 31415}, {3, 3734, 32456}, {3, 3934, 7816}, {3, 7815, 3934}, {3, 15271, 3734}, {3, 69139, 69171}, {5, 7830, 7842}, {6, 15482, 44562}, {32, 11285, 6683}, {39, 1078, 7780}, {39, 7780, 7805}, {76, 33004, 37512}, {99, 33273, 8589}, {141, 549, 620}, {141, 620, 7880}, {183, 31859, 17131}, {187, 7771, 46893}, {230, 4045, 7817}, {230, 8359, 4045}, {315, 33001, 31455}, {325, 7810, 7848}, {384, 43459, 15513}, {549, 12042, 5092}, {574, 17131, 31859}, {625, 40344, 7761}, {631, 7800, 3788}, {1078, 7824, 39}, {1506, 7750, 7843}, {2896, 7769, 7821}, {3054, 33184, 6722}, {3096, 7907, 7874}, {3526, 7784, 7862}, {3734, 7815, 15271}, {3734, 15271, 3934}, {3734, 32456, 7816}, {3785, 31401, 7759}, {3788, 7800, 7849}, {3934, 32456, 3734}, {4045, 34506, 230}, {5013, 7751, 32450}, {5024, 8667, 7798}, {6292, 7807, 7915}, {6656, 7749, 7886}, {7496, 10130, 30749}, {7746, 7791, 7861}, {7752, 7904, 7873}, {7756, 59635, 63922}, {7763, 7854, 7895}, {7764, 7767, 7882}, {7777, 7811, 7845}, {7786, 7793, 5007}, {7802, 16921, 39590}, {7804, 46893, 187}, {7853, 15810, 7831}, {7857, 7876, 7852}, {7904, 33015, 7752}, {7924, 17006, 14061}, {7928, 16923, 7899}, {8356, 37688, 115}, {8359, 34506, 7817}, {8556, 53095, 69380}, {8589, 9466, 99}, {11287, 37637, 7844}, {15513, 31239, 384}, {15815, 69381, 7781}, {16043, 69207, 7834}, {16986, 33274, 7835}, {16990, 69450, 7801}, {17004, 66414, 7790}, {31276, 33022, 7782}, {31406, 63928, 7838}, {31415, 64018, 63956}, {32027, 62362, 7947}, {32832, 32965, 7748}, {32990, 69423, 3767}, {33017, 53127, 18424}, {33215, 34229, 2549}, {33234, 69412, 69141}, {43619, 69382, 63957}, {47088, 47089, 5026}


X(72112) = 1ST ZHAO CENTER

Barycentrics    a^3(b^2+c^2)^2 : :

Points X(72112), X(72113), and X(72114) were contributed by Zhao Chen, March, 2026.

X(72112) lies on these lines: {1, 1581}, {38, 1930}, {39, 40936}, {48, 1917}, {75, 33778}, {244, 17758}, {766, 4161}, {1089, 60090}, {1237, 46183}, {1755, 70346}, {1923, 1964}, {1928, 17149}, {2275, 14620}, {3727, 8619}, {3741, 70396}, {3778, 3953}, {3970, 23414}, {7242, 64133}, {8625, 16689}, {9016, 23629}, {16600, 69105}, {17446, 46238}, {23473, 57015}, {45232, 70358}, {50190, 63497}

X(72112) = X(i)-isoconjugate of X(j) for these (i,j): {2, 52395}, {8, 41284}, {76, 59996}, {82, 3112}, {115, 57545}, {251, 308}, {523, 52936}, {689, 18105}, {733, 56979}, {804, 59026}, {827, 52618}, {1176, 46104}, {1799, 32085}, {4577, 58784}, {4580, 42396}, {4593, 55240}, {4599, 18070}, {10547, 68630}, {14970, 56976}, {17500, 39287}, {18082, 52394}, {18833, 46289}, {30505, 41296}, {40016, 46288}, {40163, 41884}, {40425, 59180}, {52376, 56186}, {52570, 57421}, {56971, 69999}
X(72112) = X(i)-Dao conjugate of X(j) for these (i,j): {39, 18833}, {141, 3112}, {688, 4117}, {826, 23994}, {3124, 18070}, {6665, 561}, {8041, 18053}, {21238, 18093}, {32664, 52395}, {34452, 82}, {40585, 308}, {52042, 1}, {55043, 52618}, {55050, 55240}, {59994, 33764}
X(72112) = crosspoint of X(38) and X(1964)
X(72112) = crosssum of X(i) and X(j) for these (i,j): {1, 33793}, {31, 18042}, {75, 18064}, {82, 3112}, {1109, 18070}, {17277, 32926}
X(72112) = crossdifference of every pair of points on line {18070, 46496}
X(72112) = barycentric product X(i)*X(j) for these {i,j}: {1, 8041}, {31, 7794}, {38, 39}, {41, 41285}, {75, 59994}, {141, 1964}, {163, 2528}, {427, 4020}, {560, 59995}, {662, 57132}, {688, 55239}, {799, 2531}, {1101, 15449}, {1401, 33299}, {1634, 8061}, {1923, 8024}, {1930, 3051}, {1973, 4175}, {2084, 4576}, {2157, 60463}, {2236, 56978}, {2530, 46148}, {3665, 40972}, {3917, 17442}, {3954, 17187}, {4553, 21123}, {4568, 50521}, {16696, 21035}, {16703, 41267}, {16887, 21814}, {17457, 52554}, {20775, 20883}, {24041, 62417}, {37134, 62454}, {46387, 52922}, {61063, 70058}
X(72112) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 52395}, {38, 308}, {39, 3112}, {141, 18833}, {163, 52936}, {560, 59996}, {604, 41284}, {688, 55240}, {1101, 57545}, {1634, 4593}, {1923, 251}, {1930, 40016}, {1964, 83}, {2084, 58784}, {2236, 56979}, {2528, 20948}, {2531, 661}, {3005, 18070}, {3051, 82}, {3954, 56251}, {4020, 1799}, {4175, 40364}, {4576, 37204}, {7794, 561}, {8041, 75}, {8061, 52618}, {15449, 23994}, {17442, 46104}, {17457, 52570}, {20775, 34055}, {20883, 68630}, {21035, 56186}, {21752, 18099}, {21814, 18082}, {33299, 62539}, {41267, 18098}, {41285, 20567}, {41331, 46289}, {50521, 10566}, {52042, 33764}, {55050, 4117}, {55239, 42371}, {56915, 56971}, {56978, 69999}, {57132, 1577}, {59167, 20889}, {59994, 1}, {59995, 1928}, {60463, 20944}, {62417, 1109}
X(72112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3116, 2085}, {1964, 4020, 1923}


X(72113) = 2ND ZHAO CENTER

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

X(72113) lies on these lines: {1, 7225}, {7, 18208}, {31, 7194}, {38, 25279}, {87, 244}, {269, 18193}, {982, 3056}, {1086, 18168}, {1106, 5018}, {1111, 20567}, {1253, 17596}, {1254, 4334}, {1357, 7145}, {2310, 3551}, {3020, 41291}, {3662, 7237}, {3865, 7185}, {3942, 18194}, {4000, 18207}, {4118, 48629}, {4475, 17891}, {4859, 71851}, {7175, 18201}, {7211, 33103}, {7289, 8300}, {7321, 20274}, {17124, 39977}, {24207, 24237}, {48632, 68892}

X(72113) = X(38813)-isoconjugate of X(56196)
X(72113) = X(i)-Dao conjugate of X(j) for these (i,j): {3810, 24026}, {41771, 7033}, {41886, 56180}, {52657, 17743}
X(72113) = barycentric product X(i)*X(j) for these {i,j}: {85, 12836}, {982, 3662}, {2185, 41291}, {2275, 33930}, {3020, 4564}, {3056, 69663}, {3061, 7185}, {3705, 41777}, {3721, 33947}, {3776, 3888}, {3777, 33946}, {3794, 16888}, {3865, 7187}, {7237, 65039}
X(72113) = barycentric quotient X(i)/X(j) for these {i,j}: {982, 17743}, {2275, 983}, {3020, 4858}, {3061, 56180}, {3662, 7033}, {3721, 56196}, {3888, 4621}, {7237, 43265}, {7248, 7132}, {12836, 9}, {33947, 38810}, {41291, 6358}, {41777, 56358}
X(72113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {982, 41777, 7184}, {4475, 48627, 17891}


X(72114) = 3RD ZHAO CENTER

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

X(72114) lies on these lines: {2, 3665}, {6, 39724}, {7, 6645}, {220, 6646}, {330, 1086}, {394, 26840}, {1111, 5025}, {1329, 59806}, {1358, 26561}, {3020, 12836}, {3061, 3662}, {3314, 16886}, {4056, 11361}, {4366, 17170}, {4389, 16969}, {7855, 70860}, {7876, 17192}, {16720, 16986}, {16781, 17302}, {16932, 39728}, {17118, 39722}, {23989, 41283}, {52085, 70614}

X(72114) = X(i)-Dao conjugate of X(j) for these (i,j): {3810, 1146}, {16584, 56196}, {41771, 17743}, {52657, 983}
X(72114) = barycentric product X(i)*X(j) for these {i,j}: {261, 41291}, {982, 33930}, {2887, 33947}, {3020, 4998}, {3061, 69663}, {3662, 3662}, {3705, 7185}, {3776, 33946}, {6063, 12836}, {16886, 65039}
X(72114) = barycentric quotient X(i)/X(j) for these {i,j}: {982, 983}, {2887, 56196}, {3020, 11}, {3662, 17743}, {3705, 56180}, {7185, 56358}, {12836, 55}, {16886, 43265}, {16888, 70315}, {33930, 7033}, {33946, 4621}, {33947, 40415}, {41291, 12}, {41777, 7132}, {57992, 14124}
X(72114) = {X(3662),X(7185)}-harmonic conjugate of X(7187)



This is the end of PART 37: Centers X(72001) - X(74000)

Part 38 will be started in the future.
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)
Centers X(72001) - X(74000) Centers X(74001) - X(76000) Centers X(76001) - X(78000)
Centers X(78001) - X(80000) Centers X(80001) - X(82000) Centers X(82001) - X(84000)